Collaborative Planning in Supply Chains Second Edition
Gregor Dudek
Collaborative Planning in Supply Chains A Negotiation-Based Approach Second Edition
123
Dr. Gregor Dudek Neuweg 15 55130 Mainz Germany
[email protected]
ISBN 978-3-540-92175-2 e-ISBN 978-3-540-92176-9 DOI 10.1007/978-3-540-92176-9 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2008943005 c Springer-Verlag Berlin Heidelberg 2004, 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Originally published in Lecture Notes in Economics and Mathematical Systems, Vol. 533. Cover design: WMXDesign, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword to the Second Edition There are only a few cases where a PhD thesis has been published in a second edition. And not only the PhD thesis by Gregor Dudek has received great attention and thus required a second edition, but also his two papers published in the European J. of Operational Research in 2005 and in the International J. of Production Research in 2007 have inspired a great number of researchers to consider collaborative planning as a rewarding and practice-oriented research area. Although the hype of Advanced Planning Systems (APS) has somewhat gone, the need to coordinate plans within a supply chain consisting of separate legal entities each with its own planning domain still exists. I very much welcome that Gregor Dudek has made great efforts to review recent publications in this area and to include these in this second edition of his PhD thesis. Still, there is much room for future research, e.g. with respect to incentives for self-interested parties to participate in negotiations and to be truth-telling. Thus, it is hoped that this second edition will inspire even more young researchers to take up the challenge and to be as successful as Gregor Dudek. Hamburg, October 2008
Hartmut Stadtler
Foreword to the First Edition In light of the vast number of publications on Supply Chain Management (SCM) it is not easy to extract those which will have a great impact both on theory and practice. The dissertation of Gregor Dudek certainly is one such valuable source because it tackles inter-organizational collaboration in a novel and effective manner. SCM is concerned with the coordination of material, information and financial flows within and across often legally separated organizational units. It has gained great attention both in industry and research as an important area for improving competitiveness. A Supply Chain (SC) can be regarded as a hybrid between a market relationship and a hierarchical organization and as such requires specific tools to support the efficient planning and execution of the order fulfillment process. Software vendors have developed so called Advanced Planning Systems (APS) to overcome deficiencies of traditional Enterprise Resource Planning systems and to better support the planning functions needed in SCM. However, APS are based on the principles of hierarchical planning which are well-suited for intraorganizational SCs but fall short when non-hierarchical collaboration between partners (companies) is needed. This is particularly true when a buyer and a supplier have to align their medium term order and supply plans. This is the starting point of the dissertation of Gregor Dudek. He devises a negotiation-based collaborative planning scheme that coordinates master plans of two individual SC partners each with his own planning domain (APS). Extensions to more general two tier SC structures are provided too. The basic idea of the negotiation scheme is that order proposals (generated by buyers) and supply proposals (generated by suppliers) are exchanged between SC partners in an iterative manner. The proposal received from a SC partner is analyzed for its consequences on local (master) planning, and a counter-proposal is generated by introducing partial modifications. Resulting is a negotiation-based process which subsequently improves SC wide costs without centralized decision making and with limited exchange of information between the partners. Specifically, only the respective order / supply proposals and associated cost effects are exchanged between SC partners. As a generic model for master planning – although not limited to it - a multilevel, capacitated, lot-sizing model (MLCLSP) is assumed. The MLCLSP is then enlarged by additional variables and constraints to mimic the specific tasks of the model in the negotiation process. Here, the generation of a compromise proposal – along the lines of Goal Programming – has to be mentioned as one of the novel features of Dudek´s research. Several valuable extensions to the basic negotiation scheme are discussed, like rolling schedules or possible compensation schemes in light of psychological experiments, contract theory, game theory, controlling and common sense. Extensive computational tests show that the proposed negotiation scheme results in less SC wide costs than achievable by pure Upstream Planning and even
VIII
Foreword to the First Edition
comes near to the minimum cost solutions of central planning after only a few (i.e. about five) iterations. In summary Gregor Dudek has developed a negotiation scheme for coordinating master plans between SC partners which • avoids the exchange of critical information like cost and capacities, i.e. only uses (uncritical) order and supply proposals by partners, • comes near to the minimum cost of central planning, • and requires only a few negotiation rounds (iterations). Since the proposed negotiation scheme can already by applied by SC partners today by making use of APS and existing Collaborative Planning modules research results of this dissertation will have a great impact on the theory and practice of SCM. The extraordinary quality of his contribution has also been acknowledged by the jury of the Management Science Strategic Innovation Prize (MSSIP) by ranking a related paper as the second best among all submitted publications in the 2003 contest. Darmstadt, August 2003
Hartmut Stadtler
Preface to the Second Edtion Five years have passed since the original version of my dissertation was submitted to the Darmstadt University of Technology and published in the “Lecture Notes in Economics and Mathematical Systems” at Springer. Over these years, the practices of Supply Chain Management and the use of Advanced Planning Systems became more white-spread and applied in many companies. Personnally, I have witnessed this development, and supported it to a little extent, with my own work in management consulting for four years, and since a year at an industrial goods company. Despite the increasing use of Advanced Planning, the interface to independent supply chain partners (suppliers and customers) still remains a major challenge in the practice of supply chain integration. Many companies exchange an increasing amount of supply chain information with their business partners, but still are far from applying a structured Collaborative Planning process. In the supply chain I deal with, we e.g. share forecasts with key customers and suppliers on a weekly or monthly basis, and at times “negotiate” changes to a partners’s forecast. However, this happens without much decision support or a formalized process. Thus, Collaborative Planning remains a topic, which needs to be further explored, in practice as well as in academics. I am therefore proud and very thankful for the chance to publish a second, revised edition of my original work, which tries to incorporate some of the developments of the last years. But what exactly does the new edition bring about to you, the reader? In summary, the new edition is hoped to be a source on Collaborative Planning, which is on the one hand up-to-date in terms of literature and references, and on the other hand more readable and easier to understand. There are three major types of updates to the original text: • Literature references are updated and references to new, interesting publications are added. This applies especially to chapters 2 (Overview of Supply Chain Management and Collaborative Planning) and 3 (Modeling Framework and Relevant Literature). • Secondly, the complete text is reworked in order to make it more digestable. To achieve this, some parts of the text were restructured (e.g. section 3.3) and others shortened (e.g. various sections of chapter 4). Across the whole text, the language was simplified where possible and unnecessarily long explanations shortened. • Finally, a list of “key points” was added at the beginning of each chapter, which shows the key messages that are conveyed in the subsequent sections. Also, selected references are given at the end of each chapter for interested readers. This revision could not have been achieved without the support of a number of helpful hands! My thanks go to Herbert Meyr, in the meantime professor for Production and Supply Chain Management at the Darmstadt University of Technology, and Martin Albrecht from the University of Hamburg for providing access to
X
Preface to the Second Edition
literature and hints on interesting publications; Professor Hartmut Stadtler for discussing the amount of updates and revisions; and finally Katharina Wetzel-Vandai from Springer, who made the second edition possible, and gave all the necessary technical support to achieve this undergoing. Mainz, October 2008
Gregor Dudek
Preface to the First Edtion The following dissertation is the outcome of a three-year research effort at the department of Production and Supply Chain Management of the Darmstadt University of Technology. When this work started in mid of 2000, the term “Collaborative Planning” was about to gain popularity, especially in practitioner-oriented publications on Supply Chain Management. Yet, in searching these publications for answers to questions of how a Collaborative Planning process should actually look like, or which goals and objectives it should serve, one quickly found that most contributions only scratched at the surface of Collaborative Planning. Most frequently, discussions focused on the technological means available for the exchange of information between independent Supply Chain partners, such as Email, Web-interfaces, or the XML technology. While the technological perspective is an important aspect, it is by itself not sufficient to realize a Collaborative Planning process. Therefore, the goal of this dissertation is to provide a process model which is concerned with the decision making and negotiation aspects of Collaborative Planning. Taking necessary technological means as a given, it sketches a detailed picture of a Collaborative Planning process at the medium-term level of Master Planning, and indicates how financial and contractual aspects are affected by the negotiations of supply quantities between buyers and suppliers. This work could not have been realized without the advice and guidance of numerous supporters. First and foremost, I like to thank my adviser Hartmut Stadtler. He not only proposed the topic of the dissertation as a potential gap in existing research on Supply Chain Management, but also gave crucial advice throughout all stages of the work. I am also very thankful to Ton de Kok from the Eindhoven University of Technology for his willingness to serve as the co-adviser and second referee of the dissertation. His general interest in the work along with numerous hints and comments helped to improve the quality of the dissertation substantially. Equally important for the progress of the project were the steady debates and discussions with colleagues and co-workers. I especially like to thank Jens Rohde and Christopher Sürie from the Darmstadt University of Technology as well as Norbert Wenig from the SAP AG. Finally, I am indebted to my family and friends for the support and encouragement on the one hand, but also for their constant reminds that there is a live beyond purely scientific matters. This applies in the first place to my girl friend Natalie Kappesser. Although actually practicing pediatrics, she not only accepted to become a Supply Chain expert in her own right, but also managed unambiguously to keep my feet on the ground. Mainz, August 2003
Gregor Dudek
Table of Contents
1 Introduction......................................................................................................1 2 Supply Chain Management and Collaborative Planning.............................5 2.1 The Concept of Supply Chains.....................................................................5 2.2 Overview of Supply Chain Management .....................................................7 2.3 Operations Planning in Supply Chains.......................................................12 2.3.1 Successive and segregated planning...................................................13 2.3.2 Hierarchical planning .........................................................................15 2.3.3 Collaborative planning .......................................................................19 3 Modeling Framework and Relevant Literature ..........................................25 3.1 Modeling ...................................................................................................25 3.1.1 Decision situation and modeling assumptions....................................25 3.1.2 Intra-domain planning model .............................................................30 3.1.3 Modeling links to adjacent planning domains ....................................35 3.2 Benefits of Information Sharing and Collaboration ...................................37 3.3 Coordination of Planning Processes Along the Supply Chain ...................42 3.3.1 Coordination by contracts ..................................................................42 3.3.2 Coordination mechanisms for mathematical programming models ...46 4 Negotiation-Based Collaborative Planning between Two Partners...........57 4.1 Assumptions and Overview .......................................................................57 4.2 Iterative Planning Steps..............................................................................61 4.2.1 Evaluating the partner proposal..........................................................62 4.2.2 Determining the preferred outcome....................................................63 4.2.3 Generating a compromise proposal ....................................................69 4.2.4 Generating additional compromise proposals ....................................83 4.3 Collaborative Planning Process in Total ....................................................91 4.3.1 Data exchange requirements ..............................................................91 4.3.2 Total process flow ..............................................................................94 4.3.3 Stopping criteria .................................................................................97 4.4 Summary and Comments .........................................................................101 5 Extensions to the Basic Collaborative Planning Scheme..........................103 5.1 Extended Supply Chain Structures...........................................................103 5.1.1 General two-tier supply chains.........................................................103 5.1.2 Multi-tier supply chains....................................................................112 5.2 Planning on a Rolling Basis .....................................................................115 5.2.1 Conceptual overview........................................................................118 5.2.2 Extensions to process flow and planning models .............................120
XIV
Table of Contents
5.3 Limited Exchange of Cost Information.................................................... 125 5.3.1 Limited exchange between two planning partners ........................... 125 5.3.2 Limited exchange between multiple planning partners.................... 127 5.3.3 Limited exchange in planning on a rolling basis.............................. 129 6 Implications on Supply Contracts and Partner Incentives ...................... 131 6.1 Contractual Consequences ....................................................................... 131 6.1.1 Compensation and savings sharing .................................................. 132 6.1.2 Adaptation of supply contracts......................................................... 140 6.2 Potentials of Opportunistic Behavior and Counteractions ....................... 147 6.2.1 Game-theoretic analysis ................................................................... 147 6.2.2 Means preventing opportunistic behavior ........................................ 158 7 Computational Evaluation.......................................................................... 165 7.1 Implementation of the Collaborative Planning Scheme........................... 165 7.2 Generation of Test Instances.................................................................... 168 7.3 Tests with a Single Buyer and Supplier ................................................... 173 7.3.1 Test classes and test program ........................................................... 173 7.3.2 Overview of test results.................................................................... 178 7.3.3 Results by cost structure, utilization profile, and iteration ............... 186 7.3.4 Results with limited exchange of cost information .......................... 190 7.4 Tests with One Supplier and Several Buyers ........................................... 193 7.4.1 Test classes and test program ........................................................... 193 7.4.2 Overview of test results.................................................................... 196 7.5 Tests with Rolling Schedules ................................................................... 201 7.5.1 Test classes and test program ........................................................... 201 7.5.2 Test results with deterministic demand ............................................ 203 7.5.3 Test results with uncertain demand .................................................. 207 8 Summary and Conclusions ......................................................................... 215 References .......................................................................................................... 219 List of Figures .................................................................................................... 229 List of Tables ..................................................................................................... 231 List of Symbols .................................................................................................. 233
1
Introduction
This book deals with collaborative planning between supply chain partners, that is independent companies or business units of large corporations, which develop close relationships in the course of engaging in Supply Chain Management. Supply Chain Management is widely acknowledged as a major avenue to increase competitiveness and boost performance of businesses in today’s increasingly challenging business environment. It grounds on the idea to link and streamline business processes along the supply chain, i.e. the network of organizations involved in creating final customer products and services. This particularly applies to the core operational activities such as production, storage, and distribution processes, as these directly contribute to products and services offered in the marketplace and incur significant portions of costs and capital needs. The coordination of operational processes across the supply chain thus bears the potential to enhance customer service and reduce operating costs. One approach to achieve coordination of operational processes is by centralized planning. The idea here is to synchronize operations by installing a central decision making unit which generates plans for all processes along the supply chain. Proponents of this solution usually suggest to implement hierarchical planning such that centralized coordination happens on a medium-term level, whereas it is left to the owners of the distinct operational processes to implement the results on the level of short-term planning and control. This approach appeals by the ease with which coordination is achieved and fits to the way in which decisions are made in hierarchical organizations. In fact, it is realized in Advanced Planning Systems (APS) offered by software vendors such as i2 and SAP. However, the downside of this solution is that the central coordinator needs access to all relevant information and the power to impose planning results on all organizational units. This requirement hampers its applicability to planning in decentralized firms and supply chains embracing independent business partners. Empirical evidence implies that, despite the benefits of supply chain integration, firms are reluctant to disclose sensitive information to supply chain partners. Moreover, the implementation of centralized planning in supply chains with independent partners can fail, simply because individual partners are involved in several supply chains; for example component suppliers in the automotive or electronics industry usually serve several large customers. Nonetheless, there is little doubt that significant efficiency potentials exist at the interfaces between independent supply chain partners, waiting to be unlocked by supply chain integration that goes beyond company borders. For example, Lowe / Markham (2001) report that winners of the 2001 “Global Excellence in Operations” award leverage supplier relationships and realize joint savings by synchronized delivery, inventory management, and planning and scheduling.1
1
C.f. Lowe / Markham (2001), pp. 52.
G. Dudek, Collaborative Planning in Supply Chains, 2nd edn., DOI 10.1007/978-3-540-92176-9_1, © Springer-Verlag Berlin Heidelberg 2009
2
1. Introduction
Similarly, a study of consumer goods manufacturers conducted by Stank et al. (2001) reveals that industry leaders increasingly pursue “external integration” with customers and suppliers.2 Among the top means to achieve external integration the authors cite “cooperative planning”. Based on such findings, the question arises of how to realize cooperative planning between independent supply chain partners. This book contributes to this question by laying out a non-hierarchical, negotiation-based approach which can be applied to coordinate operational planning tasks of independent parties linked by supply relationships. It rests on the assumption that mathematical programming models are used by the individual partners to plan their respective operations. It introduces a coordination mechanism which ensures that consistent plans covering the entire supply chain are obtained with • the exchange of uncritical and as few as possible information, • as little computational and coordinating effort as possible, • demonstrably good solutions close to the “global optimum”. In a nutshell, the idea is to pass order proposals (generated by buyers) and supply proposals (generated by suppliers) between the parties in an iterative manner. A proposal received from a supply chain partner is analyzed for its consequences on local planning, and a counter-proposal is generated by introducing partial modifications. Resulting is a negotiation-like process which subsequently improves supply chain wide costs without centralized decision making and with limited exchange of information between the partners. Specifically, only the respective order / supply proposals and associated cost effects are exchanged between the partners. The text is structured as follows. In chapter two we introduce some basic definitions of supply chains and Supply Chain Management, and describe the distinct approaches to operations planning in supply chains in greater detail, namely centralized, hierarchical planning on the one hand and collaborative planning on the other. In chapter three we describe the mathematical modeling framework and review relevant literature. The focus first lies on mathematical programming models which can be used by the supply chain partners for planning of their internal operations. Subsequently, we report on findings from literature on the benefits of collaboration between supply chain partners and coordination of planning activities along the supply chain. Chapter four contains the core concepts developed here. It deals with the negotiation-based approach to collaborative planning between two supply chain partners, a single buyer and supplier. For laying out the scheme, the various, iterative steps carried out by each partner are described in detail, including modifications to the underlying mathematical programming models. Also, the entire process flow and control associated with the collaborative planning process is presented.
2
C.f. Stank et al. (2001), pp. 62.
1. Introduction
3
In chapter five, extensions are introduced to the basic collaborative planning scheme for two supply chain partners as developed in chapter four. First, we show how the concept can be modified in order to coordinate planning in more complex supply chain settings, namely in general two-tier supply chains comprising an arbitrary number of buyers and suppliers and in multi-tier supply chains. These extensions allow to apply the collaborative planning scheme not only to isolated buyer-supplier pairs, but to more general supply chain structures. Secondly, we elaborate on how the collaborative planning scheme can be modified for use in planning with rolling schedules. This, too, is an important enhancement of its basic form, as in practical applications planning is usually repeated periodically. Finally, modifications are introduced which allow to further restrict the amount of cost information exchanged between the supply chain partners. Chapter six deals with financial implications resulting from the collaborative planning scheme. In particular, the question of compensation and savings sharing is discussed and it is demonstrated how supply contracts can be modified in order to facilitate that the partners implement the results of collaborative planning. Also, incentives of opportunistic, i.e. non-cooperative, behavior by individual partners are analyzed. Finally, in chapter seven we report computational results obtained with the collaborative planning scheme and two other, benchmark, planning concepts. The tests show that the scheme yields favorable results in the vast majority of example problems. Major findings and conclusions of this work are summarized in chapter eight.
2 Supply Chain Management and Collaborative Planning Content This first chapter intends to give an overview of Supply Chain Management (SCM) and an introduction to Collaborative Planning. In particular, it shall be clarified how Collaborative Planning relates to SCM and why it can be considered an important component of implementing SCM. The concept and understanding of supply chains is introduced in section 2.1, followed by a brief overview of SCM in section 2.2. The remainder of the chapter is dedicated to operations planning in supply chains. The traditional concept of successive and segregated planning is shortly outlined, the focus is however set on two alternate approaches to coordinating operations along the supply chain: hierarchical planning one the one hand and collaborative planning as the theme of this work on the other. Key points • Supply Chain Management (SCM) can be regarded as cross-functional, intercompany business process management which tries to integrate and coordinate all the activities required to fulfill ultimate customer demand • Planning of operations (i.e. production, inventories, logistics activities) across the supply chain is a major component of SCM • Whereas operations planning traditionally happens in a segregated and successive way, a hierarchical approach is proposed within SCM. Here, centralized planning tasks (especially the medium-term master planning) coordinate and synchronize operations across the entire supply chain • Centralized planning in practice is however limited to parts of the overall supply chain (e.g. individual companies). Therefore, the idea of Collaborative Planning is to connect and coordinate planning tasks pertaining to indivudal SC members without the installation of a centralized, all-embracing decision making unit
2.1
The Concept of Supply Chains
Based on the often cited definition by Christopher (2005) a supply chain (SC) is defined as
G. Dudek, Collaborative Planning in Supply Chains, 2nd edn., DOI 10.1007/978-3-540-92176-9_2, © Springer-Verlag Berlin Heidelberg 2009
6
2. Supply Chain Management and Collaborative Planning
“the network of organizations that are involved, through upstream and downstream linkages, in the different processes and activities that produce value in the form of products and services in the eyes of the ultimate consumer”.3 The recognition of supply chains makes apparent that no single company or business unit fully controls manufacturing and distribution of its products. Instead, it also depends on the contribution of others and, just as important, the interactions between the various parties involved in the total process. Although the concept of SCs is well established and often referred to in the literature on marketing, logistics, operations management and other disciplines,4 its application to real-world businesses is not straight forward. First, it should be noted that the SC looks different from each party’s subjective perspective. For example, the SC of a manufacturer with several suppliers is not equivalent to the SC of one of the suppliers. This is because the supplier likely serves other customers, too, but has no direct business relations with the remaining suppliers. This is visualized in Fig. 1. Part a) represents the manufacturer’s SC and part b) the supplier’s one. The framed sections are common to both SCs. Second, trying to map a company’s SC raises at least two questions, namely: how many tiers of suppliers and customers should be regarded and at which level of detail. Principally, the SC might start at the stage of raw materials such as agricultural or mining products and go through to retail outlets of consumable products. However, with such as broad understanding one obtains highly complex, unmanageable networks. To better focus on activities that are of real relevance, Lambert et al. (1998) propose to differentiate between primary and supportive SC members.5 In analogy to Porter’s (1985) value chain model,6 primary members directly add value to the final products through their operations or services (e.g. component suppliers, logistical service providers), while supportive members provide resources that are consumed (e.g. equipment suppliers). a)
b)
S
S M
M
Fig. 1. Supply chains of a manufacturer and one of his suppliers
3 4 5 6
Christopher (2005), p. 17. See Croom et al. (2000) for an overview of subject areas dealing with SCs. C.f. Lambert et al. (1998), p. 5. See Porter (1985), pp. 36.
2.2. Overview of Supply Chain Management
7
If only primary members are considered, the SC’s point of origin falls to where there are no direct suppliers and the point of consumption is where the product is no direct input but a consumed resource (e.g. an industrial machinery).7 Since the resulting network can still be large, a further limitation might be useful. Some authors therefore propose to consider only two tiers in the up- and downstream direction (the suppliers’ suppliers and the customers’ customers).8 Alternatively, one might try to evaluate which business partners are critical for and/or generally under the influence of the company of interest, and only consider these players in the SC. The appropriate level of detail to sketch a SC depends on the business context and managerial level. For example, when dealing with strategic relationships to business partners, the company itself and each supplier and customer might represent a single node of the network as depicted in Fig. 1. However, when logistical material flows are planned for, the various facilities of the company and its business partners usually each form a network node. Finally, it should be noted that SCs are sometimes regarded as a type of network organization, considered having characteristics that fall between verticallyintegrated systems and pure arms length market relationships.9 This view is not generally taken here. While the SC or a part of it might very well be managed like a network organization once Supply Chain Management techniques are applied, this is not per se the case. In fact, many of the deficiencies observed in SCs result from purely market-oriented interactions between their members.10
2.2
Overview of Supply Chain Management
The term Supply Chain Management was initially proposed to link logistics issues with strategic management.11 Early publications stress the growing importance of well-designed logistics processes in increasingly challenging business environments of the 1980’s. They propose intra-company integration of the purchasing, material handling, manufacturing and distribution functions and a reduction of inventory buffers.12 A similar understanding is expressed in many contemporary textbooks where SCM is often regarded as a synonymous term for integrated logistics management.13 However, a major difference concerns the scope attributed nowadays to SCM. Whereas initially an intra-firm perspective was predominant, 7 8 9 10 11 12 13
C.f. Lambert et al. (1998), p. 6. C.f. Stadtler (2005), p. 9. C.f. Cooper / Ellram (1993), pp. 13, Stadtler (2005), p. 15. For example the well-known bullwhip effect (see e.g. Lee et al. (1997), pp. 93). See e.g. Oliver / Webber (1992), p. 63, Houlihan (1985), p. 23. C.f. Houlihan (1985), pp. 26, Jones / Riley (1985), pp. 19. See e.g. Bowersox / Closs (1996), p. 34, Gattorna / Walters (1996), p. 12, Copacino (1997), p. 7, Simchi-Levi et al. (2004), p. 2.
8
2. Supply Chain Management and Collaborative Planning
today the idea is to consider and manage the entire SC including external business partners as described above. From this perspective, SCM is primarily concerned with establishing a seamless flow of material and information through the entire logistics channel. Stadtler (2005), for example, defines SCM as “the task of integrating organizational units along the supply chain and coordinating material, information, and financial flows in order to fulfil (ultimate) customer demands”.14 The viewpoint that SCM is essentially equivalent to integrated logistics management on an inter-firm level is in part supported in scientific discourses on the nature of SCM. Kotzab (2000) compares the two management concepts and concludes that the difference is very small, if not negligible.15 However, practices and methods proposed within the context of SCM by academia as well as practitioners, often include elements that go beyond what is usually regarded as logistics management. Prominent examples are joint product development between SC partners16 or aligned promotion activities.17 Building on these observations, some authors differentiate between integrated logistics and SCM. They argue that SCM is a broader management concept, for that it is potentially concerned with the integration of all business processes between SC partners, not just logistics activities.18 In the words of Cooper et al. (1997) “SCM ideally embraces all business processes cutting across all organizations within the supply chain”.19 Due to the emphasis of business processes, SCM can also be considered as cross-functional, inter-company business process management.20 An overview of the business processes which can be integrated along the SC is shown in Table 1. Irrespective of its precise definition, the objective of SCM can be summarized by • increasing final customer service, • lowering the amount of resources involved in servicing customers, • and ultimately improving the competitiveness of the entire SC.21
14 15 16 17
18 19 20 21
Stadtler (2005), p. 11. C.f. Kotzab (2000), p. 33. Considered a key issue of SCM by e.g. Simchi-Levi et al. (2004), p. 15. Marketing issues are mainly treated in initiatives between consumer goods manufacturers and retail chains, such as Efficient Consumer Response (see e.g. Kotzab (2001), pp. 29). C.f. Buscher (1999), p. 449, Pfohl (2000), pp. 7, Zijm (2000), p. 323. Cooper et al. (1997), p. 5. C.f. Hewitt (2001), p. 30. See e.g. Cooper / Ellram (1993), p. 14.
2.2. Overview of Supply Chain Management
9
Table 1. Supply chain business processes Business processes along the supply chain Customer relationship management Customer service management Demand management Order fulfillment Manufacturing flow management Procurement Product development and commercialization Source: Cooper et al. (1997), p. 1022
Of course the improved competitive standing of the SC should translate to competitive advantage to all SC members. However, this is not necessarily guaranteed, and must be fostered by appropriate agreements between SC partners (e.g. savings sharing). The major theme to realize the objectives lies, as implied above, in the integration and coordination of the SC and its processes.23 A major question hence is how to actually realize a tighter integration and improved coordination. Noteworthy contributions to this issue are made by Hewitt (1994), Lee (2000), and Bowersox et al. (2000). These authors (independently) propose frameworks for the integration and coordination of business processes along the SC. Based on an empirical study of SC initiatives in practice, Hewitt identifies three dimensions relevant for SC process redesign: work structure, information flow, and decision authority.24 Work structure relates to rearranging and aligning tasks carried out by various parties in a SC. For example, suppliers can take over responsibility for replenishment of the items they deliver. Information flow deals with the availability of data. For one, the speed or timeliness of available information can be increased. In addition, new, formerly unavailable data can be made accessible. Decision authority finally relates to changing decision rights and redesigning decision support systems. Hewitt stresses that truly successful SC initiatives simultaneously address work structure, information, and decision authority which, in summation, results in radically new process design.25 Lee (2000) deals with the question of what constitutes SC integration. As an answer he proposes three dimensions of SC integration: information integration, coordination and resource sharing, and organizational linkage. Informational inte22 23
24 25
A similar compilation of business processes is presented by Buscher (1999), p. 455. See e.g. Stevens (1989), p. 3, Bechtel / Jayaram (1997), pp. 19, Copacino (1997), p. 5, Lee (2000), pp. 31, Stadtler (2005), p. 11. C.f. Hewitt (1994), p. 6. C.f. Hewitt (1994), p. 5.
10
2. Supply Chain Management and Collaborative Planning
gration is viewed as the “foundation of broader supply chain integration”.26 It comprises the exchange of mere data in a first step and knowledge in a second. The latter obviously requires a deeper, trustful relationship. Coordination refers to decision rights, work activities, and resources. The first two aspects are equivalent to the framework by Hewitt, while the last means pooling and sharing of resources by SC partners (e.g. warehouses and other facilities). The organizational linkage dimension deals with the alignment of performance measures and incentives, such as costs, risks, and reward structures. Bowersox et al. develop a so-called “Supply Chain 2000” framework for SC integration.27 It consists of three contexts or components that serve to integrate organizational structures and functional activities: operational, planning and control, and behavioral. The operational context is concerned with the integration of activities within an organization as well as with external business partners. Planning and control embraces sharing of appropriate information, integrated decision making, and alignment of performance measures. The behavioral context deals with the underlying management of relationships to partners. The three frameworks share major characteristics as can be seen from the summarizing overview in Table 2. In result, they make apparent that the integration of business processes along the SC needs to tackle • the work structure (how and by whom processes are operated), • information flows (how and to whom data is communicated), • decision authorities (how and by whom decisions are drawn), • and the underlying relationships between SC partners. Table 2. Dimensions of supply chain integration Hewitt (1994)
Lee (2000)
Bowersox et al. (2000)
Work structure
Coordination and resource sharing
Operational
Decision authority Information flow
Planning and control Information integration Organizational linkage Relational Source: Hewitt (1994), p. 6, Lee (2000), p. 32, Bowersox et al. (2000), p. 72
These principles or dimensions can be used to evaluate and redesign any business process that cuts across the SC. In consequence, a myriad of different change and improvement opportunities can potentially be identified. Nonetheless, common principles or recipes for the integration and coordination of SC processes can
26 27
Lee (2000), p. 33. C.f. Bowersox et al. (2000), pp. 71. The framework was first introduced in the form of a case study in Bowersox et al. (1999), and is also discussed in detail by Stank et al. (2001).
2.2. Overview of Supply Chain Management
11
be drawn from SCM literature. For that purpose, Otto / Kotzab (2001) have analyzed contributions to SCM with respect to underlying (common) principles. The results of their study are presented in Table 3. They are not discussed in detail at this point. Instead they shall give an overview of the common approaches to SC integration as developed in the literature. It should however be noted that SCM does not necessarily aim at a holistic integration of all business processes along the entire SC. Much rather, the appropriate level of integration has to be chosen based upon the specific situation of the SC and its environment.28 Table 3. Principles of Supply Chain Management Principle Compression Acceleration Cooperation Integration Optimization Differentiation / individualization Modularization Leveling Postponement
Explanation Reducing the SC structure (e.g. no. of suppliers) Reducing time lags (e.g. lead times) Enhancing cooperation in planning, control, and operations Reducing time, cost or performance loss at the transition between two processes (e.g. eliminating buffers) Applying quantitative modeling in planning and control Increasing the specification of products / services Reducing time, cost or performance loss of replacing a part of the SC by another (e.g. changing suppliers) Reducing the variation of process parameters (e.g. production volumes) Moving the order penetration point towards the customers
Source: Otto / Kotzab (2001), p. 166
28
C.f. Lambert / Cooper (2000), p. 74, Bask / Juga (2001), p. 139.
12
2.3
2. Supply Chain Management and Collaborative Planning
Operations Planning in Supply Chains
In the following we turn our attention towards one of the SC business processes as shown in Table 1, namely the manufacturing flow management process. Regardless whether SCM is understood as inter-firm logistics management or a broader management discipline on its own, the flow of material and related information, as well as associated planning and control activities are seen as a core component of SCM.29 This is because operational activities underlying the manufacturing flow directly form the SC’s final output and incur a large portion of total costs and capital needs. Effective and efficient management of operational activities is hence imperative for a SC’s success. The focus herein is not only on manufacturing in a strict sense, but on all processes related to the flow of material, i.e. production, transport / distribution, and storage, altogether subsumed by the general term of operations.30 The coordination of operations along the SC requires well-structured planning processes. In general, planning is defined as a rational, structured decision making process which aims to find the best choice of objectives and measures to a decision situation and its environmental setting.31 The importance of well-planned operations results among others from two characteristics of operational processes. First, they interrelate one with another in many ways. For example, several operations consume identical resources such as production capacity or some processes require the output of others such as component parts needed in final product assembly. Second, operations ultimately serve to cover final customers’ demand. However, as it is usually not possible to initiate all processes upon individual customer orders, expected demands have to be forecasted and anticipated at all tiers of the SC well in time. According to Kansky / Weingarten (1999), the overall task of operations planning in the SC can be seen in deciding on: • when to produce, transport, or store • which quantities of final products, components and raw materials • at which locations in the SC such that customer demand can be met efficiently.32 Of course, this overall problem statement is usually of a daunting complexity and can hardly be tackled by a single, large decision making model that reveals all results on a detailed, implementable level. To make the overall problem yet tracta-
29 30 31 32
C.f. Simchi-Levi et al. (2004), pp. 2, Chopra / Meindl (2001), pp. 6. C.f. Nahmias (1996), p. 1. C.f. Berens / Delfmann (1995), p. 12, Scholl (2001), p. 9. C.f. Kansky / Weingarten (1999), p. 87. See also e.g. Chopra / Meindl (2001), pp. 6.
2.3. Operations Planning in Supply Chains
13
ble, several thrusts on how to deal with it are known in literature and practice and are introduced in the following. The first approach is the typical way of how operations are planned and controlled without much integration of the SC. It is therefore considered only as a benchmark situation prior to the use of SCM techniques. The two approaches presented thereafter are those suggested within the debate of SCM. They are referred to as hierarchical and collaborative planning within the SC. As noted earlier, the latter is the particular subject matter of this work. 2.3.1
Successive and segregated planning
Until recently, the predominant approach to operations planning was the concept of manufacturing resources planning (MRP II). It is implemented in traditional production planning and control systems as well as in more modern enterprise resources planning (ERP) software. Conceptually, MRP II grounds on the logic of successive planning. That is, the overall decision problem is sub-divided into several planning tasks that are executed successively in a hierarchical order. Results from super-ordinate planning levels form given input to succeeding tasks. Master Production Scheduling
Material Requirements Planning
Scheduling
Shop Floor Control
Fig. 2. MRP II planning tasks
The major planning tasks and the corresponding hierarchy are depicted in Fig. 2 and outlined in the following. It should be noted that from a conceptual perspective, the framework can include further planning activities such as medium-term aggregate planning or demand planning.33 However, computerized decision support is usually restricted to the tasks as shown in the figure.34 Master production scheduling serves as the driver within the planning framework. Its purpose is to generate master schedules, i.e. planned production quanti-
33 34
See e.g. Vollmann et al. (1984), pp. 12. C.f. Drexl et al. (1994), p. 1023.
14
2. Supply Chain Management and Collaborative Planning
ties by period, for final products. Master schedules are obtained by netting demand forecasts and on-hand inventory at the beginning of the planning interval. Material requirements planning (MRP) is the original core element within the concept. Requirements of components and parts are derived from master schedules by a bill-of-material explosion, and lot-sizes are generated based upon some predefined rules such as the EOQ-formula. Initially, only MRP was proposed as a novel, output- or program-oriented planning philosophy in contrast to thus far known inventory control policies.35 The basic idea is to derive dependent demand for parts from final product forecasts rather than from replenishment orders faced at the corresponding stage of the production system. Subsequently, the MRP logic was supplemented by other planning tasks to form the planning framework of MRP II.36 Scheduling serves to generate the order in which individual items are processed on resources such as work centers. Quantities and due dates obtained by MRP are to be obeyed. However, as limited resources availability is accounted for here, capacity shortages can occur, in which case resolutions by plan shifts need to be made. The shop floor control task finally represents the link to plan execution. It includes the release of production orders and subsequent follow-up on progress. MRP II allows a computerized, integrated planning and control of manufacturing processes. As such it was and is widely used in practice since the advent of material requirements planning in the 1960’s. Compared to control concepts known until that time, it brought a new philosophy to plan based on final demand and an increase in shop floor transparency.37 Nonetheless, the concept suffers from considerable shortcomings, especially when it comes to planning with tight capacities and on a SC level. Deficiencies originate for one in its planning logic itself, and second in its limited scope with respect to all operations and planning activities of relevance from a SC perspective. Four major conceptual weaknesses inherent in the planning logic are identified by Drexl et al. (1994). The authors put forward that in MRP II based planning systems • there is no sufficient support of company wide planning embracing various facilities as well as the distribution and sales functions, • plant orders are generated with an isolated view of the item in question, i.e. without taking account of the interdependencies with other items, • average lead times, which include waiting time, are input to the system rather than a result of planning,
35 36 37
C.f. Voß / Woodruff (2000), pp. 180. C.f. Hopp / Spearman (1996), p. 135. C.f. Hopp / Spearman (1996), pp. 105, Kuhn / Hellingrath (2001), p. 121.
2.3. Operations Planning in Supply Chains
15
• and, above all, resource capacities are not systematically considered at all as limiting constraints, except for rough, ex-post capacity checks at the scheduling level.38 The last, major point is amplified by the successive, top-down execution of the planning tasks as indicated in Fig. 2. The approach lacks any anticipative “look forward” or feedback mechanisms that would incorporate consequences of planning decisions on subsequent tasks. The second shortcoming of MRP II, that is its too narrow scope, is already implied by the first point made by Drexl et al. The problem here is that the concept lacks decision support on transport and distribution of intermediate and finished goods as well as on the links between various manufacturing facilities of one company, let alone the entire SC. In result, MRP II like systems are independently operated at various facilities based on locally available data, leading to segregated planning processes along the SC. Coordination can in that way neither be achieved within a single (large) enterprise nor across company borders. As pointed out by Stevens (1989), based on the MRP II concept manufacturing and distribution are effectively decoupled in most companies due to the lack of a coherent integration of planning systems.39 In consequence, it is of little surprise that other, novel approaches to operations planning are proposed within the discussion of SCM. They are the subject of the following sections. 2.3.2
Hierarchical planning
An improved methodology to operations planning in SCs proposed by Drexl et al. (1994), Shapiro (1999), Miller (2002), and many other authors is the concept of hierarchical planning.40 It is also the conceptual framework underlying Advanced Planning Systems (APS), new planning software packages which try to overcome the major flaws known from MRP II. In particular, the objective is to • consider the entire SC, • obey system constraints (e.g. incorporate resource capacities), • and account for the interrelations between distinct processes.41 Hierarchical production planning was first introduced by Hax and Meal (1975) in the form of a case study.42 Since then it received considerable attention in the
38
39 40 41 42
C.f. Drexl et al. (1994), p. 1025. Similar conclusions are given e.g. by Hopp / Spearman (1996), pp. 175, Zijm (2000), pp. 317. C.f. Stevens (1989), p. 7. C.f. Drexl et al. (1994), pp. 1028, Shapiro (1999), pp. 741, Miller (2002), p. 1. C.f. Kansky / Weingarten (1999), pp. 91. C.f. Hax / Meal (1975), pp. 53.
16
2. Supply Chain Management and Collaborative Planning
literature on production planning and scheduling.43 Its basic idea is in fact similar to successive planning, in that the overall planning problem is decomposed into sub-tasks which interrelate in a hierarchical way. That is, higher level decisions form a given frame for decision making at subordinate levels. This is visualized in Fig. 3 for a hierarchical planning system with two levels. The novelty of hierarchical planning however stems from the fact that the decomposition is regarded as a key aspect in creating a coherent planning system and therefore is based on a careful analysis of the overall decision or planning problem. First, sub-tasks are usually defined such that decisions with similar time horizons and many interdependencies between one and another are combined at one planning level.44 Also, the design of planning levels is oriented on the structure of the organization the planning system belongs to. For example, the number of levels can correspond to the number of layers of managerial decision makers.45 Second, distinct degrees of aggregation are used at the different planning levels. They are chosen in a way to best support the respective decision making processes. For example highly aggregated data is used in long-term, top-level planning, whereas detailed information is used for day-to-day short-term decisions.
Top Level Anticipated Base Level Anticipation (Feed Forward)
Instruction
Reaction (Feedback)
Base Level
Fig. 3. Hierarchical planning system (source: Schneeweiss (1999), p. 19)
Finally, the coupling or interaction of decisions at various levels receives particular attention.46 This is important in order to limit the sub-optimality of the total solution which naturally results from the decomposition of the overall planning problem into smaller chunks. Two concepts can be used to improve the quality of total solutions: anticipation and feedback.47
43
44 45 46 47
See e.g. Stadtler (1988), pp. 36, for a comparative study of various hierarchical production planning systems proposed in the literature. C.f. Kistner (1992), p. 1127. C.f. Scholl (2001), p. 37. C.f. Stadtler (1988), p. 31, Kistner / Switalski (1989), p. 498. C.f. Schneeweiss (1999), pp. 18.
2.3. Operations Planning in Supply Chains
17
Anticipation aims at drawing top-level decisions that do not overly hamper base-level decision making. According to Schneeweiss (1999) it can be defined as “choosing an anticipated base-level and taking into account its impact on the topdecision”.48 This is indicated in Fig. 3 by the “anticipated base level” which becomes a part of the top-level decision situation. To keep the resulting complexity manageable, the anticipated base-level model is usually limited to a rough, strongly simplified representation of the actual base-level objective and decision space.49 Still, even a simplified base-level model is often sufficient to guide toplevel decision making in a beneficial direction. Whereas base-level circumstances directly influence top-level decision making through anticipation, feedback is realized by reporting the consequences of toplevel decisions once they were incorporated into the base-level problem. Feedback communication is indicated in Fig. 3 by the dashed arrow. It can result in a reevaluation of top-level decisions even before the plan is actually put into practice. Alternatively, it may only be used to improve top-level decision making in later, subsequent planning cycles.50 In contrast to the simplified visualization in Fig. 3, hierarchical planning systems usually include more than two levels and comprise more than one separate planning task at a given level. Since there usually are interdependencies between the various planning tasks at one level, coordination among them is required. It is established by the upper level, in that the interrelations are anticipated by the upper level problem. In consequence, instructions received by the various planning tasks are hoped to be coherent one with another.51 This concept, i.e. that coordination is achieved by establishing an all-embracing upper-level, is another key characteristic of hierarchical planning. Nonetheless inconsistencies can arise due to aggregation and coordination problems.52 Aggregation flaws result from the changing level of detail used at different planning levels. Since aggregation usually incurs a simplification of the actual problem structure, it might not be possible to properly disaggregate top-level instructions at the base level. Similarly, coordination defects can occur, since wellcoordinated, aggregate instructions do not necessarily enforce consistency at the detailed, disaggregated level. For example, while weekly production quantities for components and final products are synchronized, they can still become inconsistent on a daily basis after disaggregation in separate planning modules. In order to organize SC operations planning in terms of a hierarchical system, it is useful to consider the various operational activities on the one hand, and differing time frames of decisions on the other as two distinct dimensions. The resulting
48 49 50 51 52
Schneeweiss (1999), p. 18. C.f. Homburg (1996), p. 21. C.f. Stadtler (1988), p. 139. C.f. Kistner / Switalski (1989), p. 480. C.f. Corsten / Gössinger (2001), pp. 34.
18
2. Supply Chain Management and Collaborative Planning
hierarchical planning system embedded in that framework is shown in Fig. 4, it is the so-called “supply chain planning matrix”.53 Demand planning and fulfillment are the major drivers of all planning decisions, as forecasts and known orders of the SC’s final demand are determined here. Strategic network planning and master planning are two central planning tasks which consider the entire SC, and serve to decide on how expected demand can be effectively satisfied. Herein, strategic network planning is concerned with long-range decisions on the SC’s configuration such as the selection of locations and their capacities. Master planning in contrast operates within the frame defined by strategic decisions, and establishes target quantities, e.g. for production or procurement, on a medium-term, aggregate level for the entire SC such that corresponding demand forecasts can be satisfied. On a short-term level, individual planning tasks are proposed for the different operational processes. Planning decisions comprise order generation for procured material (procurement), lot-sizing, scheduling and shop-floor control (production), and detailed planning of transport flows, tours and truck loads (distribution).54 In fact, multiple instances of these tasks are usually in place dedicated to specific locations or facilities, e.g. individual scheduling systems for each shop floor. A good example of how the various planning tasks look like and interact with each other in practical applications is described by Meyr (2004) for the automotive industry.55 proc urem ent long-term
distribution
sales
Strategic Network Planning Strategic Network Planning
mid-term
short-term
production
Master Planning Master Planning
Material Material Requirements Requirements Planning Planni ng
Dem and Planning
Production Production Planning Planning
Distribution Distribution Planning Planning
Scheduling Scheduling
Transport Transport Planning Planning
Dem and Dem and Fulfilm ent Fulfilm ent
Fig. 4. Supply chain planning matrix (source: Rohde et al. (2000), p. 10)
As discussed above, upper level planning results define the frame for subordinate levels. In particular, the coordination of the various planning modules at the short-term level is established through instructions from their top-level. Therefore, the mid-term master planning plays a crucial role within the framework. It bal-
53
54 55
Rohde et al. (2000), p. 10. Alternative, but similar frameworks are proposed e.g. by Zeier (2001), p. 36, Shapiro (2001), p. 41, Kuhn / Hellingrath (2002), p. 143. For a more in-depth overview of the planning matrix see Meyr et al. (2005), pp. 109. See Meyr (2004), pp. 447.
2.3. Operations Planning in Supply Chains
19
ances supply with expected demand and synchronizes the operational processes across the SC.56 In order to achieve this purpose, it is commonly agreed that it should be organized as a single, centralized planning task embracing the entire SC.57 However given the nature of SCs, centralized decision making is a questionable aspect of the hierarchical planning concept. Concerning strategic network planning one may argue that chances exist to implement it as a single, centralized process, e.g. owned by the most powerful member of the SC, since the planning frequency is low, data is highly aggregate and can even be gathered manually.58 At the master planning level however barriers are higher to centralized decision making across business units or company borders. From a technical perspective, it requires for one a high level of systems integration, as accurate and steadily updated data on all processes must be available. Secondly, the computational complexity grows with an increasing number of facilities and processes covered. Even more important, from an organizational perspective, independent entities in the SC will often resist to open all information to a central planning unit and accept to receive instructions in the form of plan targets. This is further complicated by the fact that individual entities can be involved in SC relationships to several, independent partners as indicated by the example of Fig. 1 above.59 In such a situation it is doubtful, whether an entity can be integrated into centralized planning with one of the SC partners. In result, hierarchical planning can regularly be realized only for a part of the overall SC, e.g. for all processes within one company or business unit. Therefore, the question arises, if there are alternative approaches to coordinate planning of adjacent operational processes without centralized decision making. Such an alternative approach is offered by collaborative planning. 2.3.3
Collaborative planning
Coordination can principally be established in two ways: by a hierarchical (also called vertical) approach or in a non-hierarchical (horizontal) way.60 As we have seen above, hierarchical coordination is achieved through a common top-level decision process which generates synchronized instructions for interrelated subordinate levels from a central perspective. This is a common way to achieve coor-
56 57
58
59 60
C.f. Rohde / Wagner (2005), p. 159. C.f. Corsten / Gössinger (2001), 33, Rohde / Wagner (2005), p. 159, Kuhn / Hellingrath (2002), p. 145. In fact, various successful implementations of SC-wide strategic planning are reported in the literature, e.g. by Lee / Billington (1995), pp. 42, Camm et al. (1997), pp. 128. C.f. Zijm (2000), p. 323. C.f. Brockhoff / Hauschildt (1993), p. 400, Wildemann (1997), pp. 423, Steven (2001), p. 969.
20
2. Supply Chain Management and Collaborative Planning
dination within companies.61 However, it comes to an end when a joint top-level embracing all interrelating units and their decision processes does not exist and the parties involved cannot agree to establish a central decision maker. In contrast, heterarchical coordination grounds on consensus-like agreements on objectives, measures, and rules between parties with (relatively) equal decision rights. It is usually achieved through communicative, negotiation-like processes.62 In the context of SCM heterarchical coordination of planning tasks is referred to as collaborative planning.63 The term collaborative planning gained popularity due to the industry initiative “Collaborative Planning, Forecasting, and Replenishment” (CPFR). CPFR represents a standardized process for implementing cooperative SC relationships between retailers and manufacturers in the packaged consumer goods industry.64 As implied by its name, the original CPRF model consists of three phases: planning, forecasting, and replenishment.65 Planning here refers to the definition of a cooperation’s mission statement including goals, tasks, and resources, and the development of a joint business plan. The latter specifies the items involved in the cooperation, how they should be marketed, and how their supply should be organized.66 Hence, in this context collaborative planning is understood as business planning, that is as a broad task which specifies how SC partners intend to cooperate. The meaning attributed to collaborative planning throughout this work is different. Here, it is understood as collaborative operations planning, i.e. as a nonhierarchical, cooperative approach to the coordination of operations planning tasks across the SC. To further specify the definition, it is helpful to introduce the concept of planning domains. A planning domain is a part of the SC (including corresponding planning processes) under the control and in the responsibility of one planning organization.67 Examples of planning domains may be the distribution stage of a SC, a regional subsidiary of a large corporation, or the part of the SC which pertains to one company. Planning processes can usually be well-structured and hierarchically coordinated within a planning domain, but are disconnected at the interfaces towards other, adjacent domains. This means, that only rough and uncertain information is available on other domains in the form of demand forecasts (in case of customers)
61 62 63 64 65
66 67
C.f. Brockhoff / Hauschildt (1993), p. 400. C.f. Steven (2001), p. 969, Zäpfel (2001), p. 13. C.f. Zäpfel (2001), p. 13, Kilger / Reuter (2005), p.259. C.f. Ireland / Bruce (2000), p. 83. C.f. Feuerstake (2002), p. 22. See VICS (2002), p. 4, for an overview of the original CPFR model which comprises a total of nine process steps. The model was redefined and partly rephrased by the VICS CPFR committee in 2004; the initial phase is since then called „strategy & planning“, but essentially still consists of the activities described above (see VICS (2004)). C.f. Lohse / Ranch (2001), pp. 58, Seifert (2002), pp. 15. C.f. Kilger / Reuter (2005), p. 259.
2.3. Operations Planning in Supply Chains
21
or supply capabilities (in case of suppliers). Now, collaborative planning is a means to link several such domains and their respective planning processes. Along the lines of Kilger / Reuter (2005) it is defined as follows: “The idea is to directly connect planning processes that are local to their planning domain in order to exchange relevant data between the planning domains. The planning domains collaborate in order to create a common and mutually agreed upon plan.”68 Similarly, Stadtler (2007) defines collaborative planning as “a joint decision making process for aligning plans of individual SC members with the aim of achieving coordination in light of information asymmetry.”69 This is visualized in Fig. 5 for two planning domains. Within each domain hierarchical coordination of planning processes can be realized. Collaborative planning however serves to establish coordination between the domains. The lowestlevel planning task which covers all operational processes within a domain is usually the mid-term synchronization by master planning. Hence, collaborative linkage of domain-specific master planning tasks is of particular interest. Planning Domain 2
Planning Domain 1
Collaborative Planning
Fig. 5. Collaborative planning visualized (source: Kilger / Reuter (2005), p. 259)
A generic collaborative planning process comprises the phases as shown in Fig. 6. Once the cooperative relationship is defined, typical activities follow a cyclical process. Initially, intra-domain plans are generated and relevant data is exchanged between the domains. The crucial phase is then to adjust the internal planning results in an agreed upon way such that a consistent overall plan is obtained and committed to (“negotiation & exception handling”). Thereafter, final results can be executed and resulting performance be measured. The process starts over after a pre-defined re-planning interval. Systems support of collaborative planning, that is support by Advanced Planning Systems (APS), is available for all phases as shown in Fig. 6. Naturally, APS support the generation of intra-domain plans. Regarding data exchange, APS offer
68 69
Kilger / Reuter (2005), p. 259. Stadtler (2007), p. 2.
22
2. Supply Chain Management and Collaborative Planning
web-interfaces for data visualization and entry by external partners. Also, automatic transmission via XML or e-mail in conjunction with Excel spreadsheets or flat files is available. For example, inventory levels, supply or transport requirements can be transmitted by e-mail to planning partners or accessed through webpages in SAP APO or the SAP Inventory Collaboration Hub.70 Various rules can be defined concerning exception handling. The basic idea here is to monitor some performance indicators such as capacity utilization, order quantities, or service levels. Alerts can then be provided in case predefined value corridors are violated. Workflows specifying how to deal with such violations can be defined, e.g. in the SAP APO Macro Builder.71 In the execution phase, plans are put into practice. It is insofar supported by APS as production, transport, or purchasing orders are created and possibly automatically directed to transactional systems (e.g. a company’s ERP system).
Ex ecu tio n
Definition
Data nge a Exch
Per f Me orman asu rem ce ent
Domain Planning
Ex & ng on ndli i t a tia go n H Ne ptio e c
Fig. 6. Collaborative planning cycle (source: Kilger / Reuter (2005), p. 271)
Finally, performance measurement is too facilitated by APS in that key performance indicators can be defined and kept track of in so-called plan monitors. Performance measurement can relate to plan figures, actual data from past periods, or comparisons of plan and actual figures. Despite these extensive support functionalities, a shortcoming to date is that only little decision aid is provided with respect to the negotiation process itself. Here, the question of which tools to utilize and how to embed their use in the entire collaborative planning process as depicted above is largely unanswered, and it is left to the individual user or implementer to define the workflows associated with alerts or violations as explained above. It is therefore the purpose of this work to develop a negotiation-based collaborative planning scheme that goes beyond mere data exchange and to demonstrate which improvements in SC performance can result from its application.
70 71
C.f. Bartsch / Bickenbach (2002), pp. 361, Kilger / Reuter (2005), p. 276. C.f. Kilger / Reuter (2005), p. 277.
2.3. Operations Planning in Supply Chains
23
A final note is in place on the applicability of collaborative planning in SC relationships. As described above in 2.1, SCs usually are complex networks comprising a number of companies, facilities, and often thousands of stock-keeping units. As collaborative planning requires substantial investments in hard (e.g. IT systems) and soft matters (e.g. team building across companies), it is clear, that it cannot realistically be implemented between all planning domains of a SC. Following Williamson’s (1985) classification of transactions by frequency and degree of asset specificity, Skjoett-Larsen et al. (2003) suggest that so-called developed or advanced CPFR (i.e. a close collaboration) should be used where transactions recur frequently and require at least some specific investments by the trading partners,72 which “lock” the SC members into a supply relationship and create barriers to switch suppliers or customers easily. Products or components requiring such dedicated investments are usually the major items dealt with in a SC (by volume and / or contribution to the value / functionality of the end-product). Specific investments around such items are often joint R&D and development actitivities which e.g. ensure, that parts fit together appropriately, can be processed in the desired way, or provide customized end-customer functionality. Even when only key items and their corresponding planning domains are regarded as candidates for collaborative planning, additional factors can come into play, which foster or inhibit the applicability of collaborative planning. Based on a survey by Barratt (2004), these mainly go back to the relationship and cultural fit between the respective SC members. Enablers of collaborative planning are personal relations across various levels and functions of the companies, mutual interdependence, openness, and (at the base) the right individual chemistry. Inhibitors on the other hand are mechanistic behavior, functional (silo-oriented) management styles, and a lack of honesty, trust and process visibility.73 Only when sufficient “enablers” are in place, collaborative planning will likely be implemented successfully. Finally, as in any SC integration project, expected benefits of collaborative planning have to be compared with the cost of initial implementation and ongoing operation of the process.74 McLaren et al. (2002) and Kilger (2005) give indications on the potential benefits (e.g. financials, service levels, as well as qualitiative factors such as improved market knowledge) and costs (system implementation and integration, process coordination costs, data translation and integration, switching costs, etc.).75 Only when expected benefits of developing and implementing a collaborative planning process exceed associated costs, an implementation can be recommended.
72 73 74 75
C.f. Skjoett-Larsen (2003), p. 538. See Barratt (2004), pp. 81, for a full overview. C.f. Kilger (2005), pp. 281. C.f. McLaren et al. (2002), pp. 355, Kilger (2005), pp. 291.
24
2. Supply Chain Management and Collaborative Planning
Recommended readings • Simchi-Levi, D. / Kaminsky, P. / Simchi-Levi, E. (2004): Managing the Supply Chain – The Definitive Guide for the Business Professional, 2nd edition, Boston et al. 2004 (especially chapter 1 “Introduction”). • Meyr, H. / Wagner, M. / Rohde, J. (2005): “Structure of Advanced Planning Systems”, in: Stadtler, H. / Kilger, C.: Supply Chain Management and Advanced Planning – Concepts, Models, Software and Case Studies, 3rd edition, Berlin et al. 2005, 109-115. • Kilger, C. / Reuter, B. (2005): “Collaborative Planning”, in: Stadtler, H. / Kilger, C.: Supply Chain Management and Advanced Planning – Concepts, Models, Software and Case Studies, 3rd edition, Berlin et al. 2005, 259-278.
3 Modeling Framework and Relevant Literature Content This chapter sets out a quantitative modeling framework for the following treatment of collaborative planning and reports on findings from literature related to the problem setting. In section 3.1 we outline the planning situation considered here and describe mathematical programming type models which can be used for planning purposes within single planning domains. Furthermore, links to other planning domains will be modeled by additional constraints. Section 3.2 contains a brief literature review on the value of information sharing and collaboration between SC partners. It casts some light on what can be gained from closer collaboration. Finally, in section 3.3 we review and comment on approaches proposed in the literature to achieve coordination of planning between independent domains. Key points • Mathematical programming models are well suited for collaborative planning at the master planning level; the multi-level capacitated lot-sizing problem (MLCLSP) is a good representative model which plans material flows over multiple tiers taking into account limited resource capacities and fixed setup/ order costs • Information sharing and integration increase the efficiency of SC operations, especially when the SC is complex (e.g. deals with multiple products and tiers and capacities are limited) and a high portion of costs accrues at upstream tiers – the benefit strongly depends on how additional information is utilized • Approaches to coordinate planning across independent domains proposed in literature are rather hierarchical (i.e. give more decision authority to individual players) and require a relatively high level of integration (i.e. sharing a sensitive information)
3.1
Modeling
3.1.1
Decision situation and modeling assumptions
In terms of the planning level, the focus of this work lies on the mid-term coordination of operations by master planning (MP). In the traditional production planning framework, MP has its origins in Aggregate Production Planning and, as implied by its name, Master Production Scheduling.76 Hence, the purpose of MP, as far as it concerns production processes, is to specify production and shipment rates 76
See e.g. Silver et al. (1998), pp. 538, Chase et al. (1998), pp. 552, Vollmann et al. (1984), pp. 12.
G. Dudek, Collaborative Planning in Supply Chains, 2nd edn., DOI 10.1007/978-3-540-92176-9_3, © Springer-Verlag Berlin Heidelberg 2009
26
3. Modeling Framework and Relevant Literature
as well as capacity adjustments for plants such that expected customer demand can be satisfied efficiently.77 The underlying planning horizon covers a medium term of 3 to 18 months (depending on the problem setting) and is usually subdivided into weekly or monthly time buckets. Due to the shift of focus towards SCs, the goal of MP is however broadened, for that it seeks to synchronize all operational processes along the SC or, given our discussion in 2.3.2, at least within the planning domain under consideration.78 In order to do so effectively, it needs to account for interdependencies between the various processes. Suppliers
Production facilities
Distribution facilities
Customers
Fig. 7. Logistical network structure (source: with adaptations from Thorn (2002), p. 31)
A typical logistical network considered in MP contains the elements as shown in Fig. 7. Procured input materials are supplied by external vendors which are not part of the planning domain. The domain’s output is created by a network of plants, potentially in a multi-stage manner linked by internal supply relationships. Final products are shipped through the distribution system (also potentially multistage) to the domain’s final customers. Building upon Fig. 7, the decisions of MP are described in Table 4. In order to ensure feasibility of planning results, it is important that all decisions are consistent with each other and in line with relevant constraints. To maintain consistency it is necessary to capture the interrelations between individual processes. For example, if input materials are needed for production, production levels must be in line with the availability of supplied material. Likewise distributed quantities must be based on what is actually planned for production, etc.
77 78
C.f. Silver et al. (1998), pp. 556, Stadtler (2000a), p. 11. C.f. Rohde / Wagner (2005), p. 159.
3.1. Modeling
27
Table 4. Basic decisions of master planning Decision type
Description
Procurement Quantities of input materials purchased from external suppliers Production / material Production and handling quantities, or output levels of other handling relevant operational processes Inventories Inventory levels at the end of planning periods Customer shipments Quantities supplied to customers and their origins Transports Transport quantities on all transport links considered Source: Rohde / Wagner (2005), pp. 159
System constraints mainly concern available resource capacities and other technological restrictions (e.g. the assignment of products to plants). They describe the configuration of the network and are largely a result of Strategic Network Planning, as explained above in 2.3.2. However, as far as they can be influenced at a mid-term level, adjustments of resource capacities can also be a part of MP and form a second set of decisions which go beyond what is presented in Table 4. For example, working times/ shifts or transport capacity reservations at third-party carriers can be adjusted on a medium term. The formal objective underlying MP decisions is usually a financial measure. Chopra / Meindl (2001) define it as “to satisfy demand in a way that maximizes profit for the firm”.79 When all demands are supposed to the covered, revenues are fixed and profit maximization is equivalent to minimizing the cost of supplying the demand. Alternatively, one may try to maximize net revenues, i.e. gross revenues less those costs of supply that are influenced by the planning decisions. However, since cost minimization and net revenue maximization can be converted one to the other, we focus only on cost minimization in the following.80 Principally, other objectives can be regarded, too, such as time-oriented or resource-oriented measures, e.g. on-time deliveries or capacity utilization.81 However, since cost rates measure the economic effort required for the various operational processes in common units, they allow for proper tradeoffs between planning decisions.82 Therefore, they form the best basis to direct planning decisions and are used as the only objective, here. Relevant types of costs are those associated with the planning decisions as described above, i.e. procurement, production and handling, inventory, distribution, and transport costs. As far as capacity adjustments are possible, corresponding costs have to be considered, too. Finally, if demand partially needs not to be cov-
79 80
81 82
Chopra / Meindl (2001), p. 103. Minimizing cost is equivalent to maximizing net revenues when missed revenues are considered as costs and the degree of demand satisfaction as a variable to be decided upon during planning. For an overview of other potential objectives see Thorn (2002), pp. 34. It is e.g. difficult to balance on-time delivery and capacity utilization, unless these measures are expressed in terms of costs.
28
3. Modeling Framework and Relevant Literature
ered or can be shipped delayed, costs of lost sales and / or backorders must be included for proper tradeoffs with remaining planning alternatives. Medium term planning does not require to consider processes, materials, and resources in full detail. In fact, a detailed perspective (e.g. based on individual stock-keeping-units) is usually neither realizable due to the problem size nor practicable. In order to keep the problem manageable and obtain meaningful results some aggregation is required. For example, families of final products are used which comprise items with similar demand patterns and resource needs.83 Similarly, plants or plant segments (e.g. manufacturing lines) are used as resources instead of individual work centers, flow lines stations etc. Moreover, not all resources and processes have to be considered. The focus should be on operations which potentially form bottlenecks or incur high costs so that an efficient utilization is imperative. Once planning decisions for the critical processes have been established, the consequences for all remaining operations can be derived in a following step. Given the various types of decisions and associated cost tradeoffs as well as the system constraints, it is obvious that MP usually deals with a complex decision situation. Finding a good, not to say the best, set of consistent decisions is a daunting task. Therefore, quantitative models are useful to support decision making. Based on the problem description, mathematical programming models (MPM) are most suitable for this purpose. As pointed out by Shapiro (1999), MPM are “the only analytical tools capable of fully evaluating large numerical data bases to identify optimal, or demonstrably good, plans”.84 In contrast to other analytical methods85 MPM are not only able to cope with the large number of alternative decisions, but also help identifying the best set of those. As with any analytical method, using MPM of course relies on some simplifying assumptions. The major simplifications are referred to as proportionality, additivity, divisibility, and certainty,86 and are shortly discussed in the following. Proportionality stands for the fact that any decision variable’s contribution to the objective function and to all constraints is proportional to the variable’s value. In our problem’s context this means that costs associated with operations grow proportionally with output levels, and that per unit input and resource needs are fixed. Additivity implies that every function within the model equals the sum of individual contributions of the respective decisions. For example, total cost follows as the sum of the costs for each of the operations considered, total usage of a resource as the sum of resource needs by individual operations etc. Divisibility re-
83
84 85
86
C.f. Hax / Meal (1975), p. 55, Stadtler (1988), p. 83. For an example method of how to compress product-process structures based on resource requirements see Billington et al. (1983), pp. 1132, and Stadtler (1998), pp. 178. Shapiro (1999), p. 740. E.g. simulation models (see Thorn (2002), pp. 49, for an overview of simulation model applications to planning in supply chains). C.f. Hillier / Liebermann (2001), pp. 36, Shapiro (2001), pp. 84. For a brief overview of mathematical programming see e.g. Stadtler (2005b), pp.473.
3.1. Modeling
29
fers to the assumption that variables can take any fractional value and only applies to linear programming (LP) models. Besides linear variables we also allow for binary variables with 0-1 values. With binary variables present, the programming model becomes a mixed-integer model. Finally, certainty means that all parameters are deterministic constants. In our context this implies that all input data such as per unit costs and resource needs are known with certainty. Assessing the applicability of the simplifying assumptions, one can state that assuming linear and additive relationships certainly is a simplification from real world relationships. On the other hand, it is a close-enough approximation for many functional relations such as between operation levels and associated costs or resource requirements. Also, the divisibility of linear variables is mostly uncritical, as rounding off resulting values does usually not affect the overall result too much. This holds true, as long as binary variables are added and used in situations, when discrete “go” / “no go” decisions have a major impact on the model’s solution. Whenever a discrete decision of this kind notably affects costs or system constraints, the divisibility assumption gives a too optimistic picture of the situation, because here rounding off is only possible to integer 0-1 values and does have a major impact on the overall result. Therefore, binary variables and hence mixed-integer models have to be used whenever discrete decisions play an important role, e.g. when production setups with fixed costs are considered. Finally, a questionable assumption is the certainty property. Clearly, some randomness is present in any real-world process, so that it cannot be perfectly described by a deterministic model. On the other hand, just as with the linearity assumption an abstraction from stochastic variations is often permissible, as long as the variations stay within some limits. In fact, as mentioned by Rohde / Wagner (2005), “reasonable results can only be expected for production processes having low output variances”. 87 Otherwise, planning results quickly become obsolete, turning planning to a rather useless effort. Given a medium term planning horizon of several months, reality will however always deviate from planning assumptions. This especially concerns demand forecasts, but also other events such as machine breakdowns can cause considerable changes to what was initially expected. In order to deal with this uncertainty and still make use of MPM, the standard procedure is periodical re-planning based on a rolling horizon basis.88 As demonstrated in Fig. 8, a plan covering T periods is only partially implemented (say for Ti periods). Thereafter a new planning cycle is initiated based on updated information. The fact that plans are regenerated on a rolling basis also brings some interesting consequences for collaborative planning between individual domains. This will be dealt with in more detail later on in chapter 5.
87 88
Rohde / Wagner (2005), p. 160. See e.g. Fleischmann et al. (2005), pp. 83.
3. Modeling Framework and Relevant Literature
30
1
Ti
T Ti+1
T+Ti
Fig. 8. Planning with rolling horizons (source: Fleischmann et al. (2005), p. 84)
3.1.2
Intra-domain planning model
Several authors have developed mathematical programming models for planning of operations at the master planning level, which are briefly discussed in the following. Thereafter we present the model which is used for intra-domain planning in this work and forms the basis of the collaborative planning scheme developed in later chapters. It is based on the literature findings reported first. An overview of the contributions regarded here and their characteristics is given in Table 5. Of course, the compilation in Table 5 is not exhaustive. In particular, contributions which date back further and where not specifically published under the theme of SCM are not included, although they may deal with a decision situation and model similar to what we consider here.89 To avoid a lengthy elaboration on each of the models, only the major commonalities and differences are outlined. All MPM mentioned in Table 5 depict a decision situation as described in the previous section. In essence, they cover a finite planning horizon of T consecutive periods, consider several final products, and a multi-level structure of processes linked by balance equations. Also, limited resource capacities for production, and partly also for distribution and procurement processes are included as constraints. As explained above, the objective function regularly consists of minimizing total costs or, in some cases, maximizing net revenues. Differences between the models occur with respect to their scope, possible adjustments of resource capacities, and discrete decisions.
89
Interested readers are referred to the review articles by Bhatnagar et al. (1993), Thomas / Griffin (1996), and Erengüc et al. (1999) for a comprehensive overview. A more detailed comparative study of recent models is given by Thorn (2002), pp. 103.
cost min
net rev. max,
prod., distr.
proc., prod., distr.
prod., distr.
proc., prod., distr.
prod.
proc., prod., distr.
proc., prod., distr.
proc., prod.
prod., distr.
prod., distr.
Özdamer / Yazgac (1999)
Escudero et al. (1999)
Barbarosoglu / Özgür (1999)
Zäpfel / Wasner (2000)
Ertogral / Wu (2000)
Haehling v. L. / Pilz-Glombik (2001)
Thorn (2002)
Rota et al. (2002)
Karabuk / Wu (2002)
Jung et al. (2005) cost min
target utilization
net revenue max
net revenue max
cost min
cost min
cost min
cost min min. utilization
cost min
cost min
prod., distr.
Erengüc et al. (1999)
Objective Fct.
Scope
Contribution
balance eq., capacity
balance eq., capacity
balance eq., capacity
balance eq., capacity
balance eq., capacity
balance eq., capacity
balance eq., capacity
balance eq., capacity
balance eq., capacity
balance eq., capacity
balance eq., capacity
Constraints
-
-
prod. setups
-
transp. setups
prod. setups
transp. setups
prod. & transp. setups
-
prod. & transp. setups
prod. & transp. setups
Discrete Decisions
-
outsourcing, under- / over utilization
-
-
type & no. of transport vehicles
type & no. of transport vehicles overtime production
-
-
no. of transport vehicles
over-/undertime prod.
Capacity Adjustments
3.1. Modeling
Table 5. Overview of mathematical programming models 31
32
3. Modeling Framework and Relevant Literature
Scope here relates to the number of stages of the logistical network according to Fig. 7 that are included in the model. The most extensive models are designed to cover procurement, production, and distribution processes. These are the contributions by Escudero et al, Zäpfel / Wasner, Haehling von Lanzenauer / PilzGlombik, and Thorn. Others take a more limited view of only a part of the potential processes. Erengüc et al., Özdamar / Yazgac, Barbarosoglu / Özgür, Karabuk / Wu, and Jung et al. consider production and distribution activities, whereas Rota et al. concentrate on procurement and production. Ertogral / Wu focus on production processes. Adjustments of resource capacities are permitted as additional planning decisions by some authors. Potential overtime for production processes is considered by Erengüc et al. and Ertogral / Wu. Karabuk / Wu allow outsourcing, i.e. external supply of final products, to cover demand peaks. Özdamar / Yazgac, Zäpfel / Wasner, and Haehling von Lanzenauer / Pilz-Glombik restrict production capacities to fixed values, but include planning decisions on type and number of vehicles to be used on transport links in the respective planning periods. Considerable differences relate to the type of discrete decisions included in the models. No such decisions at all are regarded by Escudero et al, Thorn, and Jung et al. The resulting models therefore are pure linear programs. Most other authors incorporate discrete decisions. Binary setup decisions in production and / or transportation are considered by Erengüc et al., Barbarosoglu/ Özgür, and Ertrogral / Wu. Özdamar / Yazgac, Zäpfel / Wasner, and Haehling von Lanzenauer / Pilz-Glombik go even further and model their transport decisions by integer variables which can take values other than 0 and 1.90 A special note is needed for the model of Karabuk / Wu, as its objective function contains a quadratic term for deviations of target utilization levels. Moreover, the model is a stochastic program, i.e. is based on a set of scenarios for final demand, which maximizes the expected net profit across them. In summary, it becomes clear that the models differ in varying degrees from one and another. These differences are however rather due to the specific SC setting considered by the various authors than to a truly differing modeling approach. In fact, they all share a common, principal structure: material flows planned to satisfy final demand are captured by balance equations and restricted by available resource capacities. Since it is not the purpose of this work to develop yet another (problem specific) model, we assume one of the models mentioned above to be used for planning within planning domains. In choosing the model we follow the example of Ertogral / Wu. The model they use is the multi-level, capacitated lot-sizing problem (MLCLSP). This choice is motivated by the fact that the MLCLSP is a standard problem which is well known and documented in literature. Moreover, it captures the essential planning issues presented above: several final products, a multilevel process structure, limited capacities, and discrete setup decisions.
90
Of course, these formulations can be redefined to contain only binary variables. However, this comes at the expense of a larger number of binary variables.
3.1. Modeling
33
Also, it should be noted that the collaborative planning scheme developed in later chapters is not specifically tailored to the MLCLSP as planning model within each domain. Therefore, our selection of the MLCLSP as intra-domain planning model serves more as the choice of a representative example than as a limitation to this specific problem situation. In its basic, so-called I&L version,91 the MLCLSP can be formulated as follows.92 Model 1. MLCLSP Indices t planning period 1…T j operation / item ∈ J r resource ∈R Index sets / boundaries T planning horizon J set of operations / items R set of resources set of direct successor operations of j Sj Data chj unit holding cost of operation j cfj setup cost associated with operation j unit cost of overtime at resource r cor Ej,t (external) demand for operation j in period t capacity of resource r in period t Cr, t Lj,t maximum lot-size constant for operation j
X j, t / X j, t upper / lower bound on output level of j in period t I j, t / I j,t
upper / lower bound on inventory level of j at the end of period t
O m,t / O m,t upper / lower bound on overtime on resource r in period t ar,j rj,k Variables c xj,t ij,t yj,t or,t
91
92
unit requirement of resource r by operation j unit requirement of operation j by successor operation k total cost output level of operation j in period t inventory level of operation j at the end of period t setup variable of operation j in period t overtime at resource r in period t
“I&L” abbreviates “inventory & lot-size” and means that end-of-period inventory levels and lot-sizes are directly used as decision variables (c.f. Stadtler (1996), p. 562). C.f. Tempelmeier (2003), pp. 209, Günther / Tempelmeier (1997), p. 183, Stadtler (1996), p. 562. Please note that the formulation considered here neglects setup times (for the inclusion of setup times see e.g. Tempelmeier (2003), p. 209).
3. Modeling Framework and Relevant Literature
34
Formulation
min c s.t.
T
c=∑
(1) (2)
T
∑ (ch j i j ,t +cf j y j ,t ) + ∑ ∑ cor or ,t
t =1 j∈J
t =1 r∈R
∑ r j ,k xk ,t + i j ,t
∀j ∈ J , t = 1..T
(3)
∀r ∈ R, t = 1..T
(4)
∀j ∈ J , t = 1..T
(5)
∀j ∈ J , t = 1..T
(6)
I j , t ≤ i j ,t ≤ I j , t
∀j ∈ J , t = 1..T
(7)
O r , n,t ≤ or , n,t ≤ O r , n,t
∀r ∈ R, t = 1..T
(8)
y j ,t ∈ {0,1}
∀j ∈ J , t = 1..T
(9)
i j ,t −1 + x j ,t = E j ,t +
∑ ar , j x j , t
j∈J
k∈S j
≤ Cr ,t + or ,t
x j ,t ≤ L j , t y j , t
X
j ,t
≤ x j ,t ≤ X
j ,t
The model plans output (xj,t) and inventory levels (ij,t) of all operations considered as well as expansions of resource capacity (or,t). Operations can principally represent production, transport or other value-adding operational activities. The objective function minimizes the value of variable c which, due to constraint (2), represents the total cost incurred from setups, inventory holding, and capacity expansions.93 Constraints (3) capture the flow balance between output, inventory and consumption by (external) customer demand Ej,t or successor operations.94 Constraints (4) represent capacity restrictions, while lot-sizing relationships are expressed in (5). Constraints (6) through (8) specify lower / upper bounds on variable values, as far as this is necessary. Assigning total cost to the extra variable c is not strictly required at this point, but will prove handy in later sections. As demonstrated by Stadtler (1996), there are more efficient formulations of the MLCLSP in terms of the integrality gap of the lp-relaxation and thus in terms of solution time.95 However, for the sake of simplicity and clarity we only deal with the basic I&L formulation throughout this work.96
93
94
95 96
Variable operation cost rates are assumed constant over the planning interval and thus omitted. It should be noted that without loss of generality replenishment lead times are neglected (i.e. assumed as zero). Although any fixed multiples of the planning period lengths could be used instead, this is omitted for ease of exposition. C.f. Stadtler (1996), pp. 575. Also, integrality gap and branch-and-bound solution time of the I&L formulation can be considerably reduced by strong valid inequalities as proposed by Pochet / Wolsey (1995), p. 273.
3.1. Modeling 3.1.3
35
Modeling links to adjacent planning domains
The above model depicts the isolated perspective of a single planning domain facing only external (market) demand. However, in order to realize collaborative planning it is important to explicitly regard the links to other (partnering) planning domains because the local planning situation depends on planning results of these domains, and vice versa. A planning domain can have direct links to two types of partners: customer and supplier domains. The situation is visualized in Fig. 9. It shows the part of the SC under the control of the domain under consideration (referred to as “local domain”) and corresponding planning processes. Now, the domain’s final output may be dedicated to either external customers, i.e. customers that cannot be directly influenced in what they demand, or to SC partners, i.e. customers that are able and willing to cooperate. These customers control another, more downstream part of the overall SC (referred to as “customer domain”) and corresponding planning processes. The link to a customer domain is established by order requirements requested by the customer based on the demand he faces. Similarly, the local domain usually needs supplies by vendors. To some vendors only market relationships may exist. However, others may be cooperative SC partners. The more upstream part of the SC which is controlled by a partnering supplier is called “supplier domain”. The link to a supplier domain is expressed in terms of supply requirements requested by the local domain as shown in Fig. 9. In what follows we specify the links to customer and supplier domains as additional constraints which can be added to the intra-domain planning model. The additional data items, decision variables, and constraints required to model thev links are presented in turn for the supplier and customer domain. Supplier Domain
Local Domain
Supply requirement s
Cust omer Dom ain
Order requirement s
Ext ernal dem and
Fig. 9. Links between planning domains Extension 1.1. Links to supplier domains Index sets JS set of supplied items (operations) Data XSj,t proposed supply quantity of j in period t IS j, t / IS j, t upper / lower bounds on supply inventory of j at the end of period t
Ext ernal dem and
36
3. Modeling Framework and Relevant Literature
Variables xsj,t (assumed) supply quantity of j in period t isj,t supply inventory of j at the end of period t Formulation
s.t.
T
c=∑
∑ (ch j i j ,t
t =1 j∈J
is j ,t −1 + xs j ,t =
T
+cf j y j ,t ) + ∑
T
∑ cor or ,t + ∑ ∑ ch j is j ,t
t =1 r∈R
∑ r j ,k xk ,t + is j ,t
t =1 j∈JS
∀j ∈ JS , t = 1..T
k∈S j
(10) (11)
xs j ,t = XS j ,t
∀j ∈ JS , t = 1..T
(12)
IS j, t ≤ is j ,t ≤ IS j, t
∀j ∈ JS , t = 1..T
(13)
Constraints (10) through (13) can be used in two ways. Assuming that the supplier has announced supply proposals XSj,t, these can be added to Model 1 as presented above in order to find the optimal intra-domain plan given supply quantities XSj,t ((10) replaces the original cost function of (2)). Proposed supply quantities by period XSj,t are input to the model due to constraints (12). Balance equations (11) link supplies to their consumption, thereby restricting internal operations by the availability of supply items. However, inventory holding of supplied quantities is permitted, in order not to fully dictate internal operations by supply quantities. Consequently, the cost function in (10) is enhanced by inventory holding costs of supply items. Even though these costs may in fact be covered by the supplier, their inclusion is important for ensuring a proper balancing between supply inventory holding and the remaining operations. Constraints (13) specify boundaries on the supply inventory isj,t, if this is required. Alternatively, when no supply proposals are known, constraints (12) can be skipped. In this case supply quantity variables xsj,t can take any desired value, and no inventory holding in the form of isj,t will occur. In this mode, constraints (11) reveal supply quantities (resulting values of xsj,t) that have to be requested from the supplier in order to make the resulting plan realizable. The situation is similar for the customer domain. Extension 1.2. Links to customer domains Index sets / boundaries JO set of order items (operations) Data XOj,t proposed order quantity of j in period t Variables xoj,t order quantity of j in period t Formulation i j ,t −1 + x j ,t = E j ,t + xo j ,t +
xo j ,t = XO j ,t
∑ r j ,k xk ,t + i j ,t
∀j ∈ JO, t = 1..T
k∈S j
∀j ∈ JO, t = 1..T
(14) (15)
3.2. Benefits of Information Sharing and Collaboration
37
Assuming that the buyer has announced order proposals XOj,t, constraints (14) and (15) can be used to incorporate the order quantities into the intra-domain planning model and generate the optimal plan given the proposed pattern of orders. Constraints (14) replace the original flow balance equations (3) for all items ordered by a buyer, so that two sources of demand are considered: (anonymous) demand by external customers Ej,t and orders by the collaboration partner(s) xoj,t. If no order quantities are known from the buyer, (15) can be skipped, and the extended model can be used to generate a proposal of supply quantities (resulting values of xoj,t). However, for doing so lower and upper bounds on xoj,t must be specified at a minimum, otherwise the values of xoj,t would be zero in the optimal solution. This aspect is discussed in greater detail below in chapter 4. In terms of modeling, the situation is equivalent for all planning domains joining the collaborative planning process. Only the question of who is viewed as customer or supplier depends on each planning domain’s local perspective. Thus, vendor orders generated at one domain, e.g. by adding constraints (11) to the intradomain model, become customer order requests XOj,t, once they have been communicated to the supplier domain. This makes clear that synchronized planning results for all domains can only be obtained through a well structured coordination mechanism. Coordination schemes which are proposed in the literature and applicable to this decision situation are discussed in section 3.3. Beforehand we briefly touch upon the question of what can be gained from closer collaboration in planning of SC operations.
3.2
Benefits of Information Sharing and Collaboration
Without any coordinating action domain-specific plans are generated with an isolated view of the domain in question and based on local information only. If mathematical programming models are used for planning purposes as described in the previous section, a local demand forecast (for the final output of a given domain) must be available and serves as the major driver of planning decisions. Interactions with other domains are simply ignored. However, as pointed out in section 2.3, purely isolated planning and operation of individual domains results in sub-optimization of the SC as a whole and inefficiencies such as high inventory buffers or frequent plan adjustments. Collaborative planning tries to eliminate this inefficiency and thereby to improve the SC’s performance. An important issue herein is to understand the benefit of increased SC integration. To give an idea of what can be gained from collaboration, some findings from literature are reported in the following and transferred to the problem setting considered here. Objects of information sharing and collaboration considered in the literature are operating characteristics and policies on the one hand, and demand forecasts on
38
3. Modeling Framework and Relevant Literature
the other. Since demand forecasting is not the major concern of this work, articles dealing with collaborative forecasting are not cited in what follows.97 Articles assessing the value of information sharing usually are based on simple, stylized SC settings. Mostly two partners (a retailer and a supplier), a single product, and random demand with a known distribution are considered. The SC operates by inventory control policies which trigger replenishment decisions. In order to explore the impact of information sharing, usually a traditional setting with local information for each partner and a new setting with improved information and synchronized operating rules are analyzed. It should be apparent that additional information is always beneficial, i.e. decisions made with more information cannot be worse than those based on fewer data.98 The goal of the contributions is to demonstrate ways of how to exploit additional information and to quantify the potential benefits. Bourland et al. (1996) analyze the effects of timely demand information in a two-partner SC where both parties use fixed replenishment periods which are offset by a given time interval. For example, the retailer orders every Monday while the supplier triggers production every Wednesday. They analyze the advantage of communicating actual demand at the retailer which occurred after his last order but before the supplier’s production quantity decision. Since this demand influences the retailer’s next order decision, knowledge of the demand is advantageous to the supplier. Bourland et al. find that sharing the demand information results in lower inventory holding and increased service level at the supplier. The benefits are significant when demand variability is high and the replenishment period offset is large relative to the cycle length: e.g. inventory reduction of 26% and fill rate increase from 92 to 96% with demand coefficient of variation of about 0.33 and an offset of almost the cycle length (19 vs. 20 periods).99 Chen (1998) considers a multi-tier, serial SC where replenishments are made in multiples of a base batch size. He compares operating costs of reorder point policies. In one setting, the reorder point policies are based on installation stock, i.e. the local inventory position at each tier, whereas in the other echelon stock policies are used. The second setting requires knowledge of system-wide inventory downstream from each echelon. In a computational study Chen observes cost reductions of 0 to 9.75% from using echelon reorder point policies, on average costs decrease by 1.75%. The benefit (percentage cost reduction) of echelon reorder points grows with the number of tiers in the SC and the length of replenishment lead times between adjacent tiers.100 Gavirneni et al. (1999) study a two-tier SC with fixed capacity at the supplier. When production orders exceed capacity, a costly expediting (overtime) mode is used for production. Both parties use (s,S) order-up-to policies for inventory con-
97
98 99 100
Interested readers are referred e.g. to Aviv (2001), Thonemann (2002), Zhao et al. (2002), and the references discussed there. C.f. Gavirneni et al. (1999), p. 20. C.f. Bourland et al. (1996), p. 250. C.f. Chen (1998), pp. S231.
3.2. Benefits of Information Sharing and Collaboration
39
trol. Three settings are analyzed: a traditional one with no information sharing, one with sharing of system parameters, i.e. cost rates, demand distribution, control policies and parameters, and one with sharing of actual demand data in addition to the system parameters of setting two. Cost results obtained with setting three always outperform those of setting two, which in turn outperform results of setting one. The gain between setting one and two is substantial with average savings of around 50%. Costs of setting three compared to setting two are lower by 1 to 35% depending on system parameters like supplier capacity and cost rates. Gavirneni (2002) deals with the same problem but proposes to modify the operating policy, such that the retailer is forced to place orders whenever cumulative demand since his last order exceeds a given level δ. The order quantity is not known to the supplier in advance, but yet some uncertainty is removed from the system.101 As a result, total SC operating costs are reduced through the new policy on average by 10.5% compared to the third setting in Gavirneni et al. (1999). The author therefore concludes that additional information can be better utilized by appropriately changing the operating policies as opposed to simply adjusting parameters of existing policies.102 Cachon / Fisher (2000) consider a SC with one supplier and N identical retailers. Replenishments take place in multiples of a base batch size and based on reorder point policies. They compare a traditional setting with local information to a setting where the supplier has access to the retailers’ inventory positions. Computational results show an average cost reduction vs. the traditional setting of 2.2%. On the other hand, reductions of the shipment lead time or the base batch size by about 50% lead to cost decreases of 21% and 27%, respectively.103 The authors conclude that for the model studied, improvements of operating characteristics such as lead time and batch size reductions boost performance more than mere exchange of information.104 Finally, Lee et al. (2000) study a 2-party SC with order-up-to policies in place at both, the retailer and the supplier. However unlike to other contributions, their model assumes that the retailer’s demand is auto-correlated over time. That is, a period’s demand is partly influenced by the demand of the pervious period.105 They too study two settings, one with local information and one where the supplier has knowledge of final demand. Approximate analytical results as well as simulation runs suggest significant inventory and cost reductions for the supplier with availability of demand data. The benefits increase with growing degree of autocorrelation, demand variance, and length of replenishment lead time.106 However, their results are somewhat expelled by Raghunathan (2001) who comments on the article by Lee et al (2000). He points out that their results depend on the
101 102 103 104 105 106
C.f. Gavirneni (2002), p. 645. C.f. Gavirneni (2002), p. 651. C.f. Cachon / Fisher (2000), pp. 1044. C.f. Cachon / Fisher (2000), p. 1046. C.f. Lee et al. (2000), p. 628. C.f. Lee et al. (2000), pp. 635.
40
3. Modeling Framework and Relevant Literature
fact that in the local information setting the supplier forecasts future demand based only on the most recent retailer order. If he used the entire order history, the value of shared demand information would be smaller, and in fact would converge to zero in the long run.107 This is because the order history can be used to appropriately forecast future demand given the autocorrelation of the demand process. The above contributions show that there is no common answer to the question of what can be gained from information sharing and closer collaboration. Much rather, resulting benefits depend on the problem setting or model studied and the type of analysis proposed by the authors. Nonetheless, some common observations can be extracted. First, as stated by Gavirneni et al. (1999), additional information is always beneficial as it allows better decision making than was possible before.108 Quantifying the exact value or benefit of closer integration is however a difficult task. Even in the relatively simple examples considered in the articles above, results are mostly obtained by simulation studies. One hypothesis which may be derived is that the benefit of integration increases with growing complexity of the SC setting. For example Chen (1998) observes in his model that cost reductions increase with a growing number of tiers present in the SC. Gavirneni et al. (1999) find substantial savings potentials when capacity is restricted at the supplier. Bourland et al. (1996) suggest that savings grow with increasing demand variability, whereas Lee et al. (2000) point out that a more complex (auto-correlated) demand process bears higher savings potentials from collaboration than i.i.d. random demand. On the other hand, growing complexity can as well lead to pooling of uncertainties, and hence a reduction of uncertainty. This can in turn reduce the value of information sharing as compared to scenarios without risk pooling. Cachon / Fisher (2000) e.g. observe average cost savings of 2.2% with inventory information. Although not mentioned by the authors, one potential reason for the relatively small gain can stem from the fact that their supplier serves N identical retailers, each facing random i.i.d. demand. Hence, the demand faced by the supplier is the aggregate over all retailers and therefore displays a lower variance than each retailer’s individual demand. Another interesting observation is that the value of collaboration can crucially depend on how the parties make use of shared information. As shown by Gavirneni (2002), a clever change of operating policies based to additional information can offer substantial benefits compared to simply incorporating the new data into the decision rules already in use. Now, how can these findings be transferred to the scenario considered here? The major difference to the SC settings studied in the articles above concerns the models used for decision making. Whereas rule-based inventory control policies are considered in the contributions above, we assume that mathematical programming models are utilized for generating plans. Without any coordination each domain creates a local forecast for its final output, which is updated regularly. The
107 108
C.f. Raghunathan (2001), p. 606. C.f. Gavirneni et al. (1999), p. 20.
3.2. Benefits of Information Sharing and Collaboration
41
inefficiencies resulting from isolated, domain-specific planning are caused by poor demand information, i.e. forecast quality, and the sub-optimization of the SC as a whole. With local forecasting and planning, fluctuations of the SC’s final demand propagate upstream from domain to domain with time delays and falsified by planning decisions at each domain (e.g. single period demands are aggregated to batches). Therefore, even with moderate fluctuations of final demand, demand variance often grows in upstream direction from domain to domain, as it is described by the bullwhip-effect.109 In result, moving upstream in the SC, demand becomes increasingly unpredictable. Since deterministic demand forecasts are used to drive planning by MPM, regular and substantial deviations from expected demand require frequent re-planning and lead to unexpected capacity shortages or unnecessary inventory stocks. To give an idea of the magnitude of additional costs due to low forecast accuracy, literature on rolling schedule performance can be consulted. For example, Venkataraman / Nathan (1999) study the impact of forecast errors on rolling master production scheduling. In computational tests based on data of a paint company they observe a difference in total cost of around 12% between a scenario where demand is on average overestimated by 20% and a scenario where it is underestimated by 20%.110 Even if all forecasts are perfectly accurate, local optimization within each planning domain results in sub-optimal plans for the SC as a whole. Naturally, planning domains at the SC’s most downstream tier have the privilege to plan first based on final demand forecasts. Second tier domains plan based on (forecasted) demand as requested by tier-one domains etc. From a total SC perspective this results in sub-optimization. Its degree is likely to grow with the number of tiers present in the SC, similar as in the model studied by Chen (1998). Also, results tend to increasingly deviate from the global optimum with a growing portion of total SC costs incurred at upstream domains. As we will see shortly, savings potentials of up to 35% were observed in simulation studies with three tier SCs.111 In summary, we can expect efficiency gains in line with the findings reported above. Namely that substantial cost reductions can be realized from the coordination of planning between domains, especially when demand variability is considerable, multiple tiers are present, and system constraints such as limited capacity are to be obeyed.
109 110
111
See e.g. Lee et al. (1997), pp. 93. C.f. Venkataraman / Nathan (1999), pp. 686. Unfortunately, the authors do not elaborate on cost differences to forecasts with small / none errors, i.e. high accuracy. Still, their results give an impression of the impact of accurate forecasting. C.f. Simpson / Erengüc (2001), p. 122.
3. Modeling Framework and Relevant Literature
42
3.3
Coordination of Planning Processes Along the Supply Chain
After discussing benefits of information sharing and coordination between SC partners, we now turn our attention towards how to achieve coordination. Two distinct approaches are regarded for that purpose: coordination of SCs by contract terms on the one hand and coordination mechanisms for mathematical programming models on the other. Based on the modeling framework as introduced above, the latter approach is obviously of particular importance. Nonetheless, coordination by contracts provides interesting insights into the nature of coordination issues in SCs and should therefore not be omitted.112 3.3.1
Coordination by contracts
In free-market societies economic activity is based on voluntary exchanges between independent parties who enter contracts in order to mutually commit to specific transactions.113 In SCs with independent partners, supply contracts are the major means to regulate the terms of how partners do business together and are rewarded. Each party’s decisions in operating the SC are led by local incentives (i.e. profits or costs) and the uncertainty or risk faced with respect to demand, supply or internal processes. Both the incentives of individual partners as well as the risk they face is to some extent determined by supply contracts settled with SC partners. It is therefore natural to examine the effects of supply contracts on the behavior of individual parties and to adjust the terms of pricing and accountability such that individual entities are guided towards the globally desired outcome.114 This is studied in a large and growing number of publications on the coordination of SCs by contracts. Although to date a commonly accepted taxonomy of supply contracts and related research does not seem not to exist,115 some broad categories can be defined to classify the various contributions. One such differentiation concerns the purpose of the analysis put forward. Whereas some authors merely examine the implications of given contracts on individual parties (contract analysis), others go a
112
113 114 115
Another research area often regarded around the topic of SC coordination are multiagent systems. However, as agent systems are more a technology or means to implement decentralized control of a SC, they are not reviewed here. Interested readers are referred e.g. to Fox et al. (2000) or Grolik et al. (2001). C.f. Friedman (1982), pp. 13. C.f. Whang (1995), pp. 413. C.f. Tsay et al. (1999), p. 306, Zimmer (2001), p. 50.
3.3. Coordination of Planning Processes Along the Supply Chain
43
step farther and try to devise contract terms that yield optimal performance for the SC as a whole (contract design).116 Another classification distinguishes whether only financial incentives are regarded, risk and risk sharing issues prevail, or both aspects are dealt with in conjunction.117 Finally, an important distinction should be made between contributions where full information is available to the party that sets the contract terms, and others that (more realistically) assume information asymmetry.118 A comprehensive review of this large body of literature shall not be given here.119 However, some well-known examples are introduced in the following in order to give an overview of the type of analysis and results that are brought about. 3.3.1.1
Coordination of joint lot-sizing
Monahan (1984) is among the first to elaborate on how individual cost incentives yield sub-optimal results for the SC as a whole. He considers a buyer that faces stationary, deterministic demand for a single product which he purchases from a supplier at given price and fixed ordering costs. The supplier produces lot-for-lot whenever an order arrives and is himself confronted with fixed setup costs. Since the product is stockable at the buyer (incurring holding costs), the buyer’s decision situation corresponds to the traditional economic lot-size problem (EOQ). However, the buyer’s locally optimal lot-size and replenishment interval is not optimal for the total SC, because, in determining the lot-size, he neglects the supplier’s setup cost. The resulting lot-size is hence smaller than the jointly optimal quantity. To counteract, Monahan (1984) proposes that the supplier offers a quantity discount to the buyer for orders of at least the jointly optimal lot-size.120 The total rebate (price discount × lot-size) is chosen such that the buyer is compensated for the extra cost compared to his locally optimal policy. In that way the supplier can induce the buyer to order in jointly optimal quantities. Monahan’s article sparked a series of follow-up publications that expand the basic framework. For example, Lee / Rosenblatt (1986) drop the lot-for-lot production assumption for the supplier, obtaining a significantly more complex problem.121 Weng (1995) considers the case where final demand is price-sensitive, and Chen et al. (2001) a scenario with multiple buyers and price-sensitive demand.122 For all these problems discount schemes can be determined from the supplier’s perspective that coordinate the SC, i.e. induce the buyer(s) to employ jointly optimal order policies.
116 117 118 119
120 121 122
C.f. Anupindi / Bassok (1999), pp. 201. C.f. Zimmer (2001), p. 25. C.f. Corbett (2001), p. 487. Interested readers are referred to Tsay et al. (1999), pp. 301, Zimmer (2001), pp. 50, Cachon (2003), pp. 229. C.f. Monahan (1984), p. 723. C.f. Lee / Rosenblatt (1986), pp. 1178. C.f. Weng (1995), p. 1512, Chen et al. (2001), pp. 693.
3. Modeling Framework and Relevant Literature
44
All the above contributions assume that full information is available to the supplier when defining the discount scheme. It is therefore interesting to observe how the situation changes when information is asymmetric, i.e. certain parameters of the problem setting are unknown to the supplier. A major example for this situation is presented by Corbett / de Groote (2000). They essentially deal with the problem of Monahan (1984), however assume that the buyer’s fixed order cost is negligible and, more importantly, his holding cost rate is unknown to the supplier. Without knowledge of holding cost it is not possible for the supplier to determine the jointly optimal lot-size and discount to offer to the buyer. To resolve this, the supplier announces a “menu of contracts” with several discount rates and minimum order quantities (lot-sizes). The menu is derived from estimating an interval [ h, h] of the buyer’s holding cost rate. The buyer then chooses his preferred discount scheme, thereby in effect disclosing his holding cost rate (so called revelation principle).123 However, although the resulting discount scheme improves total costs, optimality for the entire SC is no longer guaranteed. As stated elsewhere by Corbett (2001), incentive and information issues together “generally lead to inefficient outcomes, even under an optimal menu of contracts”.124 Sucky (2006) extends the work of Corbett / de Groote by including a fixed buyer order cost, which, too, is unknown to the supplier. He, however, also uses a very simplistic approach, assuming that the supplier knows that the buyer is one of two types (i.e. either has holding cost h1 and order cost x1 or h2 and x2).125 He shows that in this setting the supplier can also use a menu or contracts to induce the buyer to order the jointly optimal quantity. An overview of publications on lotsizing problems in SCs is given by Sarmah et al. (2006). 3.3.1.2
Coordinating the “news vendor”
The basic model that deals with final demand uncertainty, and hence risk sharing between SC partners, is the news vendor problem. Here the buyer faces stochastic demand for a single product which he has to order from the supplier prior to realization of actual demand. Unmet final demand incurs loss of revenue and (potentially) lost sales costs; excess supply can be sold by the buyer at a salvage rate below the actual market price.126 The supplier in turn faces linear production costs and likes to sell as large a quantity as possible at a price above unit cost. How much the retailer commits to buy depends on the contract terms, and hence on how the risk of stock-outs and obsolescence is shared between him and the supplier. A simple wholesale price contract where the supplier charges a fixed unit price fails to coordinate the SC.127 However, various contract types can be devel-
123 124 125 126 127
C.f. Corbett / de Groote (2000), p. 447. Corbett (2001), p. 488. C.f. Sucky (2006), p. 526. See e.g. Silver et al. (1998), pp. 385. C.f. Lariviere / Porteus (2001), p. 293.
3.3. Coordination of Planning Processes Along the Supply Chain
45
oped which induce the buyer to adopt the globally optimal order quantity. For example, Lariviere (1999) discusses how coordination can be achieved by franchising, quantity forcing, a buy-back option offered by the supplier, and a quantity flexibility scheme.128 Cui et al. (2007) introduce fairness considerations in the newsvendor problem and show that a wholesale price contract achieves coordination when the channel members care about fairness.129 An overview of contractual settings for the news vendor problem and various extensions, including a case with asymmetric information regarding the final demand distribution, is presented by Cachon (2003).130 3.3.1.3
Coordination of multi-level inventory systems
A more complex SC setting is studied by Lee / Whang (1999). It resembles a serial multi-echelon inventory system with stochastic final demand. Each echelon orders material from its upstream neighbor and bears holding costs for local inventory. Orders are met after a constant lead time, and backordered as far as existing inventory is insufficient to meet the full amount. Achieving coordination in such a system is again a matter of risk sharing. Since only the most downstream echelon pays backorder penalties to external customers, upstream echelons have no incentive to carry costly inventory. Hence, without any coordinating arrangements it is up to the downstream party to hedge vs. uncertainty of demand and supply, which results in sub-optimal performance. Therefore, Lee / Whang (1999) show how the optimal control policy as developed by Clark / Scarf (1960) from a central planner’s perspective131 can be implemented based upon a sophisticated incentive scheme. In particular, they propose a combination of transfer pricing, consignment, backorder penalty, and shortage reimbursement for measuring the performance of individual echelons.132 3.3.1.4
Implications for this work
In conclusion, SC coordination by contracts usually deals with relatively simple SC structures, e.g. an isolated perspective of single products is taken, assuming constant or stationary stochastic demand. Based on such models, SCs are operated according to inventory-control policies as e.g. described by the EOQ-solution or order-up-to policies in case of stochastic demand. Since supply contracts affect the choice of (locally) optimal control parameters, contract terms can be used to entice individual parties to act in a globally desired way. However, defining coordinating
128 129 130 131 132
C.f. Lariviere (1999), pp. 246. C.f. Cui et al. (2007), pp. 1302. See Cachon (2003), pp. 229. I.e. echelon stock re-order point policies (c.f. Clark / Scarf (1960), pp. 476). C.f. Lee / Whang (1999), p. 636. A similar solution to the same problem is presented by Chen (1999), pp. 1079, except that transfer payments are gathered and granted by a central coordinator, e.g. headquarters of a decentralized firm.
3. Modeling Framework and Relevant Literature
46
contract terms is a complex issue even in these relatively simple problem settings. Moreover, it requires knowledge of all relevant cost and demand parameters. Without full information the situation becomes less tractable and perfect coordination (i.e. achieving the optimal solution for the SC as a whole) is no longer achieved. What are the implications for a scenario as condisered here with multiple products competing for common resources such as capacity or raw material supplies, and where planning is based on mathematical programming models and demand forecasts by period? In such a situation, plans are re-generated periodically and optimal results are not stationary. Of course, terms of supply contracts can be incorporated in mathematical programming models too.133 However, it is hardly possible to achieve SC optimality by setting contract parameters at a single point in time. Much rather, it appears reasonable to change the order of events such that plans are coordinated first based on a given coordination mechanism. Supply contracts are then adapted in a second step in order to ensure that the parties get incentives to adhere to the defined planning results. Achieving coordination hence requires other mechanisms to integrate planning between independent domains. Such mechanisms are discussed in the following section. 3.3.2
Coordination mechanisms for mathematical programming models
Two coordination mechanisms as proposed in the literature for the coordination of MPM-based planning are introduced in the following: first the simple, sequential Upstream Planning scheme (including possible extensions to it), and second the Lagrangean relaxation approach. A structured, more detailed classification of the publications referenced below is presented in Stadtler (2007).134 3.3.2.1
Upstream Planning and extensions
Upstream Planning represents the simplest mechanism which can be utilized for the coordination of planning across several domains. It is for example described by Bhatnagar et al. (1993) and also referred to as “top-down planning” by some authors.135 The idea is to perform planning level-by-level or tier-by-tier and to pass resulting order requirements of downstream domains to their suppliers. This is visualized in Fig. 10 for two planning domains. The downstream domain plans first
133
134
135
See e.g. Tempelmeier (2003), pp. 366, for a model to plan purchasing quantities based on several discount rates offered by a supplier. The publications are classified along the SC structure studied, the decision situation captured and characteristics of the coordination mechanisms used (c.f. Stadtler (2007), p. 8.) C.f. Bhatnagar et al. (1993), p. 147, Zimmer (2001), pp. 146.
3.3. Coordination of Planning Processes Along the Supply Chain
47
based on a forecast of its external demand. Order requirements are derived from this plan and communicated to the supplier. Then the supplier domain plans based on the order quantities. If this domain in turn has suppliers, the scheme can continue analogously. Domain 2
Domain 1
Supply requirement s
Ext ernal dem and
3. Generat e opt imal plan
1. Generat e opt imal plan
4. Derive order quant it ies
2. Derive order quant it ies
Fig. 10. Upstream Planning scheme
In terms of the planning model of section 3.1 the downstream domain generates its plan by solving Model 1 enhanced by constraints (11) so that order quantities directly result from variables xsj,t. Resulting values are transmitted to domain 2 which too plans by utilizing Model 1, this time enhanced by constraints (14) and (15) so that received order quantities (XOj,t) are input to the model. Although not shown in the figure, several, independent domains (i.e. not linked by supply relationships) can be present at any tier just as well. The only prerequisite is that a tier-by-tier order of domains can be established. This is possible, as long as no cyclic supply relationships exist between domains, i.e. no domain is supplier and customer of another one at the same time, even if this happens indirectly via other, intermediary domains. Upstream Planning is superior to completely isolated planning within each domain, because order requirements are passed on from customers to suppliers and form the basis of planning at suppliers. Hence, the plans of individual domains become consistent one with another, and all ground on the demand forecast of the most downstream party. In consequence, inefficiencies from unsynchronized operations are eliminated, namely high inventory buffers at the interfaces between domains and frequent re-planning due to deviations of actual orders from local demand forecasts. Also, the scheme is straightforward to implement and requires little effort to achieve coordination. It is therefore, why Upstream Planning is the predominant form of CP found todate in practice. Suppliers get access to customers final demand data and planned order quantities and base their local planning on this information instead of using local demand forecasts. However, as Bhatnagar et al. note, Upstream Planning’s drawback is that “it ignores the interactions between various plants and will yield sub-optimal produc-
48
3. Modeling Framework and Relevant Literature
tion plans”.136 This is because each domain generates locally optimal plans (based on received order quantities and/or forecasted external demand) without taking account of the consequences of local decisions on upstream partners. Hence, from a total SC perspective, the scheme produces inferior results compared to centralized planning with a simultaneous optimization of the SC as a whole. In order to quantify the level of sub-optimality, Simpson / Erengüc (2001) perform a computational evaluation of an example SC setting. They consider three tiers with several retailers (tier 1) ordering multiple products at a single distribution center (tier 2), which in turn replenishes the products from several manufacturers (tier 3). Fixed order or setup costs are balanced with end-of-period inventory holding costs at all tiers. Simpson / Erengüc model the planning situation as a multi-level lot-sizing problem and compare tier-by-tier Upstream Planning solutions to those of centralized planning. 137 On average, they observe a cost gap between centralized and Upstream Planning of 14.1%. A key insight of the authors is that the gap grows with an increasing portion of total cost incurred at upstream domains. This is, because the effect of unfavorable order requirements on total SC costs gets larger. In the computational study, the average gap is merely 1.8% for test problems where the manufacturers bear 29% of total cost, but 9.0% when they bear 41% and 31.5% when they bear 51% of total cost.138 The study by Simpson / Erengüc makes apparent that Upstream Planning can produce sufficiently good solutions in some SC settings (namely when the most of total costs is incurred at the downstream tier). However, substantial improvements can be reached in many cases, when more sophisticated coordination schemes are used. As the Upstream Planning mechanism is easy to implement, one way to obtain better performance is by developing extensions to its basic form, intended to produce better solutions while keeping the basic tier-by-tier planning process. One such approach is developed by Zimmer (2001), who enhances Upstream Planning by anticipation.139 The idea is to add major constraints from the supplier domain (in a simplified form) to a downstream domain’s planning model, and thereby obtain improved overall planning results. Zimmer studies a scenario with two SC partners, a manufacturer and a supplier. She assumes contract terms which allow the supplier to deviate from order requirements, however at penalty costs for early and late deliveries (the total order volume must remain unchanged). Both parties use MPM for planning of their operations. The supplier’s objective is to minimize costs of operations as well as contractual penalties. When the supplier’s deliveries deviate from orders, the manufacturer needs to re-plan based on given supply availability.
136 137 138 139
Bhatnagar et al. (1993), p. 147. See Simpson / Erengüc (2001), pp. 120, for details. C.f. Simpson / Erengüc (2001), pp. 122. The concept of anticipation has already been introduced in section 2.3.2 within the overview of hierarchical planning (s. pp. 15).
3.3. Coordination of Planning Processes Along the Supply Chain
49
Zimmer considers two types of anticipation: non-reactive and reactive. In the first case, the major restrictions of the supplier domain are added to the manufacturer’s planning model so that planning results become jointly feasible. Specifically, she adds capacity constraints for order quantities by period and an upper limit on the capacity extension which the supplier may be willing to accept for ensuring timely deliveries.140 For evaluating the performance gain, a computational study is carried out similar to Simpson / Erengüc: solutions of mere Upstream Planning, Upstream Planning with anticipation, and centralized planning are compared. In result, an average cost reduction of about 20% can be realized by nonreactive anticipation. However, as mere Upstream Planning results are on average 190% off from centralized planning solutions (due to high costs of capacity extensions), the gap remains substantial.141 This is not surprising, as anticipation through additional constraints only aims at preserving plan feasibility at the supplier domain, but does not guide decisions by cost effects resulting for the upstream party. Also, only estimates of the supplier’s capacity and other parameters are available to the manufacturer. Due to these shortcomings Zimmer develops a second, more complex scheme referred to as reactive anticipation. Generally, in reactive anticipation the (likely) reaction of the base-level on top-level decisions is explicitly considered, so that cost considerations can be regarded.142 The idea is to establish an iterative procedure where the base-level reaction is simulated and fed back to the top-level model. This is re-run with the additional information to produce a revised plan, and so forth until satisfactory overall results are observed. Zimmer proposes to use such a scheme to adapt the contractual penalty cost rates for early and late deliveries in a way that induces the supplier to act in the total SC’s interest. Initially, the manufacturer solves a centralized planning model of the entire SC. Order requirements corresponding to the resulting plan and penalty rates of zero are input to the anticipated base-level model. If the anticipated supplier’s behavior differs from the centralized planning results (which is usually the case), the penalty rates are increased step-wise and the anticipated supplier model is re-solved. In this way Zimmer intends to find penalty rates which induce the supplier to adopt to the centralized planning solution.143 Computational results show that this scheme comes close to centralized planning solutions with an average gap of 8%.144 However, this comes at the expense of high information needs by the manufacturer and largely increased complexity. The entire supplier planning model must be available to the manufacturer. Also, although not commented upon by Zimmer, a significant number of iterations can
140
141 142 143 144
See Zimmer (2001), pp. 156, for details. This anticipation concept has in fact been realized in a SC project in the automotive industry (c.f. Hirzel et al. (2002), pp. 64). C.f. Zimmer (2001), pp. 197. C.f. Schneeweiss (1999), pp. 43. C.f. Zimmer (2001), pp. 181. C.f. Zimmer (2001), p. 199.
3. Modeling Framework and Relevant Literature
50
be expected necessary for finding the “optimal” penalty cost rates. Finally, it is questionable whether contract terms can be set by the manufacturer alone, as they usually are a result of negotiations, and whether they can be re-adjusted dynamically in every planning cycle. Nevertheless, this work is a valuable contribution as it outlines how mere Upstream Planning can be improved by extending planning considerations beyond local circumstances. 3.3.2.2
Lagrangean relaxation approach
For discussing the Lagrangean relaxation approach it is best to start with the perspective of centralized planning, i.e. to consider a single MPM which covers several, say N, planning domains. Such a model consists of an objective function, N sets of constraints that pertain to individual domains, and a set of constraints linking individual domains by inter-domain flow balance equations. Using the modeling framework presented above, the centralized model comprises several instances of Model 1 (each for a single domain) and inter-domain links expressed by constraints (11) and (14) linking consumption of intermediary items to their supply. The model’s matrix of coefficients is depicted in Fig. 11 (columns correspond to decision variables and rows to the objective function and constraints). Formally, it can be written as follows: min s.t.
CX A1 X ≤ B1
(16)
A2 X = B 2
where the first set of constraints corresponds to domain-specific restrictions and the second to inter-domain links. Now, it has a long tradition in Operations Research that large-scale MPM of a structure as presented in Fig. 11 are decomposed to more tractable subproblems.145 A solution to the original model is then obtained by a mechanism which coordinates the solution procedures of sub-models. The standard way to decompose the original model, called Lagrangean relaxation, is by “dualizing” the constraints linking individual domains; that is by removing linking constraints from the model’s constraint set and adding them to the objective function. Mathematically, the term λ ( A2 X − B2 ) is added to the original objective function, where λ is a vector of Lagrange multipliers λi. Without domain linking constraints the model separates into N domain-specific sub-problems which can be solved individually. Since the individual optimal solutions depend on the values of λi, which represent a penalty in each submodel’s objective function, these parameters can be used to coordinate sub-model solutions.
145
See e.g. the decomposition schemes by Dantzig / Wolfe (1960) and Benders (1962). The original goal of decomposition schemes was to divide a large MPM into smaller ones in order to reduce the computational complexity of its solution.
3.3. Coordination of Planning Processes Along the Supply Chain
51
This is usually accomplished by an iterative procedure where, for given solutions, the violation of relaxed constraints is analyzed and the parameter values λi are adjusted repeatedly.146 However, a difficulty often arises with such iterative methods when binary variables are included in domain-specific sub-models. Then, globally feasible solutions can hardly be obtained due to the models’ integrality gaps.147 In order to still find feasible solutions, heuristic methods can be used to rearrange obtained solutions such that feasibility is preserved. decisions variables constraints
Obj fct. Dom. 1 Dom. 2
Dom. N Domain links
Fig. 11. Structure of a centralized planning model (source: Holmberg (1995), p. 67)
Within the context of operations planning in SCs, Barbarosoglu / Özgür (1999), Ertogral / Wu (2000), Karabuk / Wu (2002) and Jung et al. (2005) develop Lagrangean relaxation based procedures for coordinating planning across individual domains. Barbarosoglu / Özgür study a SC with several customers who order multiple products from several depots, which in turn order at a single plant. Fixed order / setup and inventory holding costs are incurred at each facility, and production capacity is restricted at the plant. The authors first develop a single MPM for centralized planning. Then, they introduce Lagrangean relaxation with respect to the balance constraints which link production levels at the plant with shipments to the depots. In result, the model separates into sub-models for production and distribution. In order to coordinate the sub-models, sub-gradient optimization is proposed. I.e., when the sub-models are solved with given Lagrangean multipliers, the inconsistency of relaxed constraints is checked by a central agent. When the total in146
147
A heuristic search by sub-gradient optimization is mostly proposed for this process step (c.f. Shapiro (1979), p. 124, Fisher (1985), pp. 12). C.f. Fisher (1981), pp. 14.
52
3. Modeling Framework and Relevant Literature
consistency for a product-period combination is measured by γi,t, the corresponding multiplier is updated according to λi k +1 = λi k + α k γ i ,kt
(17)
where k is the iteration counter and α a normalizing factor which is dynamically adjusted through the course of the procedure.148 A difficulty is however caused by the binary variables present in both submodels. Since altering binary decisions strongly affect other variables (e.g. production levels), it is questionable whether a smooth convergence of the submodels can be expected. Unfortunately, this feature is not analyzed the Barbarosoglu / Özgür. However, they do report that consistent solutions can rarely be obtained by the scheme.149 In order to still achieve consistency, they propose a simple, hierarchical heuristic which is applied once the sub-gradient optimization has terminated: the final distribution plan is fixed and a compatible production plan is generated with the production sub-model.150 Jung et al. (2005) study a SC with a production and a distribution tier. They use separate planning models for each tier, which are coordinated by Lagrange-type penalties in the objective function for deviations between requested and proposed order quantities.151 As their planning models are linear, i.e. do not contain binary variables, reasonably good results are achieved within a few iterations – at least with a numerical example presented by the authors. Ertogral / Wu (2000) consider production planning across several plants where each plant has limited capacity and tries to minimize setup and inventory holding costs. The decision situation is first modeled from a total SC perspective by the MLCLSP as given by Model 1 above. Then, Lagrangean relaxation is applied to flow balance equations to decompose the MPM to facility sub-models just as in Barbarosoglu / Özgür (1999). To coordinate the sub-models, Ertogral / Wu first implement sub-gradient optimization. However, they report that computational tests reveal oscillations of sub-models between a few solutions depending on the values of Lagrange multipliers.152 Therefore, they expand the coordination mechanism in a way that ensures convergence of sub-model solutions. To do so, they use target values for interdomain flow variables in addition to the Lagrange multipliers. The multipliers are then used as penalty cost rates for deviations of the target values. Furthermore, multipliers and target values are updated by a central coordinator based on deviations from each sub-model’s minimum cost solution obtained in the first iteration. Thereby, the scheme does no longer aim on minimizing total SC costs, but to find
148 149 150
151 152
See Barbarosoglu / Özgür (1999), p. 474, for details. Barbarosoglu / Özgür (1999), p. 474. So, in a sense the scheme is similar to Upstream Planning. If the distribution plan turns out not to be feasible at the production stage, a simple, rule-based algorithm is used to modify distribution decisions (c.f. Barbarosoglu / Özgür (1999), p. 476). Jung et al. (2005), pp. 102. C.f. Ertogral / Wu (2000), p. 936.
3.3. Coordination of Planning Processes Along the Supply Chain
53
consistent and “fair” overall solutions. That is, solutions with equal deviations from minimum cost results across all sub-models.153 In a computational study the authors demonstrate that solutions converge, i.e. consistent results can be obtained. The average deviation of costs vs. optimal results of centralized planning is around 10%. However, Ertogral / Wu emphasize the fairness issue in discussing the results. Here, the solutions obtained by their scheme clearly outperform centralized planning. Finally, Karabuk / Wu (2002) use a Lagrangian technique to coordinate a production and distribution domain, which use stochastic, linear programs for operations planning. As the assumed models are linear, the authors can show that their scheme converges to a single solution.154 Summarizing the above, Lagrangean decomposition represents a second mechanism for the coordination of planning across individual domains. It is in fact an elegant approach, since long known techniques of mathematical programming can be directly applied to the decentralized problem environment considered here. However, as the examples of Barbarosoglu / Özgür and Ertogral / Wu indicate, it is not realizable without tackling some difficulties. For one, the common coordination method of sub-gradient optimization is troublesome when binary or integer variables are present in all or most of the submodels. Consistency between sub-models might not be achieved due to the duality gaps of the mixed-integer models. Moreover, oscillations of sub-models can occur that can entirely prevent convergence towards a stable solution. Even when these problems are resolved as in the above contributions, a critical prerequisite remains, which is the presence of a central coordinator required for updating multipliers and other directives. The standard metaphor for the decomposition approach described in literature is one of a decentralized firm where divisions take most of decisions on their own, but some control is exerted by a headquarters.155 However, the SC setting as considered here naturally lacks a central coordinator. Such a coordinating agent must therefore be newly established which in turn might not be appreciated by all partners. 3.3.2.3
Summarizing overview
Overall, we have seen three coordination schemes in the previous paragraphs. In order to give a summarizing snapshot of the different approaches, an overview and comparison of some properties concludes this chapter. Centralized planning by a single model for the whole SC is added to the overview for comparison. The coordination mechanisms are: • Upstream Planning, i.e. tier-by-tier generation of plans in upstream direction with communication of order quantities from customers to suppliers,
153 154 155
See Ertogral / Wu (2000), pp. 936, for details. C.f. Karabuk / Wu (2002), pp. 751. See e.g. Holmberg (1995), pp. 61.
54
3. Modeling Framework and Relevant Literature
• Upstream Planning with anticipation, i.e. Upstream Planning where intradomain planning models are enhanced by anticipated constraints or models of supplier domains, • Lagrangean relaxation, i.e. iterative generation of local plans (based on a common forecast of final demand), controlled by directives computed by a central coordinator between iterations, and finally • Centralized Planning, i.e. a single planning model, and hence a single plan for the entire SC generated by a central coordinator. A number of characteristics can be relevant for comparing the mechanisms, such as the quality of solutions or the computational effort to obtain them, just to mention two. However, two properties shall be regarded here in more detail, as they are of particular importance for the acceptance and applicability of the schemes to SC partnerships. These properties are: 1) the required degree of integration and 2) the schemes’ inherent level of hierarchy. Integration here refers to the type and amount of information that has to be exchanged between the partners (or between the partners and a central coordinator). It is a crucial measure, because, despite all SC integration efforts, most companies are reluctant to open sensitive information to outsiders. The level of hierarchy relates to the extent to which there are differing levels of decision authority assumed in a scheme. This, too, is a crucial question, as all parties must be willing to cooperate. However, if they are largely exposed to decisions made by others, the acceptance of a coordination scheme is questionable. The degree of integration and hierarchy can be combined to a conceptual matrix as shown in Fig. 12. When we try to place the coordination schemes into the matrix, a picture as indicated in the figure occurs. An extreme position is taken by centralized planning, as it requires both, a high degree of integration and hierarchy. The owner of the planning process (may it be one of the domains or a third party) must have all necessary information available, which requires strong informational bonds to all parties. Planning results are imposed on all domains, hence there is a high degree of hierarchy. Due to these properties centralized planning is often not applicable in settings with independent domains, as already discussed in section 2.3.2. In contrast, Upstream Planning requires a relatively low integration of planning domains. The only data exchange corresponds to order quantities passed from customers to suppliers. The scheme assumes however hierarchical relationships between planning domains, in the sense that upstream parties plan first and downstream suppliers take order quantities as given data. Hence, here too we find a relatively high degree of hierarchy. This remains unchanged in Upstream Planning with anticipation. But, as anticipation is only possible by gaining knowledge of supplier characteristics, the level of integration is higher, although clearly not as high as in centralized planning. Also, the exact type and amount of information required depends on how anticipation is realized.
3.3. Coordination of Planning Processes Along the Supply Chain
high
55
Centralized Planning
Hierarchy
Upstream Planning
Upstr. Pl. + Anticipation Lagrange Decomposition
low low
Integration
high
Fig. 12. Integration – hierarchy matrix of coordination schemes
Finally, the Lagrangean relaxation approach entails a medium degree of integration, similar to Upstream Planning with anticipation. Here, consistent demand forecasts must be available to all domains. Order and shipment quantities are communicated to the central coordinator, and, in return, coordinating directives from there to the planning domains. Obviously, some level of hierarchy is present in this coordination scheme, too. However, as domains plan individually and the central coordinator’s role is restricted on checking the consistency of individual results and adjusting some coordinating parameters, the scheme can be regarded less hierarchical than centralized and Upstream Planning. In conclusion, one can observe that information exchange is necessary to obtain coordinated results, i.e. collaborative planning is only realizable when the parties accept some degree of integration. However, the coordination schemes presented above all involve a considerable degree of hierarchy as well. This fact can hamper their acceptance, as one may argue that truly non-hierarchical coordination remains a myth here. It is for that, and also other reasons such as quality of solutions and general applicability, why an alternate, innovative scheme for collaborative planning is developed in the next chapter. Recommended readings • Rohde J. / Wagner M. (2005): “Master Planning”, in: Stadtler, H. / Kilger, C. (Eds.): Supply Chain Management and Advanced Planning – Concepts, Models, Software and Case Studies, 3rd ed., Berlin et al. 2005, 159-177. • Gavirneni, S / Kapuscinski, R. / Tayur, S. (1999): “Value of information in capacitated supply chains”, in: Mgmt. Science, Vol. 45(1), 16-24.
56
•
• • •
3. Modeling Framework and Relevant Literature Cachon, G.P. (2003): “Supply chain coordination with contracts”, in: Graves, S.C. / de Kok, A.G. (Eds.): Supply Chain Management – Design, Coordination and Contracts – Handbooks in Operations Research and Management Science, Vol. 11, Amsterdam et al. 2003, 229-339. Sarmah, S.P. / Acharya, D. / Goyal, S.K. (2006): “Buyer-vendor coordination models in supply chain management”, in: European Journal of Operational Research, Vol. 175, 1-15. Barbarosoglu, G. / Özgür, D. (1999): “Hierarchical design of an integrated production and 2-echolon distribution system” in: European Journal of Operational Research, Vol. 118, 464-484. Stadtler, H. (2007): “A framework for collaborative planning and state-of-theart”, in: OR Spectrum, online edition.
4 Negotiation-Based Collaborative Planning between Two Partners Content In this chapter we develop a collaborative planning scheme for a single buyersupplier pair. The following section describes the supply chain scenario and presents an overview of the scheme. The distinct planning steps carried out repeatedly by the collaboration partners are presented in full detail in section 4.2. Thereafter, section 4.3 deals with the resulting total process flow and its control. Section 4.4 concludes the chapter with a brief summary and some final comments. Key points • We formalize a negotiation-like, iterative process between the supplier and buyer. Order proposals (generated by the buyer) and supply proposals (generated by the supplier) are passed between the parties in an iterative manner. • A proposal received from the partner is analyzed for its consequences on local planning and a counter-proposal is generated by introducing partial modifications. Resulting is a process which subsequently improves supply chain wide costs without centralized decision making and with limited exchange of information. • Mathematical programming models as introduced in section 3.1 are used throughout all stages of the process.
4.1
Assumptions and Overview
Throughout this chapter we consider only two planning domains, a buyer and a supplier, which are connected by supplies of (physical or intangible) products. Internally, each planning domain may cover a multitude of (inter-connected) operations stages. As shown in Fig. 13, the two parties coordinate their operations by collaborative planning. All remaining customers and suppliers are assumed to be out of influence. Hence, demand (forecasts) and potentially supply capabilities pertaining to other entities represent given data. Based on our discussion in section 3.1 plans are generated within each domain by the use of MPM such as Model 1. Supply or order links to the collaboration partner can be explicitly included in the planning model as presented in section 3.1.3. We consider one-time planning, i.e. a situation where the partners coordinate their plans over the entire planning interval for a single time. In terms of the contractual setting, the supplier is assumed to charge a simple fixed unit price. Thus, the payment received by the supplier is fixed for a given total purchase volume, and therefore not explicitly regarded in the following.
G. Dudek, Collaborative Planning in Supply Chains, 2nd edn., DOI 10.1007/978-3-540-92176-9_4, © Springer-Verlag Berlin Heidelberg 2009
58
4. Negotiation-Based Collaborative Planning between Two Partners
As we have seen in the literature review of section 3.3.2, mechanisms proposed in the literature for coordinating planning by mathematical programming models assume hierarchical relationships between the parties and require a varying degree of integration of the individual planning domains. As already argued above, demanding a hierarchical structure and strong bonds between the parties may however hinder a scheme’s acceptance by independent decisions makers across a SC. Supplier
Buyer Collab. Planning
Supply
External supply Domain 2
External demand Domain 1
Collaboration
Fig. 13. Two party collaborative planning
The purpose of this chapter is therefore to develop a novel approach for collaborative planning, which should ideally exhibit the following properties: • • • •
non-hierarchical relationships, exchange of uncritical and only as few as possible data, consistent, implementable plans in each iteration, and demonstrably good solutions with a small number of iterations.
As independent decision makers will usually not be satisfied with a subordinate role of implementing pre-set decisions and reporting some feedback on those decisions at the maximum, the scheme presented here tries to give all partners similar decision rights and authority. Also, it should be clear that the willingness to participate in collaborative planning depends on the type and amount of internal data opened to SC partners. The nature of exchanged information should therefore be as uncritical as possible. Although sensitivity of data is always a matter of subjective judgment,, some type of information (e.g. order requirements) can be generally regarded less sensitive than others (e.g. internal cost rates).156 Plan consistency is a more technical, but still important requirement. It ensures that implementable plans are in place, even if the coordination scheme is aborted at some early stage. This way a compatible overall plan for all partners is obtained in any case. The fourth characteristic finally considers the computational effort re156
Kersten (2002), p. 16.
4.1. Assumptions and Overview
59
quired to obtain a satisfactory overall solution. As we face complex decision situations at each domain and hence deal with large, computationally challenging planning models, the scheme should not entail hundreds of iterations prior to realizing an improvement. Instead the total outcome should be effectively improved within a reasonable time frame. The approach developed in the following rests on the idea of a “negotiation among equals”. It assumes an equal, active role for all partners. As a metaphor we can think of supply chains planners holding a meeting to manually coordinate their respective plans. Each planner will analyze the consequences of partner plans and actively propose modifications that improve his situation. Eventually, the planners will commit to compromise solutions. The same logic applies to the scheme presented below. In a first step, any given partner order / supply proposal is analyzed. Second, as the partner requirements usually cause a deviation from the locally optimal plan, targeted modifications to the order / supply pattern are generated and proposed to the partner. The partner then carries out the same process of analyzing the modified order / supply pattern and introducing new modifications to it. Modifications can however only be made to a limited extent. Otherwise, the parties would re-generate their original order / supply pattern as their preferred situation. Therefore, the idea is to only allow for the most effective modifications. Those modifications create the largest local cost improvement per unit change, thereby also offering the greatest chance for a total supply chain cost improvement. The negotiation process is visualized by a demonstrative example in Table 6. The buyer purchases three items. The planning horizon covers 12 periods, of which only the first four periods of the order / supply pattern are shown in Table 6. The quantities represent cumulated orders / supplies from period 1 through t. As cumulated figures immediately indicate an excess or short supply up to a given period, they are commonly used for describing order / supply patterns in the following. The top contains the initial order pattern requested by the buyer based on his locally optimal plan. If the supplier fully covers the order requirements, he faces costs of 129,574 monetary units (MU). Total supply chain costs sum up to 228,241 MU. Based on this initial Upstream Planning solution, the supplier proposes a modified supply pattern as shown in the second section of Table 6.157 We see that most changes refer to item 1, item 2 supplies are modified in periods 1 and 4, and item 3 supplies only in period 2. The modifications result in a cost decrease for the supplier of 9,452 MU and in a cost increase for the buyer of 4,060 MU. Hence, the new proposal creates net savings of 5,392 MU compared to the initial situation. The buyer proposes additional modifications (section 3) by partly returning to his initial orders (e.g. item 1, period 3; item 2, period 1) and partly introducing new changes (e.g. item 2, period 4). The modifications decrease local cost by 2,048 MU and increase cost at the supplier by 337 MU. In total, additional net savings of 1,811 MU can be achieved. According to the iterative nature of the
157
Excess supplies (vs. the initial orders) are printed bold, short supplies italic and bold.
4. Negotiation-Based Collaborative Planning between Two Partners
60
process the supplier suggests further modifications, thereby once more generating significant additional savings. The process may continue as long as additional savings occur. Table 6. Negotiation process example
Data Ex- Period change Item. B→S
S→B
B→S
1
2
1
168
230
2 3
77 247 122 239 247
239 347 363 239 299
95 77 247
363 239 347
363
426
239 548
404 650
95 77 347
397
397
397
404 442
404 442
404 869
1 2 3 1 2 3
S→B
1 2 3
3
4
Cost B
Cost S
Cost Total
363
397
98,667
129,574
228,241
239 548 397 239 548
375 650 397
102,727
120,122
222,849
100,679
120,459
221,038
105,451
106,228
211,679
431 650
In order to realize the above process, the collaboration partners need to exchange the respective order / supply patterns as well as local savings incurred by the proposed modifications. With this knowledge, the planning partner can evaluate the total effect (i.e. partner + local) of the modifications. The example demonstrates that, with the proposed scheme, both partners have the same decision authority, i.e. the scheme represents a heterarchical coordination process. Also, a consistent overall plan is generated in each iteration. The example gives a first indication that significant cost improvements can be obtained with a few iterations. Of course this property will be analyzed in greater detail later.158 Besides the order / supply patterns exchanged data only comprises local savings, an aggregate measure, which we assume a rather uncritical information. With this overview in mind, we can now consider the outlined scheme in more detail.
158
Through an extensive computational evaluation presented in chapter 7.
4.2. Iterative Planning Steps
4.2
61
Iterative Planning Steps
As we have seen above each planning domain repeatedly evaluates received order/ supply proposals and generates compromises as counter proposals in reply. These basic planning activities hence represent the distinct process steps carried out in each iteration and are described in detail in the following. The way in which the compromise generation is accomplished however requires an intermediary step, which determines a party’s most preferred outcome, that can be derived from the partner’s current proposal. This process step is therefore described before the actual compromise generation. Moreover, a compromise order/ supply pattern is not guaranteed to differ from patterns proposed in former iterations. Therefore a method is introduced which compares a compromise pattern to former proposals and generates additional compromises, if the order/ supply pattern is equivalent to a previously proposed pattern. Also, in order to avoid infinite cycling, a stopping rule can terminate the generation of additional compromises.159 Although the tasks are equivalent for the buyer and supplier, the order/ supply pattern plays a different role for each party. Thus, distinct models corresponding to the buyer and supplier are presented for each process step. A flow chart of the iterative planning steps is given in Fig. 14. It shows the sequence of activities carried out by each partner in one iteration as just described. An iteration hence is defined to embrace the subsequent evaluation of the partner proposal and generation of a counter-proposal by both buyer and supplier.160 Each of the following sections is dedicated to one of the iterative planning steps as also implied in Fig. 14. 4.2.1 Evaluate partner proposal
4.2.2 Determine preferred outcome
4.2.3 Generate compromise
4.2.4 1. New compr. ? 2. Stop anyway ? no Generate additional compromise
Fig. 14. Iterative planning steps - flow chart
159 160
Details follow below in section 4.2.4. A thorough description is laid out below in section 4.3.2.
yes
62
4. Negotiation-Based Collaborative Planning between Two Partners
4.2.1
Evaluating the partner proposal
The evaluation of an order / supply pattern proposed by the collaboration partner can be accomplished by the intra-domain planning model as introduced in section 3.1.2, enhanced by links to adjacent domains. From the buyer’s perspective we expect that the supplier has announced supply quantities XSj,t by item and period for all supply items pertaining to the index set JS. In order to incorporate these quantities into local planning, the buyer can use Model 1 extended by constraints (10) to (13) as described in section 3.1.3. The resulting planning model is presented in Model 2.161 Model 2. CP(Buyer)-0 Formulation
min s.t.
c
(18)
(3) - (9) T
c=∑
∑ (ch j i j ,t
t =1 j∈J
T
+cf j y j ,t ) + ∑
is j ,t −1 + xs j ,t =
T
∑ cor or ,t + ∑ ∑ ch j is j ,t
t =1 r∈R
+ is j ,t ∑ r x k∈S j j ,k k ,t
t =1 j∈JS
∀j ∈ JS , t
(19) (20)
xs j ,t = XS j ,t
∀j ∈ JS , t
(21)
IS j ,t ≤ is j ,t ≤ IS j ,t
∀j ∈ JS , t
(22)
Proposed supply quantities XSj,t are input to the model due to constraints (21). However, as explained in 3.1.3, inventory holding of supply items is permitted. The objective is to minimize costs of local operations in conjunction with inventory holding of supply items ((19)). Constraints (3) to (9) pertain to Model 1 and correspond to balance equations, capacity restrictions, setup constraints, and bounds on variable values. Solving Model 2 reveals the cost optimal local plan given the supply quantities as proposed by the supplier. Model 3 depicts the equivalent situation for the supplier. Here, order quantities XOj,t by item and period as received from the buyer are incorporated into the intradomain planning model. It corresponds to Model 1 extended by constraints (14) and (15). Order quantities XOj,t are input to the model due to constraints (26) and represent demand in the modified balance equations (25).162 Solving the model hence
161 162
For a description of the symbols see Model 1, p. 33, and section 3.1.3, p. 35. The original demand parameters Ej,t are still present, as the supplier may also serve other (external) sources of demand. The same set of supply items JS is used in both buyer and supplier models as the items ordered by the buyer and those supplied by the supplier are identical in a two-partner scenario.
4.2. Iterative Planning Steps
63
reveals the cost optimal local plan based on the order quantities as proposed by the buyer. Model 3. CP(Supplier)-0 Formulation
min s.t.
c
(23)
(3) - (9) T
c=∑
∑ (ch j i j ,t
t =1 j∈J
T
+cf j y j ,t ) + ∑
i j ,t −1 + x j ,t = E j ,t + xo j ,t +
∑ cor or ,t
(24)
t =1 r∈R
∑ r j ,k xk ,t + i j ,t
∀j ∈ J , t
k∈S j
xo j ,t = XO j ,t
∀j ∈ JS , t
(25) (26)
In summary, the presented models can be used to find the optimal local plan based on received supply or order quantities. The optimal solutions to the models thus can be used to evaluate a partner proposal. The corresponding optimal costs c* is in every case greater than (or equal to) the cost resulting if a deviation from the partner proposal is permitted to some degree. Therefore, we will refer to it as C Bmax = c*, C Smax = c *
(27)
for the buyer and supplier, respectively. 4.2.2
Determining the preferred outcome
The purpose of this second step is to find all modifications to the received order / supply pattern which improve the local cost situation. Therefore, deviations from the received pattern are permitted and desired. Resulting is the most preferred order / supply pattern that can be devised from the one just received from the collaboration partner. The original and the most preferred pattern form the basis for finding the compromise solution proposed to the collaboration partner. A key question in obtaining the most preferred order/ supply pattern is whether there are some limits to deviations from the partner’s proposal. In fact, some kind of limits are required. Although their specification is discussed shortly, we assume for the moment that some limits exist and are known at this stage of the process. As can be expected, the planning models presented in the previous section can be used to determine the preferred outcome after introducing a few extensions. The resulting, modified model for the buyer is given in Model 4. Model 4. CP(Buyer)-1 Data min XScum, minimum cumulated supply quantity of j in periods 1 through t j, t
max maximum cumulated supply quantity of j in periods 1 through t XScum, j, t
ε
arbitrarily small number (<< 1)
4. Negotiation-Based Collaborative Planning between Two Partners
64
Variables d+j,t / d-j,t shift of supply quantity of j in t to the next / previous period Formulation T
c +ε
min
∑ ∑ (d +j,t + d −j,t )
(28)
j∈JS t =1
s.t.
(3) - (9) T
c=∑
∑ (ch j i j ,t
t =1 j∈J
is j ,t −1 + xs j ,t =
T
T
+cf j y j ,t ) + ∑
∑ cor or ,t + ∑ ∑ ch j is j ,t
∑ r j ,k xk ,t + is j ,t
∀j ∈ JS , t
t =1 r∈R
t =1 j∈JS
k∈S j
xs j ,t + d +j ,t + d −j ,t = XS j ,t + d +j ,t −1 + d −j ,t +1
(29) (30)
∀j ∈ JS , t
(31)
, min ∑ xs j , s ≥ XS cum j ,t
∀j ∈ JS , t
(32)
, max ∑ xs j , s ≤ XS cum j ,t
∀j ∈ JS , t
(33)
IS j ,t ≤ is j ,t ≤ IS j ,t
∀j ∈ JS , t
(34)
t
s =1 t s =1
Compared to Model 2, Model 4 contains new input data min max XScum, / XScum, and new variables d+j,t/d-j,t. The data items represent deviation j, t j, t limits, expressed as cumulated minimum / maximum supply quantities. Variables d+j,t/d-j,t capture intended modifications to the original order / supply proposal. The major change to the formulation regards constraints (31). Here, supply variables xsj,t are no longer equal to the proposed supply quantities. Instead, supply quantities can be shifted to the next (d+j,t ) or previous (d-j,t) period. The right-hand-side correspondingly contains proposed supply quantities plus shifts from the previous and next period. The degree to which shifts are introduced is limited by constraints (32) and (33). They guarantee that the modified pattern stays within the specified limits. The objective is still to minimize total cost in the first place. The second term (sum of shifts multiplied by a small number ε) makes sure that ineffective shifts, i.e. those which do not improve resulting cost, are avoided. Model 5 depicts the same situation for the supplier. It is equivalent to the buyer model only that minimum / maximum quantity limits here correspond to order quantities requested by the buyer. Given the equivalence to Model 4, further comments can be safely omitted. Model 5. CP(Supplier)-1 Data min XOcum, minimum cumulated order quantity of j in periods 1 through t j, t
max maximum cumulated order quantity j of in periods 1 through t XOcum, j, t
4.2. Iterative Planning Steps
65
ε arbitrarily small number (<< 1) Variables d+j,t / d-j,t shift of order quantity of j in t to the next / previous period Formulation T
∑ ∑ (d +j,t + d −j,t )
c +ε
min
(35)
j∈JS t =1
s.t.
(3) - (9) T
c=∑
∑ (ch j i j ,t
t =1 j∈J
T
+cf j y j ,t ) + ∑
∑ cor or ,t
(36)
t =1 r∈R
i j ,t −1 + x j ,t = E j ,t + xo j ,t +
∑ r j ,k xk ,t + i j ,t
∀j ∈ J , t
(37)
k∈S j
xo j ,t + d +j ,t + d −j ,t = XO j ,t + d +j ,t −1 + d −j ,t +1
∀j ∈ JS , t
(38)
, min ∑ xo j , s ≥ XOcum j ,t
∀j ∈ JS , t
(39)
, max ∑ xo j , s ≤ XOcum j ,t
∀j ∈ JS , t
(40)
t
s =1 t s =1
Solving Model 4 or Model 5 reveals the (local) minimum cost solution within the modification limits of the order / supply pattern. The solution and its corresponding costs depend on the min/ max cumulated order/ supply quantities. The situation is visualized (for the supplier) by an example in Fig. 15. It shows the received order pattern, the minimum and maximum limits, and the order pattern associated with the preferred solution.
cum
XO
/ xo
cum
XOcum,max xocum
XOcum XOcum,min
t Fig. 15. Original and preferred order pattern
Since the solution obtained in this process step incurs the lowest cost attainable within the current iteration, we refer to the resulting cost c* as
66
4. Negotiation-Based Collaborative Planning between Two Partners C Bmin = c*, C Smin = c *
(41) Also, it contains more modifications as will be present in the compromise solution. To capture the amount of changes present, we introduce the item-specific difference measure (42) D max = ( d + + d − ) ∀j ∈ JS j
∑
t∈T
j ,t
j ,t
which measures the total amount of modifications for each supply item. The importance of the deviation limits at this process step has been stressed above. In the following we therefore discuss how these limits can be specified. First, let us consider the results obtained in the case without minimum and min max = 0 , XOcum, = ∞ for the supplier and maximum shift limits, i.e. XOcum, j, t j, t equivalent 0/∞ minimum / maximum supply limits for the buyer. The preferred outcome for the buyer corresponds in this case to the locally optimal plan without any regard of the consequences for the supplier. Even worse, the optimal solution to the supplier Model 5 does not contain any shipments to the buyer in order to avoid corresponding costs. To counteract, one needs to state at minimum that cumulative shipments have to equal to cumulated order quantities over the planning horizon, i.e. (43) ∑ xo j,t ≥ XO cum j,T t∈T
Yet, the result obtained in this way at both, buyer and supplier, is still against the spirit of a collaborative process, because the individual situation faced by the collaboration partner is ignored in the local decision making process. Therefore, a twofold approach for setting tighter modification limits is laid out in the following. It consists of • the propagation of final demand forecasts to the supplier and • rules for the maximum deviation of a proposed order / supply pattern
Demand Forecast Propagation It is in the supplier’s interest that the SC is able to meet its final demand. Thus, knowledge of associated supply requirements is a cornerstone of collaborative planning as it ensures that the buyer can cover his demand in due times. Deriving minimum supply requirements from final demand forecasts involves two steps. First, final product demands are converted into respective supply item needs by means of a bill-of-material explosion. Second, time-offsets are to be set which specify when a supply item is needed by the buyer so that the final demand in a given period can be covered. In its simplest form, item-specific fixed offsets are chosen, e.g. 0 or 1 period, depending on when the item is needed at the buyer’s operations.163 Of course, fixed offsets do not consider specific, period dependent conditions such as total demand and available capacities, and hence bear the risk
163
See Glaser et al. (1992), pp. 237, for a procedure which combines bill-of-material and time-offset data in order to derive supply requirements in a single step.
4.2. Iterative Planning Steps
67
of under- or overestimating required lead time. To resolve this, more sophisticated approaches can be applied, such as the concept of utilization-dependent lead times as developed by Lautenschläger (1999).164 Without going into further details at this point, we assume in the following that reasonable minimum supply requirements min E cum, ∀j ∈ JS , t (44) j, t can be derived from final demand forecasts and passed to the supplier. If this is not possible, the second set of shift limits can be applied solely. However, meeting expected final demand is then not guaranteed. Maximum Deviation Rules As minimum supply requirements derived from final demand are relevant only for the supplier and might not even be available, additional limits on maximum allowable shifts are needed. In contrast to minimum supply requirements, these limits should be devised from the order / supply pattern proposed by the collaboration partner in order to reflect the individual solution currently considered by the partner. The question of defining deviation limits is: to which extent can the proposed order / supply pattern be modified without yielding unacceptable results for the collaboration partner. As it is hardly possible to specify a generally acceptable limit, we define heuristic rules, which limit modifications to a reasonable extent. In its simplest form the collaboration partners could agree to fixed, potentially item-specific limits based on their judgment or experience. For instance, the maximum could correspond to a shift of the entire order quantity to the previous or the next period. Given this rule, the order quantity XO1,3 (230 units) of the example in Table 7 could be already fulfilled in period 2 or delayed to period 4. A somewhat more sophisticated rule will be used here in the following. The idea is to use periods with an order / supply quantity greater than zero as limiting periods. The maximum shifts then correspond to shifts of the entire order quantity to the previous or next order period, respectively.165 The rationale behind this is as follows: Since the collaboration partner proposes a non-zero order / supply quantity in these periods, he has a general need of the item at these points in time. Hence, there is a realistic chance that he can make use of a surplus supply with relatively small adjustments to his current plan (e.g. without additional setups in production). In result, the method accounts for the partner’s current plan and the specific order / supply frequency and pattern of each item.
164
165
See Lautenschläger (1999), pp. 81, for details. Similar proposals were made by Missbauer (1998), pp. 219, and Karmakar (1992), pp. 287. The idea has been adapted from a multi-stage lot-sizing heuristic developed by Simpson (see e.g. Simpson (1999), pp. 18).
68
4. Negotiation-Based Collaborative Planning between Two Partners
Table 7. Example of order / supply pattern shift limits
Period Item.
1
2
3
4
Orders
1 2 3
199 208 243
0 0 312
230 31 0
90 … 141 … 51 …
Cumulated Orders
1 2 3
199 208 243
199 208 555
429 239 555
519 … 308 … 606 …
Minimum Cumulated Orders
1 2 3
0 0 0
0 0 243
199 208 243
429 … 239 … 555 …
Maximum Cumulated Orders
1 2 3
429 239 555
429 239 606
519 308 606
… … … … … …
…
The example in Table 7 demonstrates the method from the supplier’s viewpoint. Order periods of items 1 and 2 are (1, 3, 4), and of item 3 (1,2,4). Hence the maximum shift of e.g. XO1,3 (230 units) is to move the total amount to either period 1 or 4. Likewise, the total quantity of XO3,2 (312) can be shifted to either period 1 or 4. Based on cumulated order quantities and order periods, we obtain the minimum and maximum cumulated orders shown in Table 7. Formally, the underlying rules can be expressed as max XOcum, = XOcum ∀j ∈ JS , t (45) j, next t j, t ⎫ ⎧⎪ XOcum j, prev t if XO j, t > 0⎪ min XOcum, = ⎬ ⎨ cum j, t else ⎪⎭ ⎪⎩XO j, prev t −1
∀j ∈ JS , t
(46)
where prevt and nextt represent the previous and next order periods relative to a given period t. (45) states that the maximum cumulated amount which can be supplied up to a period t corresponds to the cumulative order up to the next order period. According to (46), the minimum amount equals to the cumulated order up to the previous period, if period t is an order period. Otherwise (XOj,t=0) the order quantity of prevt can be shifted beyond t. Hence the minimum amount to be supplied through to t correspond to XO cum . j, prev −1 t
Cumulated minimum and maximum supply quantities for the buyer are determined equivalently based on the received supply proposals XSj,t, i.e.
4.2. Iterative Planning Steps max XScum, = XScum j, next t j, t
∀j ∈ JS , t
⎧⎪ XScum ⎫ j, prev t if XS j, t > 0⎪ min = XScum, ⎨ cum ⎬ j, t else ⎪⎩XS j, prev t −1 ⎪⎭
∀j ∈ JS , t
69
(47) (48)
Finally, if both minimum requirements from final demand and rule-based shifts are available to the supplier, the ultimate minimum quantities have to be computed as min min min XO ′j,cum, = max XO cum, , E cum, ∀j ∈ JS , t (49) t j, t j, t
{
}
such that they correspond to the tighter of the two bounds. 4.2.3
Generating a compromise proposal
The minimum cost solution obtained above contains all modifications (within the defined limits), which yield a decrease of local cost. Among those modifications some are more effective than others, i.e. some incur significant marginal savings while others only have a minor impact on cost. In terms of the negotiation metaphor, the order / supply pattern corresponding to the minimum cost solution represents a “maximum claim”, that is a counter proposal which could not be better from the local perspective. However, real life examples show that maximum claims often are unacceptable to negotiation partners. The same principle applies here: Since modifications tend to increase cost for the collaboration partner, his cost increase will be the higher, the more modifications are present in the counter proposal. Therefore, only modifications with high impact on local costs should be included in a compromise proposal. These most effective modifications also offer the greatest chance among all of them to improve the overall cost outcome (assuming that all modifications cause comparable per-unit degradations for the partner). The following section discusses methods of finding effective compromise proposals. Thereby, we can make use of the planning models shown above, once more in somewhat extended versions. 4.2.3.1
Model-based methods for finding compromise proposals
The purpose of this process step is to find an order / supply pattern with only few, but highly cost effective modifications. The optimal compromise proposal is one which offers maximum cost savings (vs. the cost associated with the partner proposal) per unit deviation from the original order / supply pattern. This objective can be formally expressed as (50) max (C max − c) d where d corresponds to a measure of the total deviation (or degree of modification).
70
4. Negotiation-Based Collaborative Planning between Two Partners
The interdependence between cost savings and deviation is visualized by an example in Fig. 16.166 The diagram shows the functional relationship between the deviation from the original pattern (expressed in terms of a percentage measure167) and relative cost savings, i.e. associated savings Cmax-c divided by the maximum savings potential Cmax-Cmin (curve “relative savings”). It can be seen that, in this example, savings first occur at an almost constant rate, followed by a steep increase around a deviation of 0.1. Thereafter, the marginal effect of additional modifications steadily declines. Also shown is the ratio between relative savings and deviation. It has its maximum in the region with largest incremental savings. Thus, the solution at a deviation of about 0.1 represents the optimal compromise proposal in this example.
2.5
Relative Savings
[100%]
2
Rel. Sav. / Rel. Dev.
1.5
1
0.5
0 0
0.2
0.4
0.6
0.8
1
Total deviation d
Fig. 16. Interdependence between savings and deviation
In order to obtain compromise proposals with the planning models presented above, following modifications are required: With a new variable d we can derive an extended model formulation by replacing the objective function with (50). Also, an extra constraint has to be added for the calculation of the total deviation measure d. Solving the resulting model then yields the optimal compromise proposal.
166
167
The example was obtained from a test instance by parametric optimization, i.e. restriction of the maximum deviation to an incrementally increased upper bound of x%. The precise definition of d is develop in the next section 4.2.3.2.
4.2. Iterative Planning Steps
71
However, the objective function based on (50) is non-linear, converting the model into a non-linear programming problem of the type (51) f (x) max (52) g i ( x ) ≤ bi ∀i = 1..m s.t. where f and gi are given functions. 168 If d is computed linearly, then the constraint set remains linear and can be rewritten as Ax ≤ b (53) where A represents the matrix of coefficients and b the column vector of values bi. Since the objective is in the form of a fraction, the model more specifically corresponds to a fractional programming problem.169 Unfortunately, non-linear programming problems are in general difficult to solve and a standard solution algorithm as for LP and MIP is not available.170 A heuristic which could potentially be applied to the resulting fractional program is Successive Linear Programming (SLP).171 This method is “a differential technique which utilizes the linear programming algorithm repetitively in such a way that the solution of the linear problem converges to the solution of the non-linear problem”.172 However, applying SLP to the model regarded here poses difficulties. For one, there is a need of differentiability of the objective function in all variables. Since the model may contain binary variables, this is not given. Second, even if this could be resolved, SLP algorithms are complex and require a large number of iterations to obtain satisfactory solutions.173 Because of these issues and since it is not crucial to find the truly optimal solution for our purpose of generating a good compromise proposal, we will not try to make use of SLP for solving the non-linear program. Instead we utilize an approximate approach which is easier to implement. It grounds on the idea to consider the numerator and denominator of (50) as two separate objectives, i.e. 1) maximize cost savings and 2) minimize the amount of modifications.
168 169
170
171
172 173
C.f. Hillier / Liebermann (2001), p. 654. C.f. Hillier / Liebermann (2001), p. 669. Fractional programming problems with an objective function of a special type can be converted to linear programs by a variable substitution (c.f. Neumann / Morlock (1993), pp. 575). However, the above fractional program does not satisfy the necessary conditions (e.g. non-zero denominator values in the entire feasible region). C.f. Domschke / Drexl (1998), p. 165. Specific solution methods only are available for special problem structures such as the “Modified Simplex Method” for quadratic programming problems (c.f. Hillier / Liebermann (2001), pp. 686). Also called Method of Approximation Programming (c.f. Griffith / Stewart (1961), p. 379). Griffith / Stewart (1961), p. 379. Zhang et al. (1985) observe an average of several hundreds for some problem structures in their computational study.
72
4. Negotiation-Based Collaborative Planning between Two Partners
Then, instead of maximizing the ratio according to (50) a simultaneous optimization of the two (conflicting) objectives can be pursued. A widely used technique for dealing with multiple objective optimization is goal programming which can be applied here, too. The term goal programming (GP) was coined by Charnes / Cooper (1961) who have developed the method in order to solve infeasible linear programs with a minimum violation of the problem constraints.174 Since then numerous authors proposed GP models in dealing with various types of multiple objective problems.175 GP comprises the specification of target values for the respective goals and the formulation of a (linear) programming model which minimizes deviations from the pre-set target values. GP models can be classified into two subsets: models which aim at minimizing the (weighted) sum of deviations from all goals and models with priorities for goals.176 Only the first type is considered in the following. The standard model formulation is as follows:177 K (54) min ∑ ( win ni + wip pi ) i =1
(55) x ∈ CS (56) ni ≥ 0, pi ≥ 0 ∀i = 1..K (57) where x is a vector of variables and fi(x) are (linear) objective functions with target values Bi. Non-negative variables ni and pi measure negative and positive deviations from the target values which are minimized in the objective function. Parameters wni and wpi represent (optional) weights attached to the respective deviations. Cs is the set of hard constraints which defines the problem’s feasible region. Depending on the value domains of variables x, the GP model is an LP or MIP and can be solved to optimality by standard Simplex or Branch & Bound algorithms. Its optimal solution exhibits the minimum weighted sum of deviations from the target values. Thus, it represents the optimal compromise between the conflicting objectives. An important issue of GP models is so-called incommensurability. It means that different units of measure may be used for the individual goals and their target values. In result “the relative magnitudes of measures taken from differing populations […] bias the solution process in favor of the parameters what will yield the largest reduction in deviation”.178 To counteract, a normalization of the deviations is required.179 The most intuitive normalization procedure utilizes the target values s.t.
174 175
176 177 178 179
fi ( x) + ni − pi = Bi
∀i = 1..K
C.f. Charnes / Cooper (1961), pp. 215, Cooper (2002), pp. 36. C.f. Aouni / Kettani (2001), p. 225. See e.g. Schniederjans (1995), pp. 73, for an overview. C.f. Tamiz et al. (1998), p. 570. C.f. Tamiz / Jones (1996), p. 299. Schniederjans (1995), p. 28. C.f. Tamiz / Jones (1996), p. 202.
4.2. Iterative Planning Steps
73
as normalizing constants (called “percentage normalization”). In result a revised GP objective function is obtained of the form (58) K wn wp min ∑ ( i ni + i p i ) Bi
i =1
Bi
With this extension in place all deviations contribute with the same order of magnitude to the GP objective function.180 With regard to finding a compromise order / supply pattern, a GP model can be devised from the conflicting objectives stated above. However, objective one (“maximize cost savings”) has to be reformulated in order to define a reasonable target value. Since we know the that minimum possible costs are Cmin, minimizing the deviation from Cmin rather than maximizing savings vs. Cmax forms the first objective. The target values hence correspond to minimum cost Cmin for the cost savings objective and zero for the deviation objective. As both goals are measured in different units, an appropriate normalization is needed. Resulting costs c can take values between Cmin and Cmax, so that the interval (Cmax-Cmin) can be used to normalize deviations to values between 0 and 1. Likewise, we assume that the measure of total deviation is normalized to the 0-1 interval (its precise definition is derived in the next section). The resulting GP model for the buyer is presented in Model 6. Model 6. CP(Buyer)-2 Data Cmax maximum cost (CP-0 solution) Cmin minimum cost (CP-1 solution) WC weight of cost objective WD weight of modification objective Variables ∆ deviation from minimum cost d percentage modification of supply pattern Formulation min
s.t.
WC C
max
−C
min
∆ +W D d
(59)
(3) - (9), (29) - (34) d = f ( XS j ,t , xs j ,t ) c−∆=C
min
(60) (61)
Except for the objective function and the additional constraints (60) and (61), the model is equivalent to Model 4. (60) and (61) capture the deviations from the target goal values. Since the definition of the modification measure follows below, (60) only indicates that the total distance d is calculated from original and current
180
It should however be noted that percentage normalization requires non-zero target values Bi.
4. Negotiation-Based Collaborative Planning between Two Partners
74
supply quantities. The deviation variable ∆ captures the cost increase above Cmin. The objective function contains the weighted sum of the target value deviations. As explained above, ∆ is normalized by the interval width of (Cmax-Cmin). The weight parameters are discussed in more detail below in section 4.2.3.3. The corresponding supplier model is obtained identically from Model 5, only that deviations from order values (XOj,t) are considered here. The formulation is given in Model 7. Model 7. CP(Supplier)-2 Formulation min
s.t.
WC C
max
−C
min
(62)
∆ +W D d
(3) - (9), (36) - (40) d = f ( XO j ,t , xo j ,t )
(63) (64)
c − ∆ = C min
Solving the GP models does not guarantee maximization of the original objective according to (50). However, it produces a compromise close to the maximum, as it contains only those modifications which have a higher impact on cost savings than on the deviation measure. The optimal GP solution represents a compromise where cost savings and deviations are balanced one vs. the other. 1
Goal programming objectives
0,9
∆% + d
0,8 d
∆%
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Total deviation d
Fig. 17. Relationship between goal programming objectives
1
4.2. Iterative Planning Steps
75
The situation is visualized in Fig. 17 for the same example as considered above in Fig. 16. It shows the conflicting relationship of the two objectives and how ∆% (the normalized cost increase above Cmin) decreases with growing deviation d. Also shown is the sum of the two target value deviations (∆%+d). As can be seen, the sum takes its minimum at a deviation d of about 0.1, right in the vicinity of the maximum to the original objective according to (50). Applying the above GP models is an efficient way to generate compromise proposals, as we obtain the compromise order / supply pattern by solving a single additional planning model. Also, the method can be easily extended such that additional compromise proposals are generated, a feature which will prove useful shortly. Irrespective of the method used to obtain a compromise proposal, the total amount of modifications present in the compromise is smaller than in the minimum cost solution to Model 4 / Model 5. This is depicted in Fig. 18 for the supplier. It shows received cumulated order quantities (XOcumj,t), and cumulated order quantities obtained with Model 5 (xocum,1) and Model 7 (xocum,2). As indicated, the solution of Model 7 is closer to the original order pattern, because only a part of all possible modifications is contained in the compromise. The savings realized with the compromise are (65) ∆C = C max − c * when c* is the cost associated with the compromise solution. The definition of the deviation measure d, which has been deferred so far, is described in the following section. XOcum / xocum XOcum xocum,1
xocum,2
t Fig. 18. Cumulated original and compromise order quantities
4.2.3.2
Distance measure for order / supply patterns
Based on the definition by Jain et al. (1999) “a distance measure is a metric (or quasi-metric) on the feature space used to quantify the similarity of patterns”.181 Distance measures are for example used in Cluster Analysis where they are
181
Jain et al. (1999), p. 270.
76
4. Negotiation-Based Collaborative Planning between Two Partners
needed to identify similar objects which can be grouped to a cluster.182 Similarity is usually determined from a set of parameters xj of the objects considered. Generally, parameters can have discrete or continuous value domains, however only the latter are of relevance in the following. Given two objects k and h with continuous parameter vectors xk, xh of dimension N, the Minkowski metric 1/ P (66) ⎡N ⎤ d k ,h = ⎢ ∑ x kj − x hj ⎢⎣ j =1
P
⎥ ⎥⎦
is often used as a measure of the dissimilarity or distance between the objects.183 Most popular are the first and second order cases (P=1, P=2). The first is the socalled City-Block Metric or L1-norm while the latter represents the Euclidean distance or L2-norm between the points xh and xk in ℜ N space.184 Similar as goal deviations in GP models, varying magnitudes of parameter values have a distorting impact on the contribution of individual parameters to the total distance measure. Therefore, appropriate normalization is required to balance the effects of various parameters. For the generation of compromise order / supply patterns, the amount of modifications or the total deviation from the received proposal has to be determined. Hence, the set of parameters distinguishing alternative patterns is made up by cumulated order or supply quantities xoj,tcum / xsj,tcum. Furthermore, since the distance measure is incorporated into the GP models, a linear distance calculation is required, making the L1-norm introduced above the obvious choice. The question however is how individual parameters can be appropriately normalized and combined to a total distance. First, we can sum up all parameters pertaining to a single item, as they are expressed in identical unit measures. The absolute item-specific deviation measure hence is calculated for the buyer as185 (67) d ABS = XS cum − xs cum ∀j ∈ JS j
∑
t∈T
j ,t
j ,t
The definition in (67) can be further simplified, if we recap that shift quantity variables d-j,t/d+j,t link received proposals XOj,t / XSj,t and the respective variables xoj,t / xsj,t.186 Due to the corresponding balance equations the values of shift quantities d-j,t/d+j,t represent the cumulated excess or short supply vs. the original proposal. Therefore, the difference term in (67) can be replaced by the sum of shift quantities to previous and next periods, yielding187 182 183 184
185
186 187
C.f. Backhaus et al. (1996), p. 264. C.f. Hartung / Elpelt (1995), p. 72, Jain et al. (1999), pp. 271. C.f. Backhaus et al. (1996), p. 274. The Euclidean distance resembles the length of a connecting line between the points xh and xk in two and three dimensional space. The calculation for the supplier is equivalent but based on cumulated order quantities XOcumj,t. See e.g. constraints (31) of Model 4, p. 64. Mathematically, we have from constraints (31)
4.2. Iterative Planning Steps d ABS = j
∑ (d +j ,t + d −j ,t )
77
(68)
∀j ∈ JS
t∈T
The total item-specific quantity can then be normalized by the maximum shift quantity Djmax contained in the most preferred, minimum cost solution to Model 4 / Model 5.188 Resulting is an item-specific percentage deviation according to dj =
d jABS D max j
=
∑ (d +j ,t + d −j ,t )
t∈T
(69)
189
D max j
In a second step, the item-specific percentage measures have to be combined to a single, overall distance. The natural approach to accomplish this task is by averaging item-related values. Using a simple arithmetic mean (i.e. the sum of itemspecific measures divided by the number of items), the total distance is d=
1 JS
∑d j
(70)
j∈JS
However, the above calculation can result in a misleading total distance, because it ignores the relative importance, e.g. total order volume, of individual items. As an example let us consider a two-item case with 100% distance for one item and 1% for the other. The mean distance here is 50.5%. However, if the first item is perceived much more important than the second, one would intuitively attach a higher total distance to this scenario. Vice versa, if item one is considered miscellaneous compared to item two, a smaller total distance seems appropriate. To incoporate this, a weighted average of the form d=
∑ wjd j
∑
=
j∈JS
j∈JS
wj ⎛ ⎞ ⎜ (d +j ,t + d −j ,t ) ⎟ ⎟ max ⎜ ∑ D j ⎝ t∈T ⎠
(71)
can be used. Assigning weights however requires a careful assessment of the consequences. in order to avoid so called “naïve relative weighting”, i.e. a situation where chosen weights do not accurately reflect the true proportional importance.190 Two ways of XS j ,t − xs j ,t = d +j ,t + d −j ,t − d +j ,t −1 − d −j ,t +1 and hence cum XS cum j ,t − xs j ,t =
=
d +j ,t
t
∑ ( XS j , s − xs j , s )
s =1
− d −j ,t +1 + d −j ,1 − d +j ,0
=
d +j ,t
=
t
∑ (d +j , s + d −j ,s − d +j , s −1 − d −j , s +1)
s =1
− d −j ,t +1
= d +j ,t + d −j ,t +1
(the last two simplifications are valid because d-j,1=d+j,0=0 by definition and only one of d+j,t or d-j,t+1 is greater than zero at any one time). Thus, we obtain cum ∑ XS cum j ,t − xs j ,t
t∈T 188 189 190
=
∑ (d +j ,t
t∈T
+ d −j ,t +1 ) =
∑ (d +j ,t
t∈T
+ d −j ,t )
(the last transformation is possible given that d-j,1=d-j,T+1=0). See equation (42), p. 66. If Djmax equals zero, a small number ε (<< 1) is added. C.f. Schniederjans (1995), p. 28.
78
4. Negotiation-Based Collaborative Planning between Two Partners
how to assign weights are introduced here: pre-defined priorities attached to individual items and each item’s contribution to the maximum deviation obtained by Model 4 / Model 5. Item-related priorities can be agreed upon by the collaboration partners. They serve to give an idea of the criticality of individual items. Items receive a high weight when modifications tend to be harmful or problematic for the collaboration partner. Lower weights are attached to items regarded as uncritical. In result, modifications of critical items contribute more strongly to the overall distance measure than uncritical components. The second possibility makes use of the maximum deviations obtained by solving Model 4 / Model 5. The idea here is to use the ratio between the maximum item-specific shift quantity and the total shift quantity over all items as the weighting factor. This however requires that item-specific quantities can be summed up. Depending on the range and type of supply items, it can be more or less difficult to find a common unit-measure for such a summation. Generally, the more similar the items are by nature, the more likely a common measure can be defined. If a common unit measure cannot be found, the value of each item’s shift volume, i.e. the product of maximum shift quantity and unit value or price, can be used as a common basis of measurement. When maximum item-specific shift quantities are all expressed in common units, the weighting factors can be calculated to wj =
D max j
∑ Dkmax
∀j ∈ JS
(72)
k∈JS
These relative weights and the resulting overall distance measure fit to the intuitive distance perception, which is demonstrated in Table 8 for the two-item example. In case a), the overall distance comes up to 98% because of a 100% distance of item 1, which has a 98% share in the overall shift quantity of 102 units. In case b) on the contrary, the total distance calculates to a mere 3% as only three out of 102 maximum shift units are present. Finally, since both items have an equivalent share in the maximum shift quantity in case c), a mean distance of 50.5% is obtained here. Also, item-specific weights wj overall sum up to one. Hence, the maximum value of the deviation measure d according to (71) is one, too. This results when each item’s deviation equals to its maximum value Djmax. In order to include the distance calculation based on equation (71) into the GP models, the general distance functions in constraints (60) of Model 6 and (63) of Model 7 have to be replaced by equation (71). The weighting factors wj are input data to the models and can be calculated as shown in (72).
4.2. Iterative Planning Steps
79
Table 8. Item weighting example
Rel. distance Total distance dj d
Max. shift quantity
Item weight wj
Abs. distance
a) Item 1 Item 2
100 2
98.04% 1.96%
100 0.02
100% 1%
98.1%
b) Item 1 Item 2
100 2
98.04% 1.96%
1 2
1% 100%
2.9%
c) Item 1 Item 2
100 100
50.0% 50.0%
100 1
100% 1%
50.5%
4.2.3.3
d jABS
Anticipation of partner cost increases
Anticipation is a concept of hierarchical planning and was already introduced in section 2.3.2. Its general purpose is to improve the overall quality of top-level decisions. This is achieved by roughly capturing consequences of top-level decisions on the base-level.191 The approach developed by Zimmer (2001), which was discussed in section 3.3.2.1, shows that anticipation can be utilized in collaborative planning, as well.192 A type of anticipation, which is of particular relevance here, is the anticipation of costs. It is useful when cost minimization forms the primary objective of hierarchical planning at both top and base-level.193 Given the formal top-level objective function as (73) min CT T where C represents top-level costs, a modified objective includes anticipated base-level costs CB to result in (74) C T + Cˆ B min The “hat” symbol in (74) indicates that only an estimation of actual costs associated with chosen decisions is available, i.e. the anticipated base-level model includes an estimation of base-level costs that follow from top-level decisions. The collaborative planning process developed here is in total non-hierarchical as was argued above. However, the compromise generation by one partner and the evaluation of the compromise proposal by the other within each iteration can be regarded as a hierarchical planning process, in analogy to Zimmer’s (2001) understanding of Upstream Planning. A conceptual diagram of the situation is shown in Fig. 19. Therefore, anticipation of the base level can be helpful here, too, in order to improve top-level decision making. An anticipation procedure can be realized by
191 192 193
See section 2.3.2, p. 15. See p. 46. C.f. Steven (1994), p. 184.
80
4. Negotiation-Based Collaborative Planning between Two Partners
estimating partner cost increases caused by compromise proposals. This approach is useful here since the compromise generation aims at decreasing local cost, while the actual objective is to improve the total, joint cost outcome. Estimating partner cost increases thus allows to capture the total effect of local decisions. Generally, cost anticipation is realized as shown above in (74). For the compromise generation by GP models (Model 6 / Model 7) a simple approach is however possible by using the objective function weights WC and WD for this purpose.194 Top L.: Partner 1 Compromise Generation Anticipated Base Level Anticipation (Feed Forward)
Instruction XOj,t/XSj,t Base L.: Partner 2 Compromise Evaluation
Fig. 19. Compromise generation and evaluation as hierarchical planning
Until now both GP objectives, i.e. cost increases vs. Cmin (∆) and total deviation (d), where normalized to values between zero and one regardless of their absolute values. In consequence, the GP model produces one and the same optimal compromise, no matter what the absolute effect on local costs corresponds to. Neither it takes any account of the magnitude of partner cost increases that are associated with the modified order / supply quantities. For illustration, the optimal GP solution of the example in Fig. 17 appears at a deviation (d) of 0.1 and a relative cost increase above Cmin (∆%) of 0.8. This remains unchanged regardless of the absolute value of the local savings potential (Cmax-Cmin) and its contribution to total SC costs. However, we can expect that absolute cost effects play an important role in finding good compromise proposals. To illustrate this, let us consider a scenario with potential local cost savings of 1000 MU and, say, associated partner increases of 10 MU. In this case, almost all modifications can be included in the compromise proposal as local savings outweigh partner cost increases by far. If, on the other hand, the situation is reverse, only a few modifications (if any) should be proposed since they likely cause enormous damage to the partner’s cost outcome.
194
See Model 6, p. 73.
4.2. Iterative Planning Steps
81
These observations can be incorporated into the GP models. Suppose that the partner cost increase associated with the minimum cost solution (∆=0, d=1) is known and abbreviated by ∆P.195 Then local and partner cost effects can be reflected in the GP objective function by assigning the following values to the GP objectives: (75) W C = C max − C min (76) W D = ∆P min Now increases above C contribute with their absolute value to the GP objective function. Total deviation d on the other hand is multiplied with ∆P. In result, the GP objective function represents the sum of local costs above Cmin and a linear approximation of the partner cost increase. This is visualized in Fig. 20 for the example of Fig. 17, assuming potential local savings (Cmax-Cmin) of 41,000 MU and a partner cost increase associated with the minimum cost solution of 35,000 MU. The resulting GP objective function now has a different shape and takes its minimum at a deviation of 0.65 and local cost of 10,000 above Cmin. Hence, compared to the original situation in Fig. 17, the compromise proposal contains more modifications. This is due to the fact that the local savings potential is almost 20% greater than associated partner cost increases, justifying a compromise with more modifications.196 Thus, the anticipated base-level model used in this approach is a linear function which assumes proportionality between the total deviation d and associated partner cost increases. Obviously, this is a rough, simplified picture of the true effects of modifications. However, it is straightforward to implement. Also, a more sophisticated estimation of the cost increases can hardly be realized, because the true effects depend on the various constraints and interrelationships within the partner’s planning model. To give an indication of how appropriate this anticipation scheme is, Fig. 21 exhibits anticipated and actual partner cost increases for the above example. In fact, it can be observed that there is, in tendency, a good fit between estimated and actual increases. Although the anticipation seems to underestimate true effects in the particular example, there is no reason for this being true in general. A final point concerns the question of how to estimate the partner cost increase ∆P. An exact way to determine ∆P is by a direct inquiry to the collaboration partner. The order / supply pattern corresponding to the minimum cost solution could be transmitted to and evaluated by the partner. In return, the partner could announce the associated cost increase ∆P. This solution however requires an intermediate interaction between the collaboration partners.
195 196
A method for determining ∆P is introduced shortly. Local savings of up to 41,000 MU vs. partner cost increases of 35,000 MU.
82
4. Negotiation-Based Collaborative Planning between Two Partners
45000 40000 c-Cmin + ∆P d
Cost Increases [MU]
35000 30000
c-Cmin 25000
∆P d
20000 15000 10000 5000 0 0
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
1
Total deviation d
Fig. 20. Weighted GP objective function
To avoid a direct inquiry, the partner’s increase can be estimated from previous compromise proposals and their cost effects. Knowing the effect of the previous iteration’s compromise on partner costs (abbreviated by ∆Picomp −1 ), the partner’s increase associated with the minimum cost solution can be estimated as (77)
comp ∆Pˆimax d i*−1 −1 = ∆Pi −1
d*i-1
where is the value of the deviation measure in the previous compromise solution.197 In order to decrease sensitivity vs. varying outcomes in individual iterations, an average over the history of these estimates can be calculated in a second step. Since we can assume that effects by recent compromises are closer to the situation faced in the current iteration, a weighted average seems a reasonable choice.198 Therefore, first order exponential smoothing is applied to the individual estimates by iteration.199 In result, the estimate of the partner’s increase associated with the current minimum cost solution is obtained as (78) ∆Pˆ = (1 − α ) ∆Pˆ + α∆Pˆ max i
197
198 199
i −1
i −1
The formula represents a linear extrapolation of ∆Picomp and the associated deviation −1 d*i-1 to the maximum deviation of one. C.f. Chase et al. (1998), p. 510. See e.g. Silver et al. (1998), pp. 89, Tempelmeier (2003), pp. 47.
4.2. Iterative Planning Steps
83
where α is a parameter of value between 0 and 1. Although the partner’s actual cost increases vary from iteration to iteration, they are usually of a similar magnitude. Therefore, using forecast values as shown in (78) proves to be an effective, sufficiently accurate approximation. The above sections describe the approach developed here for the generation of compromise proposals. In summary, it was shown how a goal programming model can be utilized for this task. The deviation measure was described which is used to determine the degree of deviation from the original order / supply quantities. Finally, we demonstrated how the GP objective function weights can be used for anticipation of partner cost increases. 40000
Partner cost increase [MU]
35000
30000
25000
20000
15000
Anticipated Actual
10000
5000
0 0
0.2
0.4
0.6
0.8
1
Total deviation d
Fig. 21. Anticipated and actual partner cost increases
4.2.4
Generating additional compromise proposals
This section deals with the last iterative process step, i.e. how to pursue when the selected compromise proposal is equivalent to the compromise of an earlier iteration. It first requires to compare the current proposal to former ones and then to decide about the course of action to take in case of equivalence. Both aspects are discussed in turn.
4. Negotiation-Based Collaborative Planning between Two Partners
84
4.2.4.1
Proposal comparison
From real life negotiations we know that making the same counter proposal twice is of little use, since the partner’s reaction to it is already known. The same applies here. Since deterministic planning models are used, the partner’s reaction will be identical to the first time when he was confronted with the compromise. In result, the collaborative process starts to cycle, leaving no space for further improvements. Hence, it makes little sense to make the same proposal for a second time. The comparison of the current with a fomer compromise proposal can be achieved by examining the respective order / supply quantities. Again, cumulated orders / supplies up to any given period can be used for this purpose. An obvious prerequisite for carrying out the comparisons is that each partner keeps track of former compromise proposals. To quantify the difference between two order / supply patterns we can use the distance measure developed for the compromise generation. As a starting point the absolute distance per item can be computed similar to equation (67) as (79) δ ABS = xs cum,i − xs cum,k ∀j ∈ JS
∑
i ,k , j
t∈T
j ,t
j ,t
where i and k index two order / supply patterns. Second, in order to obtain an overall measure, item-specific distances have to be normalized. Potential normalizing constants are the total cumulated quantity xsj,Tcum or the average per-period volume xs j .200 Resulting are item-specific relative distance measures δ i,k , j =
δ iABS ,k , j xs j
∀j ∈ JS ,
(80)
(assuming that the average per-period quantity is used for normalization). Finally, item-specific values need to be combined to an overall measure. In analogy to the discussion above, a weighted average can again be calculated from item-specific distances. One possibility for specifying item weights is to use an item’s percentage contribution to the sum of average quantities according to ωj =
xs j
∑ xsl
∀j ∈ JS
(81)
l∈JS
As was argued above, a common unit of measurement must be available for this calculation. The rationale behind the weight assignment is similar to section 4.2.3.2: the role of an item within the total measure is proportional to its contribution to the total purchase volume. In absence of a common unit of measurement, average values (volume times unit price) can be used here again. In result, the total difference between two order / supply patterns i and k calculates to (82) δ i ,k = ∑ ω j δ i , k , j j∈JS
200
I.e. xscumj,T / T.
4.2. Iterative Planning Steps
85
Given the distance measure, we can determine whether the current proposal differs from all previous ones by inspecting the smallest measure among all the comparisons. Formally, when i is the iteration counter we focus on δ = min {δ i ,k } (83) k =1..(i −1)
When δ is sufficiently large, the new compromise is not equivalent to a former one and can be proposed to the partner. However, a difficulty arises from the fact that order / supply quantities have continuous values. While a complete equivalence (δ=0) rarely occurs, a small difference may still bring no significant change to the partner. Therefore, the following approach is taken here: First, we define a threshold or minimum distance that can be safely regarded as significant. Second, a distance of zero can be declared as unacceptable. Finally, since clear judgments on values between zero and the threshold are hard to make, corresponding proposals are randomly accepted or denied with a probability that grows from zero (for the zero distance case) to one (when the distance equals to the threshold value).201 For specifying the threshold value it is helpful to start with a single-item case. In this situation, i.e. when only one item is supplied to the buyer, we assume that an absolute distance of an average per-period quantity xs j is large enough to result in a meaningful difference for the partner.202 In terms of the relative itemspecific measure according to (80) this corresponds to a threshold value of one. Once the single-item threshold is defined, an extension to the multi-item case can be made based on the following observation. With multiple items a smaller difference per item is sufficient to form a new situation for the partner, since itemspecific differences add up to the total change. To illustrate this, think of a oneitem case with minimum difference of 10 units. Now, when two items are present, a difference of 5 units per item can be sufficient, as it yields the same total change of 10 units. Therefore, given a relative, minimum one-item threshold of one,203 the threshold for the multi-item case follows from dividing it by the number of items yielding (84) 1 min δ
=
JS
Hence, the more items are present in the order / supply pattern, the lower is the average per-item distance that can be accepted. In result, if the smallest distance measured (δ) exceeds the threshold, the new pattern safely differs from former ones and is proposed to the partner. Otherwise,
201
202
203
A similar approach is used below in section 4.3.3, pp. 97, for accepting solutions with a degradation in total costs. It is adapted from meta-heuristic search procedures, namely Simulated Annealing. Links to Simulated Annealing and corresponding references are discussed below in 4.3.3. This definiton is of course still arbitrarily chosen. A verification or adjustment should be undertaken for individual problem settings. Or any other number that seems appropriate.
86
4. Negotiation-Based Collaborative Planning between Two Partners
we draw a random number r1 from a uniform distribution over [0,1] and compare it to an acceptance function according to (85) (δ min −δ ) p1 = e
− ln( K )
δ min
with a large constant K (e.g. 103).204 When r1 is smaller than p1, the new proposal is accepted despite its similarity to a former pattern. If the opposite is true, it is denied. The shape of the function p1 is depicted in Fig. 22. As can be observed, chances for acceptance are very small as long as δ is close to zero, but grow rapidly when it approaches δmin. 1
0.8
0.6
p1 0.4
0.2
0 0
0.2
0.4
0.6
min
(δ
0.8
1
min
-δ)/δ
Fig. 22. Shape of acceptance function
Finally, one can ask how to proceed, when the current proposal is denied. The simplest approach consists of stopping the entire collaborative planning process. However, this bears the risk that promising solutions have not been sufficiently explored. Therefore, one may try to generate an additional, differing compromise proposal. This can in fact be accomplished by modified versions of the GP models as presented above, and is discussed in the next section. There is however no guarantee to find a new, i.e. so far unknown, pattern. Depending on the individual problem, there may only exist a handful of feasible solutions which might all be known after a few iterations. Hence, the additional attempt can fail, too, raising the question whether to try for a third time, etc. At
204
(85) is derived from the random acceptance function of Simulated Annealing. For details see 4.3.3, pp. 97.
4.2. Iterative Planning Steps
87
some point the process clearly has to come to a halt in order to avoid endless looping. To resolve this final issue, we again draw a random number r2 and use a simple acceptance function, namely the ratio of one over the number of attempts to generate a new pattern, i.e. p2 =
1 N
(86)
where N stands for the number of attempts. Just as above, the process of generating additional compromises is continued, when r2 is smaller than p2, and terminates otherwise. That is, a second attempt is always made, a third with probability 0.5, etc. Terminating without a new compromise proposals then indeed means that the entire collaborative planning process stops due to the lack of a new proposal to be made to the partner. The total sequence of decisions and process steps is visualized by the flow chart in Fig. 23. Initial compromise
Equivalence??
no
New proposal
no
Termination
yes Next attempt? yes Additional compromise
Fig. 23. Compromise generation process flow
4.2.4.2
Model-based approach for additional compromise proposals
As mentioned above, a GP model formulation devised from Model 6 and Model 7 can be utilized to obtain additional compromise proposals. The underlying idea again builds upon the definition of two conflicting objectives with associated target values. These objectives are to minimize the deviation from • the optimal GP objective function value of Model 6 / Model 7, and • a target characteristic of the additional compromise proposal.
The first objective should be immediately clear. Since solving Model 6 or Model 7 yields the optimal value of the GP objective function, the additional compromise should bring a solution as close as possible to the optimum.
88
4. Negotiation-Based Collaborative Planning between Two Partners
The rationale behind the second objective is as follows. We define target properties for the additional compromise which correspond to a maximum differentiation from the pattern generated by Model 6 / Model 7. By stating that the additional compromise should be as close as possible to these target properties, we hope to find a solution that substantially differs from the known compromise. As a basis for the target properties, item-specific distance measures dj can be used as defined in (69). Corresponding values can be easily computed ex-post from the partner’s proposal and the order / supply pattern obtained by Model 6 / Model 7. The set of item-specific distance measures can be referred to as a vector v of dimension JS : v = (d1 , d 2 ,..., d
JS
)
(87)
Given such a vector v we can define a target “point” by a second vector vT which is at a maximum distance from v and has component values according to vT = ( D1 , D2 ,..., D JS ) (88) As an example, consider a two-item case with a known compromise proposal with, say, v=(0.05, 0.8). Here, the target point corresponds to vT=(1.0, 0.0). The example demonstrates that the target point always has extreme component values of 0 or 1. Otherwise a more distant target point could be determined by replacing any other component value with either 0 or 1, depending on whether it is smaller or greater than 0.5. The exact procedure of how to determine the target values of vT based on one or several known compromise solutions with corresponding vectors v is discussed below. For the moment we assume that a target point with component values Dj can be specified. Given the target point on the one hand and the optimal objective function value of Model 6 / Model 7 (referred to as G) on the other, the GP Model 8 can be used to obtain an additional compromise proposal (for the buyer). Model 8. CP(Buyer)-3 Data wj weight of item j in distance measure and deviation from target point Dj target value for relative distance of item j (component of vT) Djmax maximum absolute distance of item j G optimal GP objective function value (CP-2 solution) Variables dj relative distance of item j dpj positive deviation from target distance of j dnj negative deviation from target distance of j gp relative deviation from optimal GP objective function value
4.2. Iterative Planning Steps
89
Formulation 1
min
s.t.
W
C
+W
D
−G
gp +
∑ w j (dp j
j∈JS
(3) - (9), (29) - (34) ⎞ 1 ⎛ d j = max ⎜⎜ ∑ (d +j ,t + d −j ,t ) ⎟⎟ D j ⎝ t∈T ⎠
+ dn j )
∀j ∈ JS
(89)
(90)
∑ w jd j
(91)
c − ∆ = C min
(92)
⎛ ⎞ WC ⎜ ∆ + W D d ⎟ − gp = G ⎜ C max − C min ⎟ ⎝ ⎠ d j − dp j + dn j = D j
(93)
d=
j∈JS
∀j ∈ JS
(94)
Model 8 contains the following modifications compared to the original Model 6: the relative item-specific distance is captured within the model by variables dj (constraints (90)), additional constraints (93) and (94) measure the deviation from the two goal targets discussed above, and the objective function aims at minimizing the deviations from the new goal targets. The left-hand-side of (93) contains the original GP objective function of Model 6 and gp, a measure of its deviation from the optimal value G, which represents the right-hand-side. Constraints (94) keep track of positive or negative deviations from the target point values according to Dj.205 The objective function (89) comprises deviation variables associated with both goals. gp is normalized to the interval [0,1] by the maximum value that it can ever take. This upper bound corresponds to the sum of the two original GP weights WC and WD less the optimal value to the original GP model (G). Target point deviations are averaged by the weights wj to give a single deviation measure between 0 and 1. The corresponding formulation for the supplier is fully equivalent and given in Model 9 only for completeness. Model 9. CP(Supplier)-3 Formulation min
s.t.
205
1
W
C
+W
D
−G
gp +
∑ w j (dp j
j∈JS
(3) - (9), (36) - (40) ⎞ 1 ⎛ d j = max ⎜⎜ ∑ (d +j ,t + d −j ,t ) ⎟⎟ D j ⎝ t∈T ⎠
+ dn j )
∀j ∈ JS
(95)
(96)
Depending on the value of Dj (0 or 1) either positive or negative deviations can occur.
90
4. Negotiation-Based Collaborative Planning between Two Partners
∑ w jd j
(97)
c − ∆ = C min
(98)
⎛ ⎞ WC ⎜ ∆ + W D d ⎟ − gp = G ⎜ C max − C min ⎟ ⎝ ⎠ d j − dp j + dn j = D j
(99)
d=
j∈JS
∀j ∈ JS
(100)
Solving Model 8 / Model 9 yields another compromise solution. It is intended to yield a value to the original GP objective which is as close as possible to its optimum as determined before. In addition the new solution also comes as close as possible to the target distance measures, so that a substantial difference from the order / supply quantities associated with the original compromise is hopefully realized. However, since there is no guarantee that a differing pattern can be obtained, comparisons with former compromises and deduction of appropriate action is newly required, as implied by the flow chart of Fig. 23. As a final point a general approach for determining the target point vT needs to be set forth. In general, there can already exist a set of compromise solutions obtained within the current iteration which are all considered equivalent to formerly generated compromises. For each such compromise solution there is a vector vi of relative item-specific distance measures. As argued above, potential target points are made up by combinations of extreme values (0,1) for each component j. Hence, when JS items are contained in JS
candidate target points. The the order / supply pattern, there is a total of 2 ideal target point is at a maximum distance to all known compromise solutions vi. It can be identified as follows: For each candidate point the distance to all existing compromise solutions vi is computed in order to find the closest compromise point and the associated minimum distance. Then, the target point can be chosen as the candidate with the largest minimum distance to any known compromise solution. To avoid additional complexity, the distance is calculated using the L1-norm as introduced above. Thus, given a compromise solution with vector vi and a candidate point vCP, the distance is formally obtained as (101) ∆ = ∑ D −d CP ,i
j∈JS
CP , j
i, j
A candidate’s minimum distance to any one compromise can be found as ∆ CP = min( ∆ CP ,i ) (102) i =1.. N
Then, the candidate with the largest minimum distance is chosen as target point. A watch-out comes into play when Model 8 / Model 9 is repeatedly used within one iteration and hence target points are determined several times. Repeated use of one identical target point has to be avoided here, since this would yield the same compromise solution as seen before. In consequence, once target points are selected, they have to be deleted from the list of candidates.
4.3. Collaborative Planning Process in Total
91
JS
This makes apparent that the approach offers a maximum of 2 attempts to find a new compromise proposal. Thereafter, no candidate points are left over. However, since the probability of additional attempts declines with a growing number of unsuccessful (equivalent) solutions as discussed above, the number of candidate points is usually sufficiently large. In case it becomes empty in some instances, the process halts without a new compromise proposal.
4.3
Collaborative Planning Process in Total
So far we have considered the distinct planning steps carried out by the collaboration partners in each iteration. In short, these comprise the evaluation of the order / supply pattern proposed by the partner and the generation of a new counter proposal in return. Now we turn our attention towards the total sequence of these process steps and the interactions between the collaboration partners. In tackling this issue, we first discuss the data items that need to be exchanged. Thereafter, the resulting total process flow is considered. Stopping criteria which can be used to ultimately halt the planning process are laid out as a final point. 4.3.1
Data exchange requirements
Two categories of data have to be transmitted between the planning domains in the collaborative planning process. For one, the order / supply patterns pertaining to compromise proposals need to be announced to the partner. Second, data regarding the cost effects associated with compromise proposals have to be communicated. Both categories are discussed in more detail in the following. 4.3.1.1
Order / supply patterns
Order / supply patterns make up the basic pieces of data exchanged between the planning domains. Therefore, we consider how they are obtained from the compromise solutions to the GP models from the distinct perspectives of the supplier and the buyer. As described above, the supplier receives order quantities from the buyer referred to as XOj,t. For generating a compromise proposal a partial deviation from the requested quantities is permitted. In result, quantities planned for delivery correspond to the values of variables xoj,t which can differ from the quantities proposed by the buyer due to constraints (38) of Model 7.206 The new compromise
206
See p. 74 and p. 65.
4. Negotiation-Based Collaborative Planning between Two Partners
92
supply pattern consists of the xoj,t variable values, i.e. supply quantities XSj,t proposed to the buyer are obtained according to XS j ,t = xo j ,t ∀j ∈ JS , t (103) The buyer receives supply proposals XSj,t from the supplier. In his compromise counter-proposal, values of supply variable xsj,t can deviate from received quantities XSj,t due to constraints (31) of Model 6.207 Hence, the compromise order pattern could directly be derived from supply quantity variables xsj,t. However, the actual consumption of supply items can take place later than their scheduled delivery expressed by xsj,t. This is captured by balance equations (30) in Model 6. Now, in order to ensure feasibility of the buyer’s plan, a sufficient item supply relative to the planned consumption has to be guaranteed. Therefore, consumption quantities rather than modified supply quantities can form the compromise order pattern. The order quantities XOj,t transmitted to the supplier thus are calculated as in (30) by (104) XO j ,t = ∑ r j , k xk ,t ∀j ∈ JS , t k∈S j
It should however be noted that the computation of order quantities from the consumption of supply items as in (104) requires an adaptation of the “compromise comparison” process step described above.208 Now the pattern comparison needs to be based on cumulated consumption quantities xc cum j ,t rather than cumu209 lated supply quantities xs cum j ,t as stated in equation (79).
Finally, if minimum supply requirements derived from the buyer’s final demand forecasts shall be used by the supplier as shift limits, the buyer also needs to 210 announce corresponding minimum cumulated quantities E cum j ,t as given in (44). Since these quantities do not change during collaborative planning, it is sufficient to transmit them only once, at the beginning of the collaborative planning scheme along with the buyer’s initial order pattern. 4.3.1.2
Cost information
Throughout this chapter a trustworthy behavior of the collaboration partners is assumed which includes the truthful communication of cost data. Of course, when it comes to communicating cost effects, the correctness of data received from the collaboration partner cannot always be taken for granted. Therefore further limita-
207 208 209 210
See p. 73 and p. 64. See section 4.2.4.1, p. 84. See p. 84. See p. 67.
4.3. Collaborative Planning Process in Total
93
tions to the exchange of cost effects can be considered in order to reduce cheating incentives. This is dealt with in more detail in a separate section below.211 The objective of the collaborative planning process is to reduce total cost compared to the initial outcome obtained by Upstream Planning. Any improved situation bears savings to the supplier but cost increases to the buyer, since his optimal plan is the starting point of the negotiation. A total improvement thus occurs when the supplier’s savings outweigh the buyer’s cost increases. To determine the total cost outcome associated with a compromise proposal, it is therefore necessary to transmit the effect of the compromise solution on local costs along with the order / supply pattern. Given these data, the partner can evaluate the proposed pattern and determine the effect on total SC costs by adding the partner’s and his local cost effect. An intuitive suggestion here is to ask the collaboration partners to announce to the partner their total costs associated with a compromise. However, it is actually sufficient, if each partner announces the cost difference between his initial Upstream solution and the compromise proposal. For the supplier, this difference usually represents savings as a compromise improves his situation vs. Upstream Planning. For the buyer, on the contrary, the difference represents a cost increase, because the initial Upstream plan is locally optimal. Mathematically, when CSUP refers to the supplier’s initial Upstream solution and CS*,i to the cost associated with the supplier’s compromise proposal in iteration i,212 the supplier’s local savings associated with the compromise can be calculated as (105) ∆C i = C UP − C *,i S
S
S
From the buyer’s perspective, the local cost increase pertaining to a compromise generated by the buyer can be calculated as (106) ∆C i = C UP − (C *,i − ∑ ∑ ch is *,i ) B
B
B
t∈T j∈JS
j
j ,t
with CBUP representing the cost resulting from the buyer’s initial Upstream solution and CB*,i the cost associated with his current compromise proposal (is*j,t represent supply item inventory levels within the compromise solution). Since the compromise order pattern is derived from consumption quantities as described in the previous section, inventory holding costs of supply items potentially contained in CB*,i must be deducted. In conclusion, the cost effect as given in (105) is computed by the supplier and transmitted along with the compromise supply pattern to the buyer. The buyer, on the other hand, calculates the local effects of his compromise proposals based on
211
212
See section 5.3, pp. 125. Also, cheating incentives and potential counter-actions are analyzed in 6.2, pp. 147. CSUP represents the solution to Model 3 (see p. 63) based on the buyer’s initial order pattern and CS* the (compromise) solution to Model 7 (see p. 74). The definition of an “iteration” follows below in 4.3.2, p. 94.
4. Negotiation-Based Collaborative Planning between Two Partners
94
(109) and transmits them together with the compromise order pattern to the supplier. A second piece of cost information, which needs to be communicated to the collaboration partner, is the cost increase caused by the partner’s current compromise proposal. It is required for the anticipation of partner cost increases as described above.213 Since the partner’s current compromise is derived from the proposal made in the previous iteration, here the cost increase is to be measured vs. the cost associated with this previous compromise. Hence, it can be computed for the supplier as (107) ∆P i = C max,i − C *,i −1 S
S
S
In (107) CSmax,i refers to the cost associated with the partner’s current proposal obtained by Model 3. CS*,i-1 represents the cost outcome of the supplier’s previous compromise proposal (iteration i-1). The cost increase is calculated similarly at the buyer’s side. However, inventory holding cost of supply items again have to be subtracted from the total cost result. max,i max,i i ∆PB = (C B − ∑ ∑ ch j is j ,t ) − t∈T j∈JS (108) *,i −1 *,i −1 − ∑ ∑ ch j is j ,t ) (C B t∈T j∈JS The parameters ∆PB/S are communicated to the collaboration partner for being used in the partner cost anticipation scheme as was set forth above. 4.3.2
Total process flow
A cyclical model of the total process flow is shown in Fig. 24. It builds on the sequence of iterative, model-based planning steps as depicted in Fig. 14.214 In addition, activities required for the control of the entire scheme and the transmission of data between the partners are included. As can be expected, the distinct tasks and process steps are equivalent for both partners. The planning models applied at the various tasks and resulting costs are given next to the description of each task. As also indicated in Fig. 24, an iteration is here defined to cover one full process cycle. It starts with the generation of a compromise proposal by the buyer and ends with the evaluation of the counter-proposal generated by the supplier and the application of stopping criteria to the associated outcome in terms of total costs. Thus, one iteration includes the generation of two compromise proposals, one by each partner. For examining the scheme more closely, let us assume that, as the starting point of iteration i, the buyer generates a new compromise and transmits all data to the supplier. The supplier evaluates the pattern by solving Model 3. The local cost ef-
213 214
See section 4.2.3.3, p. 79. See p. 61.
4.3. Collaborative Planning Process in Total
95
fect of the compromise pattern, measured vs. the initial solution as discussed above, is obtained as the difference between resulting costs and the initial Upstream Planning outcome (CSUP) (109) ∆C i ,1 = C UP − C max,i S
S
S
Given the local savings, the supplier can obtain the net cost effect ∆Ci,1 as the sum of local savings and the buyer’s cost increase vs. his initial solution ∆CBUP, calculated by the buyer according to (109) and transmitted along with the compromise patterns as described in the previous section. (110) ∆C i ,1 = ∆C i ,1 + ∆C i ,1 B
S
Also at this point, the supplier computes the cost increase caused the buyer’s new proposal ( ∆PSi ) as given in (107) above. Supplier
Buyer Evaluate partner proposal (Model 2→CBmax,i ) and check improvement
Prepare data and transmit yes
Stop
no
New compromise ?
Generate compromise (Model 7 / 9→CS*,i ) Determine most preferred pattern (Model 5→CSmin,i) yes
Stop
no
Stopping Criteria Go on ? Evaluate partner proposal (Model 3→ CSmax,i) and check improvement
Iteration
end
begin
Stopping Criteria Go on ?
no
Stop
yes
Determine most preferred pattern (Model 4→CBmin,i ) Initialization Locally optimal plan (Model 1→CBUP )
Generate compromise (Model 6 / 8→CB*,i ) New compromise ?
no
Stop
yes
Prepare data and transmit
Fig. 24. Process steps overview
Based on the net cost effect ∆Ci,1, checks can be made on the improvement brought by the new solution compared to the previous and the best outcome known so far. The results of the improvement check form the input to the stopping criterion applied to decide whether the collaborative planning process should be continued or ultimately stopped.215 If the process continues, the remaining iterative planning steps are executed. First, the most preferred outcome is obtained by solving Model 5. Then a new compromise is generated by solving Model 7 and, in case of equivalence to a for-
215
Details regarding improvement checks and stopping criteria follow in the next section.
96
4. Negotiation-Based Collaborative Planning between Two Partners
mer proposal, possibly repeated use of Model 9 as described above.216 In case that no new compromise pattern can be found, the entire scheme halts. On the other hand, when a new compromise proposal is available, the process continues by transmitting all necessary information to the buyer. For that purpose, the supplier calculates the local cost effect of his new compromise according to (105) and transmits the supply patterns as well as the cost effect to the buyer. When the buyer receives the respective data from the supplier, he proceeds analogously to the supplier. Differences occur only in the calculations of cost effects. The local cost effect is measured vs. the locally optimal Upstream solution with costs CBUP so that we obtain UP i,2 max,i max,i ∆C B = C B − ( C B − ∑ ∑ ch j is j ,t ) t∈T j∈JS
(111)
The total effect then results by adding the supplier’s savings associated with his compromise proposal (referred to as ∆CSi,2)
∆C i , 2 = ∆C Bi , 2 + ∆C Si , 2
(112)
Also, the cost increase caused by the supplier’s current proposal ( ∆PBi ) is calculated according to (108). In summary, the following data items have to be exchanged between the partners: • • • • • •
compromise order / supply pattern, local cost effect of compromise pattern ∆CiB/S, cost increase due to partner’s previous proposal ∆PiB/S, total cost effect of previous solution ∆Ci, total cost effect of best solution ∆C*, identifier of best solution.
The total cost effects of the previous and the best solution are required for the improvement checks. The identifier of the best solution is a reference to the best solution detected so far in the process. It serves for re-installing the best solution once the entire process terminates. At the start of the planning process in iteration one, the process is initiated with the buyer’s Upstream solution. The associated order pattern makes up the first proposal transmitted to the supplier. In consequence, the buyer’s cost increase above minimum ∆CB1,1 is zero. The supplier proceeds with evaluating the order pattern. Since the outcome CSmax,1 represents the benchmark value CSUP, here too the local cost effect ∆CS1,1 is zero. Also, the first compromise generation by Model 7 lacks the partner cost increase parameter ∆PB1 as it cannot yet be estimated. Therefore, a buyer’s cost in-
216
That is, the “generate compromise” task in Fig. 24 actually represents an aggregate view of the compromise generation process flow shown in Fig. 23, p. 87.
4.3. Collaborative Planning Process in Total
97
crease equivalent to the supplier’s local savings potential is assumed as a backup solution in iteration one, i.e. (113) ∆P1 = C max,1 − C min,1 B
S
S
Similarly, the supplier’s cost increase caused by the buyer’s compromise proposal cannot yet be calculated as defined in (107), since there is no previous compromise of the supplier available. In order to provide the buyer at least with its possible order of magnitude, the cost increase ∆PS1 is initialized by the difference between the supplier’s initial outcome and his first compromise solution, according to (114) ∆P1 = C max,1 − C *,1 S
S
S
Once the first iteration is completed at the supplier, all necessary data items can be arranged for the buyer and the process can continue as described above. The process flow and associated cost effects are illustrated by an example in Table 9. It shows the iteration number, the direction of the data transmission, the absolute cost outcomes, net cost effects, and the best solution known up to any given point. The process starts with minimal costs for the buyer (98,667 MU) and a total outcome of 228,241 MU. The corresponding net effects are all zero. Based on the initial pattern, the supplier generates a compromise with local savings of 9,452 MU, which causes a cost increase at the buyer of 4,060 MU. In total, net savings of 5,392 MU occur so that a new best solution is found as the second outcome of iteration one (indicated by “1,2”). In iteration 2 the buyer generates a counter proposal which improves his local and the total cost outcome. Hence, the best solution indicator is again updated. The supplier reacts with a new compromise, yielding a substantial improvement of total costs to 211,679 MU. In the following (iteration 3), a degradation of total costs is caused by the buyer proposal. Only in iteration 4 an additional improvement of the total outcome is found. Table 9. Process flow example
It. 1 2 3 4
4.3.3
Flow Dir. B→S S→B B→S S→B B→S S→B B→S
Cost B 98667 102727 100679 105451 103611 106788 102633
Cost S 129574 120122 120459 106228 118299 109172 107850
Cost Total 228241 222849 221138 211679 221910 215960 210483
∆CB
∆CS
0 -4060 -2012 -6784 -4944 -8121 -3966
0 9452 9115 23346 11275 20402 21724
∆C
∆C*
0 5392 7103 16562 6331 12281 17758
0 5392 7103 16562 16562 16562 17758
Best Sol. 1,1 1,2 2,1 2,2 2,2 2,2 4,1
Stopping criteria
As already described in the above section, the stopping criteria determine whether or not to continue the iterative process based on the current, previous and best cost
98
4. Negotiation-Based Collaborative Planning between Two Partners
outcome detected so far. Hence, it makes up an important building block of the entire scheme and influences its overall performance. An intuitive answer to the question of how long to go on with the process is to continue as long as total costs improve. However, it might actually be worthwhile to accept some degradations of the total outcome, because they can give way for additional improvements in subsequent iterations. This situation has a well-known equivalent in meta-heuristics for combinatorial optimization problems. Meta-heuristics, such as Tabu Search and Simulated Annealing,217 often make use of local search procedures which try to improve an existing solution by exploring its “neighborhood”, i.e. solutions derived by incremental permutations of variable values.218 Whenever a neighboring solution improves the objective function, the current solution is updated accordingly and the process continues iteratively. However, a purely improvement-oriented approach gets stuck in a local optimum, where no neighboring solution yields a better objective function value. To overcome this deficiency, several methods are applied in meta-heuristics such as a restart of the local search at a different seed solution or the (occasional) acceptance of a detrimental solution.219 One approach which is transferable to the context here is used in Simulated Annealing, whose name refers to its analogy to the physical process of annealing.220 In Simulated Annealing solutions of a lower quality are accepted with a certain probability. Given a difference ∆ in objective function values between the original (S) and new candidate (S’) solution ∆ = c( S ' ) − c( S ) (115) the probability or acceptance function is expressed for a minimization problem by if ∆ < 0⎫ ⎧1 p = ⎨ −∆ / T ⎬ else ⎭ ⎩ e
(116)
That is, solutions which improve the objective function value, are accepted with probability one. However, the probability that an “uphill move” is accepted diminishes as the parameter T declines and, for a fixed parameter value, small uphill moves are more likely to be accepted than large ones.221 The parameter T, the so-called “temperature”, is adjusted through the course of the search process according to a pre-defined rule. Its purpose is to allow for larger degradations at the start of the search and only for small ones towards the end, so that the search eventually comes to an end. The acceptance decision is made by drawing a random number r from the [0,1] interval. If r is smaller than p, the new solution is accepted, otherwise denied. In case of denial another neighboring candidate solution is picked for examination. The entire search process terminates, when no improved solution is found over a pre-set number of iterations.
217 218 219 220 221
See e.g. Pesch / Voß (1995), pp. 55, for an overview. C.f. Fink (2000), p. 74. See Fink (2000), pp. 77, for an overview of the various counter actions. See e.g. Schocke (2000), pp. 38, Johnson et al. (1989), pp. 867, for details. C.f. Johnson et al. (1989), p. 867.
4.3. Collaborative Planning Process in Total
99
In our context, a stopping criterion is used to decide whether to go on with the negotiation process. Nonetheless, the situation is similar to Simulated Annealing. Improved solutions impose no problem and the process can continue. Detrimental solutions can get accepted, for they can lead to further improvements subsequently. However, the higher the magnitude of a degradation, the smaller are the chances to find a new best solution in following iterations. Thus, an acceptance check similar to Simulated Annealing can be made and the process be terminated in case of denial. To implement the approach, a further specification of the parameters is required. First, once again a normalization is necessary for the magnitude of cost increases. This is necessary, because without normalizing the absolute value of cost increases associated with a solution would influence the acceptance check. As a normalizing constant we can e.g. consider the savings corresponding to the best solution ∆C*, assuming that it is of a value greater than zero. Thus, given savings of the previous (∆Ci-1) and current (∆Ci) solution, we obtain a relative difference measure ∆=
∆C i − ∆C i −1 ∆C *
(117)
The meaning of the normalizing constant is apparent when the previous outcome represents the best one known, i.e. ∆Ci-1=∆C*. In this case a relative increase of value one corresponds to a new solution where all savings generated so far are abandoned and the total outcome is at the level of the initial solution (∆Ci=0). Taking the example of Table 9, the increase from solution 2 of iteration 2 (∆C=16,552) to solution 1 of iteration 3 (∆C=6331), in total 10,221, corresponds to a relative increase of 62% (10,221 / 16,552). Second, the “temperature” parameter has to be specified. Similarly as we used the number of unsuccessful attempts as an indicator for trying to generate additional compromise proposals,222 here the number of solution degradations encountered so far in the process (including the current one), abbreviated by U, can be utilized. In analogy to section 4.2.4.1, we assign a probability p (∆C i −1 − ∆C i = ∆C*) =
1 U
(118)
to the case with a relative cost increase of one. Since the probability according to −
1 T
, the temperature parameter takes the value (119) Resulting is an acceptance function according to
(116) equals at that point to e T = 1 / ln(U )
⎧ 1 ⎪ p=⎨ ∆C i −1 − ∆C i −ln(U ) ⎪e ∆C * ⎩
222
See 4.2.4.1, pp. 84.
if ∆C i −1 − ∆C i < 0⎫ ⎪ ⎬ ⎪ else ⎭
(120)
100
4. Negotiation-Based Collaborative Planning between Two Partners
The functional relationship is shown in Fig. 25 for varying values of U. It can be seen that the first detrimental solution (U=1) always gets accepted, whereas the probability declines with growing values of U and the cost increase. As implied by (118), the probability is 1/U for relative cost increases of one. U
Probability p
1,0
1
0,8 0,6 0,4 2
0,2
3 4 5
0,0 0
0,5
1
1,5
2
Relative Cost Increase
Fig. 25. Acceptance function for detrimental solutions
The approach just developed assumes that the best solution found in the negotiation process offers savings vs. the initial outcome, i.e. ∆C*>0. As this cannot always be guaranteed (in particular, ∆C* is zero in the first iteration), the latter case requires a special treatment. As a simple resolution a probability ⎧1 ⎪ p=⎨1 ⎪⎩U
if ∆C i −1 − ∆C i < 0⎫⎪ ⎬ else ⎪⎭
(121)
is used in this situation, regardless of the magnitude of the degradation. In result, detrimental solutions are accepted and the process is continued with a probability that declines with a growing degree of degradation and increasing number of degraded solutions that were already accepted in the course of the process. In terms of information requirements, both partners need knowledge of the current value of U. It can be transmitted directly in addition to the data items described in the previous section. Alternatively, it can also be updated locally, by inspecting the data received from the partner: Whenever the best solution indicator is not changed by the partner, he accepted a degraded solution. Otherwise, the indicator would have been updated or the process ultimately stopped.
4.4. Summary and Comments
4.4
101
Summary and Comments
The foregoing sections describe a negotiation-based scheme for collaborative planning between two supply chain partners. The underlying principle is to evaluate order / supply patterns proposed by the partner and to introduce modifications which yield an improvement of the local cost situation. As shown in section 4.2, planning models as used for planning of operations within the planning domains can be utilized in all planning steps. Some enhancements to the original models by additional constraints and modified objective functions are required for this task and discussed in detail in paragraphs 4.2.1 through 4.2.4. The resulting collaborative planning process consists of a repeated exchange of order / supply proposals and associated local cost effects. It is controlled by probabilistic acceptance checks for new compromise proposals and total cost outcomes. New compromises, which are considered similar to previous ones, are only accepted with a certain probability that approaches zero in case of full equivalence. In this way, cycling of the planning process is avoided. Detrimental solutions also are accepted with a certain probability depending on the degree of degradation and the progress of the process. In conclusion, the scheme developed here is non-hierarchical in its nature and requires only limited exchange of information between the collaboration partners (order / supply patterns and cost effects). It ensures that an implementable plan is obtained in each iteration so that even an early termination of the process results in compatible plans of buyer and supplier. The scheme aims at improving the cost situation compared to the initial outcome of Upstream Planning. This is possible since modifications to order / supply patterns are introduced where they are most cost effective. However, from a theoretical viewpoint an improvement of total cost can neither be guaranteed nor predicted with some likelihood. Therefore, as it is common practice in the field, a computational study is conducted in chapter 7. Without going into details at this point, it documents that the scheme substantially improves the initial outcome of Upstream Planning in the vast majority of cases. The next chapter deals with the application of the scheme developed here for one-time planning between a single buyer and supplier to more complex supply chain settings. Recommended readings • Schniederjans, M.J. (1995): Goal Programming – Methodology and Applications, Norwell et al. 1995. • Cooper, W.W.: “Abraham Charnes and W.W. Cooper (et al.): A brief history of a long collaboration in developing industrial uses of linear programming”, in: Operations Research, Vol 50(1), 35-41.
102
•
4. Negotiation-Based Collaborative Planning between Two Partners Pesch, E./ Voß, S. (1995): “Strategies with memories: local search in an application oriented environment”, in: OR Spektrum, Vol. 17, 55-66.
5 Extensions to the Basic Collaborative Planning Scheme Content In this chapter we show how the negotiation-based scheme for collaborative planning can be applied to more complex settings than dealt with in the preceding chapter and actually allows to further reduce the amount of cost information exchanged between SC partners. Specifically, we first consider more general SC structures than the single buyer / supplier pair assumed so far. Thereafter, we abandon the restriction that planning happens only one time and comment on how the scheme can be utilized when planning is repeated on a rolling basis. Finally, we focus on limiting the amount of cost information exchanged between collaboration partners. Key points • With limited extensions the negotiation-based scheme can be applied to collaborative planning between one supplier and several buyers, one buyer and several suppliers, and general 2-tier supply chains. • When collaborative planning is repeated on a rolling basis, the scheme should be modified such, that there is a limited “negotiation horizon” over which orders/ supplies are modified. A negotiation over the entire planning horizon is inefficient, as negotiation outcomes of later periods are abandoned in succeeding planning cycles. • The amount of cost information exchanged between the collaborative planning partners can be further reduced to “compensation claims” requested by the buyer(s) from the supplier. The supplier does not need to disclose any cost information.
5.1
Extended Supply Chain Structures
In the following we consider more general SC structures than the two party situation studied in the previous chapter. The collaborative planning scheme as developed above can be applied to such settings, too. 5.1.1
General two-tier supply chains
In this section, we focus on general two-tier SCs. As shown in Fig. 26, three types of two-tier SCs can be encountered next to the basic two-party case dealt with above. In what follows, we first comment on how the collaborative planning
G. Dudek, Collaborative Planning in Supply Chains, 2nd edn., DOI 10.1007/978-3-540-92176-9_5, © Springer-Verlag Berlin Heidelberg 2009
5. Extensions to the Basic Collaborative Planning Scheme
104
scheme can be applied to scenario a) of Fig. 26, where one supplier can exploit the efficiency potential inherent in relationships to multiple buyers. Given our findings in that part, we reverse the perspective and consider a SC where a single buyer is supplied by several vendors. Finally, we obtain a collaborative planning scheme for a general two-tier SC with multiple buyers and suppliers by combining the approaches to a) and b). All assumptions and characteristics laid out at the beginning of chapter 4 for the two-partner scenario are still valid in the following. In particular, we still assume that all partners generate local plans based on Model 1 as presented in chapter 3, and hence can make use of the extended model formulations developed for the various planning steps carried out in the course of the collaborative process. Supplying Stage
Buying Stage
Buying Stage
Supplying Stage
Buyer 1
Supplying Stage
Buying Stage
Buyer 1
Supplier 1
Supplier 1 Buyer 1
Supplier 1 Buyer K
a)
Supplier K
Supplier K
b)
Buyer M
c)
Fig. 26. General two-tier supply chain structures
The only novelty obviously concerns the number of partners involved in the scheme, since multiple suppliers, buyers or both are considered now. The scheme as developed for two partners can be applied to these new settings, because the situation faced by each of the partners remains essentially the same. When one party faces several suppliers or buyers as collaboration partners, their respective order or supply proposals can be combined to give a single order or supply pattern as used before when only one partner was present. Once such a consolidated order or supply proposal is available, the iterative planning steps can be carried out as before, starting with an evaluation of the current pattern and leading to a new compromise proposal to be submitted to the partners. Of course, extensions to the original scheme are still required and are set forth in detail in the remainder. 5.1.1.1
Several buyers
In describing the adaptations to the basic scheme, we follow the total process flow as shown above in Fig. 24.223 Fig. 27 depicts the corresponding flow chart for the single supplier – multiple buyers scenario. Here, each of the buyers of course has to undertake the iterative planning steps shown in the diagram. However, changes
223
See p.97.
5.1. Extended Supply Chain Structures
105
are necessary with respect to some of the original process steps. They relate to those process steps highlighted by a bold frame and are discussed subsequently. At the supplier side, the prevailing novelty is that orders are received from several buyers. In order to account for that change, a new index k (=1..K) is used in the following to reference individual buyers, resulting e.g. in order quantities XOk,j,t per buyer, item and period. This extension affects all planning models and hence all the iterative planning steps as described in 4.2. First, Model 3 which is used to evaluate buyer proposals for their consequences on the supplier, needs to be extended as shown in Model 10. Supplie r
Buye r 1 Evaluate partner proposal and check improvement
Prepare data and transmit yes
Stop
no
....
New compr. ?
Buye r K Evaluate partner proposal and check improvement no
- Go on ?
Stop
yes
Stop
Generate compromise
Determine most preferred pattern
Determine most preferred pattern
Determine most preferred pattern
Generate compromise
Generate compromise
yes
no
Go on ?
New compr. ?
New compr. ? no
yes
Evaluate partner proposal and check improvement
Prepare data and transmit
yes
no
Prepare data and transmit
Fig. 27. Process flow with multiple buyers Model 10. CP-General(Supplier)-0 Indices k buyer 1…K Index sets / boundaries K number of buyers JSk set of items j supplied to buyer k KJj set of buyers k provided with item j Formulation
min c s.t. (3) - (9) T
c=∑
∑ (ch j i j ,t
t =1 j∈J
(122)
i j ,t −1 + x j ,t = E j ,t +
xok , j ,t = XOk , j ,t
T
+cf j y j ,t ) + ∑
∑ cor or ,t
(123)
t =1 r∈R
∑ xok , j ,t + ∑ r j ,k xk ,t + i j ,t
k∈KJ j
∀j ∈ J , t
k∈S j
∀k = 1..K , j ∈ JSk , t
(124) (125)
Order quantities and variables are enhanced by the buyer index k. Therefore, the assignment of proposed orders to order variables in (125) is now specified for
5. Extensions to the Basic Collaborative Planning Scheme
106
all buyers, items and periods. Correspondingly, flow balance equations are updated in (124) to include orders by all of the K buyers. Given the solution to Model 10, the supplier can determine the total cost effect associated with the buyers’ order proposals. In order to do so, the original computation for the two-partner case as defined in (110)224 has to be extended to ∆C i ,1 =
∑
k =1..K
∆C Bi ,1,k + ∆C Si ,1
(126)
where ∆C Bi ,1,k represents the local cost effect of buyer k. This means, that the total net effect is calculated as the sum of individual buyer effects and the supplier’s one. Building on the modifications to Model 3, it is obvious that the supplier’s model for determining the most preferred outcome (Model 5) needs to be revised accordingly. Resulting is an updated formulation as given in Model 11. Model 11. CP-General(Supplier)-1 Formulation K
c +ε ∑
min
T
∑ ∑ (d +k, j,t + d −k, j,t )
(127)
k =1 j∈JSk t =1
s.t.
(3) - (9), (123) - (124) xok , j ,t + d k+, j ,t + d k−, j ,t = XOk , j ,t + d k+, j ,t −1 + d k−, j ,t +1∀k = 1..K , j ∈ JSk , t t
(128)
, min ∑ xok , j , s ≥ XOkcum , j ,t
∀k = 1..K , j ∈ JSk , t
(129)
, max ∑ xok , j , s ≤ XOkcum , j ,t
∀k = 1..K , j ∈ JSk , t
(130)
s =1 t s =1
The extension here for one concerns cumulated minimum and maximum supply quantities which too are now specified by buyer, item and period ((129), (130)). The limit values themselves can be determined in the same manner as with a single buyer by making use of previous and next order periods as described in 4.2.2.225 Secondly, quantity shifts to preceding and succeeding periods d+/d- are obtained for each buyer and item as laid out in (128). Due to that extension, the second term in the objective function is also enhanced by a summation across all buyers. The generation of compromise proposals by goal programming is subject to similar extensions. Here, deviations from order quantities are considered for each buyer separately. The resulting model is given in Model 12.
224 225
See p. 95. See Model 7, pp. 66.
5.1. Extended Supply Chain Structures
107
The model largely rests on the original GP formulation above,226 Buyer-specific deviation measures are determined here as given in (132). The underlying calculation is fully equivalent to the above definition in (71), only that the summation is restricted to the order pattern of each respective buyer. In consequence, a (weighted) sum across all buyer-specific deviations is included in the GP objective function. Model 12. CP-General(Supplier)-2 Formulation
min s.t.
WC max
K
min
∆ + ∑ W kD d k
−C C k =1 (3) - (9), (123) - (124), (128) - (130) wk , j ⎛ ⎞ ⎜ (d + + d k−, j ,t ) ⎟ dk = ∑ max ⎜ ∑ k , j ,t ⎟ j∈JS k Dk , j ⎝ t∈T ⎠
(131)
∀k = 1..K
c − ∆ = C min
(132) (133)
The meaning of the extended objective function becomes clear when we recap that the deviation measures’ weight WD is used for anticipating cost effects resulting for the buyers. According to (76), an estimate of the buyer’s cost increase ∆P is assigned to WD which would follow from suggesting the minimum cost solution Cmin as the compromise.227 With multiple buyers, separate estimates ∆Pk are available as reported by each partner, which are used in the objective function according to WkD = ∆Pk
∀k = 1..K
(134)
Thus, the above GP model trades-off local cost improvements with estimated cost increases for the buyers. The latter follow from deviations introduced to their original order patterns. In that way expected cost increases by buyer direct the compromise generation such that modifications are first suggested to orders of buyers, whose expected cost increases are smaller relative to those of others. This in turn supports the search for solutions that yield a maximum improvement of total SC costs. Finally, the equivalence check of a GP solution to former compromise proposals as well as the generation of additional compromises have to be adapted. The equivalence check can basically be carried out as described above in 4.2.4.1. However, since supply proposals are generated for all the K buyers, the check is performed separately with respect to each individual buyer. An additional compromise needs to be sought for only, if the supply proposals to all buyers are equivalent to what was suggested by the supplier in a previous iteration.
226 227
See p. 74. ∆P is roughly determined from cost effects of previous compromise proposals as laid out above (see pp. 82).
5. Extensions to the Basic Collaborative Planning Scheme
108
In order to generate additional compromise proposals, the original Model 9228 has to be extended in the same way as the models presented above by accounting for multiple buyers. The result is shown in Model 13. The model assumes that the optimum GP objective function value to Model 12 is known and referred to as G and that target points v k ,T = ( Dk ,1 , Dk ,2 ,...Dk , JSk ) have been determined for each buyer’s order pattern as set forth above.229 Model 13. CP-General(Supplier)-3 Data CGP normalizing constant for goal programming objective (see (141) below) Formulation
min s.t.
1 C GP
gp +
1 K
K
∑ ∑
k =1 j∈JS k
wk , j (dp k , j + dn k , j )
(3) - (9), (123) - (124), (128) - (130) ⎞ 1 ⎛ d k , j = max ⎜⎜ ∑ (d k+, j ,t + d k−, j ,t ) ⎟⎟ Dk , j ⎝ t∈T ⎠ dk =
∑ wk , j d k , j
∀k = 1..K , j ∈ JS ∀k = 1..K
j∈JS k
c − ∆ = C min
(135)
(136) (137) (138)
K ⎛ ⎞ WC ⎜ ∆ + ∑ WkD d k ⎟ − gp = G ⎜ C max − C min ⎟ k =1 ⎝ ⎠ d k , j − dpk , j + dnk , j = Dk , j ∀k = 1..K , j ∈ JS
(139) (140)
Relative deviation measures per buyer and item are computed in (136) and subsumed to total deviations per buyer in (137). In (139) the offset from the optimum GP solution of Model 12 is captured by variable gp, whereas positive or negative deviations from the target point values Dk,j are determined in (140). Both, gp and deviations from the target points, are simultaneously minimized in the objective function. The latter are averaged per buyer based on item weights as in the calculation of dk and averaged across all buyers by a simple arithmetic mean. gp’s contribution is accordingly normalized to values between zero and one by a constant CGP. Since the largest value that gp can take is the difference between the maximum and optimum value of (131), CGP can be specified as follows: C GP = (C max − C min ) +
K
∑ WkD − G
(141)
k =1
Solving Model 12 should ideally produce a novel compromise proposal for at least one buyer. If a newly obtained compromise is again equivalent to a former
228 229
See p. 89. See pp. 90.
5.1. Extended Supply Chain Structures
109
constellation, the model can be re-solved with updated target points as described in 4.2.4. At some point the supplier hopefully generates a new compromise counterproposal and the respective supply patterns can be transmitted to the buyers. A last modification is however required with regard to the local cost increase caused by the buyers’ current compromise proposal, ∆PSi , used for cost anticipation in the buyers’ GP models.230 Communicating the entire cost increase to each buyer would assume that each buyer is fully responsible for it due to the compromise proposal he has submitted. However, the cost increase actually results from all buyers’ proposals in conjunction. Therefore, individual buyers would overestimate the harm they cause, if they each used the entire cost increase ∆PSi in their GP models. Therefore, the total cost increase needs to be sub-divided among individual buyers. In order to avoid much additional complexity, the allocation of the cost increase to individual buyers is accomplished here based on their total order volume. That is, the total cost increase is split proportionally among the buyers according to ⎛ ∆PSi ,k = ∆PSi ⎜ ∑ XO k , j ⎜ j∈JS k ⎝
⎞
∑ ∑ XO l , j ⎟⎟
l =1..K j∈JSl
(142)
⎠
where XO k , j represent average order quantities of item j by buyer k. (142) again requires that all quantities are measured in common units or are expressed in their economic value. At the buyers’ side the process continues with the evaluation of the supplier’s compromise proposal. The proposal can be assessed individually by each buyer based on Model 2. However, a major change to the original scheme is required, when it comes to determining the total cost effect of the supplier’s compromise. As each buyer only has knowledge of the effect on his local costs ∆C B,k , a ceni,2
tral agent needs to be established which is notified of the local results and determines the total cost effect according to ∆C i , 2 =
∑
k =1..K
∆C Bi ,,2k + ∆C Si , 2
(143)
Based on that total effect, the central agent can carry out the improvement checks and apply the stopping criteria as described above. In result, he can inform the buyers whether the process continues, in which case they individually take care of the remaining planning steps. The central agent can be either one of the partners (any one buyer or even the supplier) or a third party. A similar situation as with the total cost effect actually concerns the equivalence check of compromise proposals to former ones. In a strict sense, this check needs to be handled centrally by combining all buyers’ individual proposals. However, to keep the process simple, local checks and potentially attempts to generate additional patterns by Model 8 can be made by each buyer. If a buyer is not 230
See 4.2.3.3, pp. 79.
5. Extensions to the Basic Collaborative Planning Scheme
110
able to find a new compromise proposal, he does not abort the process. Instead he transmits all data to the supplier, including a notification that a new proposal was not obtained. The supplier collects information from each buyer and terminates the planning process, when all buyers report that no new pattern was detected. As long as one buyer has found a new compromise proposal, the planning process can continue. 5.1.1.2
Several suppliers
Next we can turn towards scenario b), i.e. multiple suppliers and a single buyer. The corresponding process flow chart is depicted in Fig. 28. As above, modified building blocks are highlighted by a bold frame and discussed subsequently. Supplie r 1
.....
Prepare data and transmit
Supplie r K Prepare data and transmit
yes
no
yes no
New compr. ?
New compr. ?
Buye r Evaluate partner proposal and check improvement Go on ?
no
Stop
yes
Generate compromise
Generate compromise
Determine most preferred pattern
Determine most preferred pattern
Determine most preferred pattern
Generate compromise
Stop
no
yes
yes
Go on ?
Evaluate partner proposal and check improvement
Evaluate partner proposal and check improvement
New compr. ?
no
Stop
yes
Prepare data and transmit
Fig. 28. Process flow with multiple suppliers
An important requirement here is that the buyer specifies order quantities per item and supplier. That is, a situation does not occur, where the buyer announces to order an item and leaves it to the suppliers to decide by whom the order is covered. This assumption is reasonable, because the buyer considers the suppliers as individual collaboration partners which perform planning each on their own. Orders per item and supplier are always obtained in case of “single sourcing” where each item is provided by one dedicated supplier.231 This is the situation we focus on in the following. In laying out the modifications to the original scheme, we start with the buyer’s planning steps. As can be expected, the changes are very similar to those reported for the supplier in scenario a). Namely, all planning models are enhanced by an additional index k to reference individual suppliers. This first concerns Model 2 used to evaluate the proposals made by suppliers. Since the model extensions are fully equivalent to those of Model 3 as presented in Model 10 above, a reprint of
231
C.f. Christopher (2005), pp. 40.
5.1. Extended Supply Chain Structures
111
the model is omitted at this point. It should be clear that supply quantities by supplier and item, i.e. XSk,j,t, are used now. Based on the solution to the extended version of Model 2, the buyer can determine the total cost effect ∆Ci,2 associated with the suppliers’ current proposals. For that purpose the computation given in (132)232 needs to be reversed to include cost effects of each supplier according to ∆C i , 2 = ∆C Bi , 2 +
∑
k =1..K
∆C Si ,,2k
(144)
Assuming that the scheme continues, the buyer can carry out all remaining planning steps once again by using appropriately modified versions of the respective planning models. In particular, shift quantities by supplier and item ( d k+, j ,t / d k−, j ,t ) are used in Model 4 and deviation measures by supplier dk in goal programming of Model 6 and Model 8, as described from the supplier’s perspective in Model 11 to Model 13. Since cost increase estimates ∆Pk are expressed per supplier, the compromise generation again favors shifts where they are least costly. Before transmitting the new order patterns to the suppliers, the cost increase factor ∆PBi needed for cost anticipation finally needs is subdivided by supplier. Similar to the supplier’s perspective discussed above, a cost increase by partner is roughly obtained as a portion of the total increase based upon each partner’s supply volume ⎛ ∆PBi ,k = ∆PBi ⎜ ∑ XS k , j ⎜ j∈JS k ⎝
⎞
∑ ∑ XS l , j ⎟⎟
l =1..K j∈JSl
⎠
(145)
Once the suppliers receive all data, they can each evaluate the new proposal for its effect on their local costs. However, just as above in the case of multiple buyers, the total outcome can only be assessed by summing up all local effects and centralizing the improvement check as indicated by the “Go on ?” – check in Fig. 28. If the centralized improvement check does not halt the process, the remaining iterative planning steps can be carried out by each supplier individually. Concerning the “new compromise” check, each supplier submits the new proposal to the buyer, even if a new compromise was not detected, because, from the buyer’s perspective, it is sufficient that one of the suppliers has obtained a new compromise pattern. In case that no supplier has found a new compromise, the process is terminated by the buyer as explained above. 5.1.1.3
Several buyers and suppliers
Finally, we can tackle the general two-tier structure as shown in part c) of Fig. 26 by meshing the findings related to scenario a) and b). The corresponding process flow can be obtained by replacing the supplier stage of the diagram in Fig. 27 with the flow chart for multiple suppliers as shown in Fig. 28. In result, a central agent 232
See p. 89.
5. Extensions to the Basic Collaborative Planning Scheme
112
is required here for assessing the cost improvement at both tiers, since multiple parties are present at the supplier as well as at the buyer stage.233 Beyond that, the checks for new compromises also have to be centralized, as only a part of the overall order or supply pattern is relevant for each individual partner. 5.1.2
Multi-tier supply chains
In the previous section we demonstrated how the collaborative planning scheme can be applied to general SC structures with two tiers. Building on these results, we now expand the scope farther to deal with general SCs that consist of several tiers. Tier 4
Tier 3
Tier 2
Tier 1
Partner 4,1
Partner 3,1
Partner 2,1
Partner
1,1
Partner 4,K(4)
Partner 3,K(3)
Partner 2,K(2)
Partner
1,K(1)
Fig. 29. General multi-tier supply chain structure
This requires for one that no cyclic supply relationships are present between any two partners, not even indirectly via some intermediate SC members. Moreover, each supplier must provide items only to partners that are located at the next downstream tier and, vice versa, each buyer receives items only from partners of the adjacent upstream tier. This general situation is depicted in Fig. 29. As laid out in the previous section, we again presume all assumptions presented in chapters 3 and 4 as valid, except for the SC structure and number of partners involved. The negotiation-based scheme as developed in chapter 4 cannot be directly applied to this setting, because it assumes that each partner acts strictly as a buyer or a supplier. In the situation faced here with more than two tiers, at least some of the collaboration partners are buyers and suppliers at the same time, namely the members of tier two and any other “intermediate” tier. Principally, the original scheme could be expanded such that a planning domain can receive order proposals from buyers and supply proposals from suppliers simultaneously. It would then evaluate the proposals for their consequences on local
233
There can either be a single central agent responsible for the improvement checks at both tiers, or two distinctive central agents (one at each tier).
5.1. Extended Supply Chain Structures
113
planning and generate compromise counter-proposals to buyers and suppliers at the same time. This would however require fundamental changes to the models used at the various planning steps and is therefore not discussed in detail here. Instead, we lay out how the basic scheme designed for two tiers can be utilized in the multi-tier structure. In essence, this becomes possible by splitting up the overall problem such that only two tiers are regarded at any one time. Two such “decomposition” approaches are possible. In the first approach, collaborative planning takes place in an interface-byinterface manner in upstream direction. In a first phase, planning domains of tiers one and two perform the negotiation-based planning process just as discussed in the foregoing section. Once they settle to a specific outcome, the resulting supply quantities provided to tier one are fixed. Now collaborative planning can be initiated between tier two (acting as the buying stage) and tier three. Tier 4
Negotiation 3
Tier 3
Tier 2
Negotiation 2
Tier 1
Negotiation 1
Fig. 30. Interface-by-interface planning process
At some point in time the partners of tier two and three agree on a solution which still ensures that the demand expressed by tier one can be covered. Then, tier three can consider the negotiation outcome towards tier two as fixed and initiate collaborative planning with tier four, and so forth. This process is visualized in Fig. 30. In consequence, collaborative planning takes place sequentially at the interfaces between any two tiers until an overall agreed upon plan for the entire SC is obtained. The resulting plan and associated total SC costs hopefully represent an improved outcome compared to what could have been realized by mere Upstream Planning as described in section 3.3.2.1.234 This can however not be guaranteed. In fact, even an increase in total costs compared to Upstream Planning can occur. This is because the interface-by-interface planning process bears the risk that the outcome fixed at a downstream interface poses such unfavorable consequences on subsequent tiers that total SC costs grow higher than without any negotiations.
234
See p. 46.
114
5. Extensions to the Basic Collaborative Planning Scheme
Of course, one may think of modifications to the overall process that decrease this risk. One possibility is for example as follows. When the planning process is finished at one interface, then the best outcome needs not to be fixed automatically. Instead, all or say the X-best outcomes can be tested for their consequences on the next upstream tier. The outcome ultimately picked should be the one which results in the lowest cost across the two tiers that have negotiated and the upstream tier. The corresponding outcome is then fixed and serves as the basis for collaborative planning at the succeeding interface. In that way the risk to run into a high cost situation for the entire SC is not eliminated, but at least the negotiation outcome is chosen which is most advantageous with respect to the next upstream tier. Another possibility is to re-visit a downstream interface in case that some predefined events occur at subsequent tiers, e.g. capacity overruns, which cannot be resolved by a negotiation at the corresponding interface. In such incidences others than the best outcome at the downstream interface can be tried as basis for planning at the current location, offering a chance to obtain better results than with the initial one. Tier 4
Tier 3 Tier 2 Negotiation 2
Tier 1
Negotiation 1
Negotiation 3 Fig. 31. Bilateral negotiations in multi-tier supply chain
Finally, we briefly outline a second, completely different approach to negotiation-based collaborative planning in the multi-tier structure. The basic idea here is to start with an existing overall SC plan, e.g. obtained by Upstream Planning, and to perform collaborative planning selectively at some chosen interfaces. This is indicated in Fig. 31 where collaborative planning processes are represented by bold arrows. When the “buyer” within any internal supply relationship considers the demand he faces from downstream partners as fixed, he can enter into collaborative planning with one of his suppliers with the objective to improve their joint costs compared to the status quo. This can be accomplished with the basic twopartner scheme described in chapter 4. Actually, various of such bilateral negotiations can take place simultaneously at different interfaces within the SC. Unlike the interface-by-interface approach, here degraded solutions as compared to the status quo cannot occur, for they would simply not replace the existing outcome of two partners. Also, since cost
5.2. Planning on a Rolling Basis
115
improvements can be clearly attributed to individual supply relations, savings can be directly shared between the two partners involved in each such negotiation. On the other hand, it can be doubted whether the full improvement potential vs. Upstream Planning can be realized by negotiations at some interfaces, while plans remain fixed at others. Nonetheless, the approach offers an easy to implement way to achieve improvements compared to an existing status quo situation. The above paragraphs make apparent that the collaborative planning scheme can be utilized and be of value in more general SC structures. Of course, it is here even more difficult than in the two-partner situation to predict which improvements in costs can be realized. Also, potential pitfalls have to be watched out for, as we have seen in the interface-by-interface planning process which might eventually result in overall increases of total costs.
5.2
Planning on a Rolling Basis
In real-world planning is not a one-time issue, but is repeated periodically. This is because decision problems usually exist for longer time frames than can be covered by a single decision support model and, even if that could be realized, reliable information on input parameters is not available over long time periods.235 As a consequence, planning models as used throughout this work consider a relatively small number of future periods. In order to obtain planning results for the time beyond the periods included in the model, planning results could be implemented as far as available and a new planning cycle be initiated when the end of the planning interval is reached. However, implementing results up to the planning horizon is usually not recommended as the (forecast) quality of input data declines from period to period. One may argue that the time interval covered by a planning model could be limited to a time frame for which reliable input data is available. This however leads to poor planning results due to the so-called “truncated horizon effect”:236 If a model only covers a short time interval, then results are of a poor quality with respect to subsequent planning cycles, since the decision model implicitly assumes that the planning problem “ends” at planning horizon.237 In consequence, planning models have to cover a sufficiently long time interval, even though only results pertaining to the first or a couple of periods are actually implemented, and plans are re-generated on a rolling basis of one or a few periods. Embedded in such a re-planning mechanism, even exact optimization methods, i.e. algorithms detecting the optimal solution to a finite horizon planning model, produce heuristic solutions to the overall (infinite time) planning problem.238 This
235 236 237
238
C.f. Troßmann (1992), p. 126. C.f. Federgruen / Tzur (1994), p. 457. For example, in production planning a model covers demand only up to the planning horizon, whereas in reality demand also occurs beyond that point in time. C.f. Troßmann (1992), p. 128, Stadtler (2000b), p. 318.
116
5. Extensions to the Basic Collaborative Planning Scheme
gives rise to a number of questions concerning the performance of solution methods and the influence of various design parameters. Many of these questions have been tackled in literature on operations planning. One such issue is to determine the effect of the planning interval length on the overall solution quality. Baker / Peterson (1979) develop an analytic framework to assess the impact of the interval length on resulting average costs per period in production planning with quadratic cost functions. Their result suggests that solutions improve with increasing length, but incremental increases give diminishing additional benefits, i.e. beyond some limit solution improvements become minimal and no longer pay for the extra model complexity.239 Although this result is derived for the special problem studied, it is supported by computational results on more complex problem structures e.g. by De Matta / Guignard (1995) (scheduling of multiple flow lines) and Simpson (1999) (multi-level lot-sizing).240 Contributions by Chand et al. (1992) and Federgruen / Tzur (1994) go in a similar vein in that the authors calculate minimum planning horizons for single item lot-sizing; that is, maximum time spans over which a period’s demand can affect the production decision of the first period. There is no value in extending the planning horizon beyond this bound, since this would not influence period-one decisions. However, calculations of minimum horizons prove to be cumbersome and cannot be generalized to more complex problem settings.241 Another idea is to keep the planning horizon short, but to define terminal conditions in the form of additional constraints to the planning model which improve overall solutions. This is proposed being more effective than longer horizons by McClain / Thomas (1977) and supported by analytic results by Baker / Peterson (1979) who investigate this matter, too.242 Similarly, Stadtler (2000) suggests to reduce setup costs in single item lotsizing for setups towards the end of the horizon when corresponding lots cover demand that occurs beyond the planning horizon. Computational results show that this adaptation outperforms other exact and heuristic lot-sizing methods in resulting costs.243 Another issue concerns the influence of the frozen horizon, i.e. that part of a resulting plan that is implemented before a new planning cycle is initiated. Mostly a re-planning interval of one period is assumed, but principally longer frozen horizons can be chosen and result among others in fewer plan adjustments and hence higher stability. Sridharan et al. (1987) analyze cost effects of different frozen horizons in dynamic lot-sizing by computational tests. Their results imply that no significant efficiency losses occur when the frozen interval is expanded up to half the planning interval, only beyond this limit substantial cost increases are ob-
239 240
241 242 243
C.f. Baker / Peterson (1979), p. 346. C.f. de Matta / Guignard (1995), p. 571, Simpson (1999), p. 21, see also de Matta / Guignard (1994), p. 501. See Chand et al. (1992), pp. 1037, Federgruen / Tzur (1994), pp. 460. C.f. McClain / Thomas (1977), p. 735, Baker / Peterson (1979), p. 349. C.f. Stadtler (2000b), p. 324.
5.2. Planning on a Rolling Basis
117
served.244 However, a crucial assumption of the study is that demand uncertainty is negligible. If, on the contrary, expected and actual demand deviate, re-planning obviously has to take place more often in order to correct for the changes. Related to the length of the frozen interval is the question of plan stability or nervousness. Frequent re-planning ensures an adjustment to updates in input data, but comes at the expense of changes to plan results. These changes are not entirely welcome, as former plan results may have triggered action that becomes partly obsolete when plans are revised. For example, planned production levels can be used to plan for resources such as manpower or supply material. Changes to production levels then also impose modifications to these other decisions. In order to determine the degree of instability, Kimms (1998) proposes a stability measure based on deviations in plan results, weighted by the period they pertain to.245 In that way, changes in early periods contribute more strongly than changes towards the end of the planning horizon. Furthermore, he discusses methods to reduce instability. This can for example be accomplished by adding the stability measure and a bounding limit as an additional constraint to the planning model. A similar proposal is made by Calhoun et al. (2002). They however use a goal programming approach to balance between instability and cost reduction in re-planning.246 Alternatively, plan changes weighted with cost rates can be incorporated into a model’s objective function, thereby capturing their economic effects as suggested by Carlson et al. (1979).247 This however requires to estimate the costs of plan changes. An extensive overview of various approaches of how to increase stability of schedules is given by Jensen (1996).248 We now comment on how the negotiation-based scheme can be enhanced and modified for a situation where collaborative planning is performed on a rolling basis. The discussion is limited to two planning partners as in chapter 4. Again, all findings can be converted to more complex scenarios as considered in the previous section. This is however not explicitly discribed with in the following. Furthermore, we assume that the major parameters of rolling planning are known and given, namely the planning horizon, referred to as TP, and the frozen horizon, abbreviated by TF. The planning horizon should be chosen such that the planning interval covers a full seasonal cycle of demand.249 On the other hand it should be as small as possible given the above observation of diminishing benefits of increased planning horizons. The frozen horizon here defines the period up to which the plan is implemented by the collaboration partners before a new planning cycle is initiated. It covers a small fraction of the planning interval, usually a single or the first few periods.
244 245 246 247 248 249
C.f. Sridharan et al. (1987), pp. 1144. C.f. Kimms (1998), pp. 359. C.f. Calhoun et al. (2002), pp. 161. C.f. Carlson et al. (1979), pp. 756. See Jensen (1996), pp. 102. C.f. Rohde / Wagner (2005), p. 159.
118
5. Extensions to the Basic Collaborative Planning Scheme
From a purely algorithmic perspective, one may argue that, with the planning and frozen horizon given, there is no need for modifications to the collaborative planning scheme. After all, the scheme as developed in chapter 4 can take place in each planning cycle. The only novelty concerns the input data which is updated from one planning cycle to the next. To ensure consistency, a link between individual planning cycles needs to be established such that ending inventory positions resulting from implemented decisions of the previous cycle become starting inventories of the next. However, two reasons still call for changes. First, in the original scheme modifications to order / supply proposals are introduced anywhere across the planning interval. But, assuming that the frozen horizon covers a single period, each period’s negotiated outcomes are discarded (Tp-1)-times, since planning is repeated Tp-times with respect to each period, and only the result associated with the last planning cycle is actually implemented. Hence, “negotiating” over the entire planning interval for a good deal represents a wasted effort. Second, whenever the collaborative planning scheme yields cost improvements vs. the initial Upstream Planning result, this bears savings for the supplier but a cost increase to the buyer. In order to make the new outcome acceptable to the buyer, he must be at minimum compensated for the cost increase. Although contractual implications are regarded in greater detail in the next chapter, it should be clear that the supplier pays a compensation to the buyer for his commitment to the negotiation outcome. However, when only the first (frozen) part of the negotiated plan is implemented, then the exact savings and compensation pertaining to these periods are not known. It would therefore be difficult to devise payments from the negotiation outcome, when a part of the negotiated plan is actually discarded. Given these observations, the extensions presented in the following aim to reduce the inefficiency of repeated but discarded negotiations and to establish a clear basis for determining savings and compensations of individual planning cycles. 5.2.1
Conceptual overview
The key idea here is to define a negotiation horizon TN up to which negotiations take place in each planning cycle. It can take values between the frozen horizon TF and the planning horizon TP. Given the negotiation horizon, modifications to order / supply proposals are no longer considered over the entire planning interval, but only up to TN. On the other hand we require that the negotiation outcome up to TN is entirely committed to by the planning partners. This means that negotiation results beyond TF are not simply discarded. Instead, they are used as a basis, or starting, solution in the next planning cycle. This is visualized in Fig. 32. The two bars represent the buyer’s and supplier’s iterative planning results with orders / supplies according to variables xoj,t or xsj,t. Supply quantities, that ultimately result at the end of the scheme, are referred to as XS*. These supply quantities are implemented up to TF, and form the basis for the next planning cycle regarding periods thereafter.
5.2. Planning on a Rolling Basis
119
The collaborative planning scheme takes place in each planning cycle as before, only that modifications to the order / supply pattern are restricted to periods 1 through TN. The initial order pattern requested by the buyer covers all periods up to the planning horizon TP, so that the supplier too can plan up to TP. Planning results are however only implemented up to TF and used in the buyer’s starting solution of periods 1 to TN-TF in the new planning cycle. schedule s
buyer xs supplier xo TN TF results XS* implemented basis
TP
schedule s+1
TF
TN
TP
implemented basis Fig. 32. Rolling collaborative planning with negotiation horizon
In result, compensation and savings sharing payments can be fully attributed to the periods within the negotiation interval and be granted, when the buyer implements negotiation results up to TF and adheres to them as starting solutions in periods 1 to TN-TF of the subsequent planning cycle. Negotiation “gains” of the next planning cycle can be treated identically, i.e. be granted in addition to those of the previous cycle, when the outcomes are again implemented and used as the starting basis, and so forth. It mainly depends on the uncertainty of underlying planning data, namely on the reliability of demand forecasts, to decide which negotiation horizon can actually be used. The more likely updated information deviates from that used in a previous planning cycle, the fewer of the previous negotiation results form a useful starting solution in the next cycle. In consequence, the result itself as obtained in the previous cycle turns out to be misleading as expected cost reductions were derived from unreliable input data. This makes apparent that the negotiation horizon can reasonably only cover periods up to which the uncertainty of demand, available capacities and other data is limited. Why then not simply use TF as negotiation horizon? In fact, it is always possible to set TN to this minimum value. However, in that case the collaborative planning process can just reveal relatively narrow cost reductions. This is because modifications to order / supply proposals and associated cost reductions are achieved by quantity shifts from one period to another. Hence, the fewer periods
5. Extensions to the Basic Collaborative Planning Scheme
120
are included in the negotiation interval, the fewer cost improving shifts can be introduced. Therefore, the negotiation horizon should be set to as large a value as seems reasonable given the accuracy of input data. Of course, assuming increasing uncertainty from period to period, the negotiation horizon will be limited to a few periods beyond the frozen horizon TF in most situations.250 To give an indication of the influence of the negotiation horizon on costs and other results, different values are analyzed under varying degrees of uncertainty in the computational evaluation in chapter 7.251 5.2.2
Extensions to process flow and planning models
As in section 5.1, extensions to the original collaborative planning scheme are discussed along the resulting total process flow. The corresponding flow chart is depicted in Fig. 33. Modified elements as compared to the original scheme shown in Fig. 24 are highlighted by bold frames. Supplier
Buyer Evaluate supplier proposal up to T N
Prepare data and transmit yes no
Stop
New compr. ?
Evaluate corresponding buyer orders
Generate comprom ise
Determ ine most preferred pattern yes
Stop
no
Go on ?
Stop
Determ ine most preferred pattern Generate comprom ise
Go on ? New compr. ? Evaluate buyer proposal and check improvement
no
yes
Initialization: Optimal plan based on XS* no
Stop
yes
Prepare data and transmit
Fig. 33. Process flow rolling planning
Most changes relate to the buyer’s process steps. In short, these first comprise the incorporation of pre-negotiated supply quantities XS* into the generation of the buyer’s initial plan in iteration one and second the evaluation of supply proposals. An entirely novel element here is formed by an intermediate re-evaluation of the buyer’s orders derived from supply quantities up to TN. Finally, the com250
251
In effect, the partners are confronted with a “negotiation dilemma” as it is advantageous to use a large negotiation horizon from a cost improvement perspective, but to stick to a small negotiation horizon due to the uncertainty of planning data. See section 7.5, p. 201.
5.2. Planning on a Rolling Basis
121
promise generation is slightly adapted at both, buyer and supplier. The modified process steps are described in detail subsequently. The first change concerns the buyer’s initial plan and order proposal. As argued in section 4.3.2, in “one-time” planning the buyer generates his initial plan without any account of available supply quantities. As a consequence, the initial plan represents the buyer’s minimum cost solution which can only degrade in the course of the collaborative planning process. Drawing on the above discussion of the negotiation horizon and starting solution, it is clear that the generation of the initial plan needs to be adapted such that pre-negotiated supply quantities XS* for periods 1 to TN-TF are incorporated.252 For doing so, the following Model 14 can be used in the initial process step. Model 14. Rolling planning – initial buyer model Data TF frozen horizon TN negotiation horizon initial inventory level of item j Ij0 ISj0 initial inventory level of supply item j penalty cost rate for extra supply of item j cxsej Variables xsej,t extra supply quantity of item j, period t Formulation min
TN −TF
c+
∑ ∑
j∈JS
s.t.
t =1
(146)
cxsej xs ej ,t
(3) - (9), (19), (20), (22) xs j ,t = XS *j ,t + xs ej ,t
∀j ∈ JS , t = 1..(TN − TF )
(147)
i j ,0 = I 0j
∀j ∈ J
(148)
is j ,0 = IS 0j
∀j ∈ JS
(149)
The model is largely equivalent to Model 2 as used to evaluate supply proposals.253 The objective is in the first place to minimize the buyer’s cost as defined in (19) while obeying internal constraints as specified in (3) to (9). In addition, constraints (20) ensure that required supply quantities are captured by variables xsj,t. Now, these variables are set to the base values according to XS*j,t for periods 1 to TN-TF in (147), thereby ensuring that the resulting plan adheres to pre-negotiated supply quantities. For the periods beyond TN-TF, supply quantities can be chosen freely as in one-time planning. Furthermore, since updated demand forecasts may require larger supply than expected in the previous planning cycle, extra supply quantities xsej,t can be planned for. Such extra quantities however cause a deviation from pre-agreed supplies XS* which, in effect, costs the buyer a part of the
252 253
See Fig. 32, p. 119. See p. 62.
122
5. Extensions to the Basic Collaborative Planning Scheme
payments agreed upon the previous negotiation outcome. Therefore, they should be limited to an amount strictly needed to cover additional, formerly unexpected demand, and hence are penalized by prohibitive costs in the model’s objective function. For the same reason, smaller supply quantities than agreed upon are not foreseen in the model. If fewer material is actually needed, the surplus is kept in inventory (constraints (20)) and used up in periods after TN-TF. Constraints (148) and (149) describe links to the previous planning cycle (starting inventories of internal and supply items are set to initial values resulting from the previous planning cycle). In summary, solving Model 14 results in the minimum cost plan achievable by obeying pre-agreed supply quantities up to period TN-TF. It should be noted that when the buyer complies to quantities XS*, the initial plan does not necessarily represent his solution with lowest possible cost. Therefore, he might now too realize cost improvements in subsequent iterations. This however does not affect the logic and calculations of the scheme as developed in chapter 4. Once the initial plan is available, the corresponding order pattern can be transmitted to the supplier who carries out the distinct planning steps as before, i.e. evaluates the order pattern, determines his preferred outcome, and generates a compromise counter-proposal. In particular, the compromise generation takes place as before, meaning that modifications are introduced anywhere across periods 1 to TP. Although the negotiation horizon is actually limited to period TN, this is important since modifications in one part of the pattern usually are inter-linked with modifications elsewhere. The only change to the compromise generation concerns the total deviation measure and is described below. When a new compromise proposal is found, the pattern and all related data is transmitted to the buyer. The crucial change as compared to the original scheme regards the evaluation of the supplier’s proposal by the buyer. Here the negotiation horizon comes into play such that supply quantities are considered only up to TN. Beyond the negotiation horizon the buyer ignores supply proposals and freely chooses required supply, as these periods are not yet subject to negotiations. In order to evaluate the proposal up to TN, Model 2254 can be used as before, only constraints (21) have to be replaced by xs j ,t = XS j ,t ∀j ∈ JS , t = 1..TN (150) so that proposed quantities XSj,t are assigned to supply variables xsj,t in periods 1 to TN but are ignored in subsequent periods. With this adaptation, the total cost effect of the supplier’s proposal can no longer be obtained by adding the supplier’s savings associated with the compromise to the buyer’s cost increase. This is because the supplier’s savings can (partly) be caused by quantity shifts occurring beyond TN which accompany shifts in periods 1 to TN. These shifts are however ignored by the buyer. Therefore, in order to determine the actual savings accruing to the supplier only due to his supply proposals in periods 1 to TN, the buyer’s order pattern associated 254
See p. 62.
5.2. Planning on a Rolling Basis
123
with the evaluation step by Model 2 (with constraints (150) instead of (21)) needs to be sent back to the supplier. The supplier determines his actual savings in a completely new process step by evaluating the order pattern with his Model 3.255 ~ He can then communicate his actual savings (referred to as ∆C Si ,2 ) to the buyer who can finally compute the total cost effect according to ~ ∆C i ,2 = ∆C Bi , 2 + ∆C Si , 2
(151)
The above situation is visualized by a demonstrative example in Table 10 based on three items, a planning horizon TP of 6 periods and a negotiation horizon TN of 3. It shows the buyer’s initial pattern of orders, the supplier’s counter-proposal, and the buyer’s order pattern that results when he complies to the supply quantities up to TN, but ignores them in periods thereafter. As can also be seen, the supplier realizes savings of 9,667 MU with his counter-proposal. The buyer faces cost increases of 5,574 MU by obeying to the supply pattern up to TN. Now, resulting total savings of 4,097 MU do not represent the true cost outcome, since the buyer ignores supply proposals beyond TN. Therefore, he needs to transmit the associated order pattern back to the supplier. The orders are equivalent to supply proposals up to TN, but partly differ in periods 4 to 6. By evaluating the associated pattern, the supplier determines actual savings of 7,881 MU which he reports to the buyer. With this information, the buyer can compute actual total savings and proceed to the improvement check. Table 10. Example effects of negotiation horizon
Pattern orders
1
168 77 247 supplies 122 239 247 associated 122 buyer 239 orders 247
2 230 239 347 363 239 299 363 239 299
3 TN 363 239 548 397 239 548 397 239 548
4
5
6 TP 397 158 64 375 81 202 650 0 341 397 24 77 431 0 65 650 0 369 411 0 87 431 0 65 650 169 200
Savings S 0
Increase B Total Savings 0 0
9,667
5,574
4,097
7,881
5,574
2,307
If the process continues after the improvement check, successive planning steps are carried out by the buyer in the usual fashion, only that supply proposals XSj,t are again used as input data only up to period TN as in (150). Finally, as mentioned above an adaptation of the total deviation measure used in the compromise generation by the GP models is helpful, when the collaborative planning scheme is applied on a rolling basis. The adaptation is motivated by the fact that, so far, quantity shifts pertaining to any period contribute equally to total
255
This is indicated in Fig. 33 by the “evaluate corresponding buyer orders” box.
124
5. Extensions to the Basic Collaborative Planning Scheme
deviation as defined in (71).256 This is reasonable in one-time planning, as equal importance is attributed to all shifts regardless whether they concern the first or the last period. This situation however changes in planning on a rolling basis. Since only negotiation results up to the frozen horizon TF are implemented, it is particularly important to exploit the improvement potential that originates in the first couple of periods. A way to induce the compromise generation to put more emphasis on modifications in early periods is by adapting the deviation measure as defined above in (71) accordingly. In particular, period-dependent weights can be used when shifts by period are added to a total shift quantity per item. This extension leads to a new item-specific deviation measure (152) 1 + − dj =
D max j
∑ wt (d j ,t
t∈T
+ d j ,t )
To define the period weights wt. we can draw from the stability measure for rolling schedules as proposed by Kimms (1998). Kimms’ idea is to use the ratio 1 / t as a weight when adding schedule changes by period to a total stability measure.257 In effect, changes in early periods contribute decisively more strongly than changes in late periods. Transferring this concept to the situation here, the ratio needs to be reversed yielding the period index t as weighting factor. The reversion is due to the fact that, here, shifts in late periods should contribute more strongly to the deviation measure, so that shifts in early periods are favored in goal programming. Also, since the sum of weights across all periods must equal to TP,258 a normalizing factor has to be introduced. Resulting is a period weight according to (153) 2t wt =
TP + 1
Incorporating the revised deviation measure into the GP models (constraints (60) and (63), respectively) yields compromise proposals with more modifications in early periods than in late ones. Although we cannot demonstrate analytically that this extension indeed results in an improved performance of the scheme, it proves to yield favorable results in the computational tests reported below. Given all changes and extensions described above, the collaborative planning scheme can be utilized on a rolling basis. As computational results in chapter 7 will show, substantial improvements in total costs as compared to Upstream Planning can be realized in this mode, too.
256 257 258
See p. 77. C.f. Kimms (1998), p. 360. A sum of weights of one would result in a weighted average. Since a weighted sum is sought for here, weights need to add up to TP.
5.3. Limited Exchange of Cost Information
5.3
125
Limited Exchange of Cost Information
The disclosure of sensitive information to SC partners is cited in the introduction to chapter 4 as a major road block to participate in collaborative planning. For that very reason, the collaborative planning process developed above is restricted to the exchange of order / supply patterns and associated cost effects as realized by modifications to the partner’s proposal. The negotiation-based scheme however allows to limit even further the amount of cost data exchanged between the planning partners. In essence, the communication of cost effects can take place only unidirectionally from one partner to the other, but not the other way round. As a consequence, data exchange requirements are farther reduced, and hence objections by SC partners to join in collaborative planning can be potentially reduced. In the following, the limited exchange of cost information and accompanying adaptations to the collaborative planning scheme are first described for the basic two-partner situation. Thereafter, the concept is in turn transferred to more complex SC settings and to planning on a rolling basis. 5.3.1
Limited exchange between two planning partners
It has been argued repeatedly that without collaborative planning, the buyer implements his initial Upstream Planning solution as it represents the cost-optimal plan from his local perspective. In collaborative planning the buyer commits to results which incur higher costs locally, and hence needs to be compensated for the cost increase by the supplier. In other words, the supplier “buys” the buyer’s commitment to the new solution by offering an appropriate reward or bonus. If such a scheme is put into practice, the supplier obviously needs knowledge of the “price” the buyer demands for accepting a compromise solution. However, the buyer does not necessarily have to be informed about the full benefit that accrues to the supplier, as long as he receives his compensation and potentially some additional portion of net savings. Therefore, one may omit the communication of the supplier’s cost effects to the buyer and rearrange the collaborative planning scheme such that only the buyer announces “prices” for accepting compromise solutions. It is then up to the supplier to decide which solution to select given local savings associated with each compromise on the one hand and the buyer’s compensation claims on the other. The flow chart illustrating the collaborative planning scheme modified accordingly is depicted in Fig. 34 and discussed in the following. Those process steps changed compared to the original scheme are again highlighted.
5. Extensions to the Basic Collaborative Planning Scheme
126
Supplier
Buyer
Transmit supply proposal only
Evaluate partner proposal (→C Bmax,i)
yes
Stop
no
New comprom ise ?
Generate comprom ise →C S*,i
Determ ine most preferred pattern →C Smin,i
Iteration
end
Determ ine most preferred pattern →C Bmin,i
begin Generate comprom ise →C B*,i
yes
Stop
no
Stopping Criteria - Go on ?
Evaluate partner proposal (→C Sm ax, i) and check improvement
Check whether new comprom ise found
Initialization (Model 3.1 →C BUP )
Prepare data and transmit
Fig. 34. Process flow with limited exchange of cost effects
First of all, the supplier now transmits only the compromise supply pattern, but no corresponding cost effects as just explained. The major changes then relate to the buyer’s process steps. As the buyer is not aware of the supplier savings associated with a compromise, he cannot perform the improvement check as before. In result, the buyer never terminates the scheme. Instead, he always evaluates the supplier’s proposal, generates a counter-proposal and transmits the compromise order pattern along with the cost increases, i.e. compensation needs, associated with the supplier’s last and his new compromise to the supplier.259 This even happens, if the buyer does not succeed to find a new compromise pattern. In that case, he notifies the supplier accordingly. However, he still needs to transmit the cost effect of the supplier’s last proposal, so that the planning partner can assess this last solution for its total cost outcome. Once the supplier receives the data, he first evaluates the buyer’s new counterproposal and then proceeds to the improvement check and stopping criteria. Here the actual change for the supplier occurs, since not just the current solution corresponding to the buyer’s counter-proposal is inspected for improvement, but also that associated with the supplier’s last compromise. Corresponding total cost effects can be obtained as given in (110) and (115), respectively.260 The logic and decision rule of the improvement check can still remain unchanged. That is, whenever a degradation in total cost is encountered, a stochastic acceptance check according to (120) is carried out.261 The check is first applied to
259 260 261
In the terminology introduced in chapter 4 he transmits ∆CBi-1,2 and ∆CBi,1 (see pp. 95). See p. 95. See p. 99.
5.3. Limited Exchange of Cost Information
127
the outcome of the supplier’s last proposal. If it is accepted, i.e. the scheme is not terminated, then a second check is applied to the solution associated with the buyer’s current proposal. In result, the scheme continues, if both new solutions are accepted. Otherwise, i.e. if one compromise fails to pass the stopping criteria, the scheme terminates. Finally, it should be noted that the buyer’s compromise generation has to be altered slightly. Since no cost data is available from the supplier, the estimate of the partner cost increase ∆PS as used in the cost anticipation described in 4.2.3.3262 is unknown. Therefore, in absence of better information the buyer assumes that the supplier’s cost increase that corresponds to his minimum cost solution CBmin is equivalent to the gain, which he can achieve with that preferred solution, i.e. (154) ∆P i = C max,i − C min,i S
B
B
This “backup” solution is equivalent to the estimation used regularly by the supplier in iteration one, when no better information is available.263 The novel scheme with no disclosure of cost information by the supplier basically leads to similar results as the original one. The first change presented above, i.e. the re-allocation of the assessment of supplier proposals from the buyer to the supplier, does not affect the performance realizable with the scheme, as long as true cost effects are communicated by the buyer. Some performance loss can however be expected from the simplified cost anticipation at the buyer. That change can yield other, less favorable, compromise proposals which in turn can inflict poorer overall solutions. This last point is further analyzed by computational experiments in chapter 7. 5.3.2
Limited exchange between multiple planning partners
In the following we consider limited exchange of cost data in more complex SC settings, as dealt with in section 5.1. A similar approach can be realized here too by restricting the communication of cost effects to one direction and adapting the collaborative planning scheme accordingly. We first regard the scenario with one supplier and multiple buyers. The situation is largely identical to the single supplier and buyer case. Namely, each of the buyers can announce the compensation he requests in order to accept a compromise solution, whereas the supplier can choose the most favorable solution by adding the compensation claims of the buyers and his savings associated with each known compromise. The supplier however does not disclose the total cost benefit accruing to him. The resulting process flow corresponds to that of Fig. 27 only that the centralized improvement check at the buyer tier can be abandoned. Hence, the buyers can separately evaluate the supplier’s proposal, generate new compromises, and send
262 263
See p. 79. See (113), p. 97.
128
5. Extensions to the Basic Collaborative Planning Scheme
the order patterns and respective cost effects to the supplier. The supplier then consolidates the data, evaluates the new order patterns, and determines the total cost effects of his last and the buyers’ new proposals as defined in (126) and (143).264 Given the two total cost outcomes, the supplier can carry out the improvement checks and potentially generate a new compromise proposal to be sent to the buyers as described in 5.1.1. Just as in the situation with a single buyer, the buyers again generate compromises without the estimate of the supplier’s cost increase ∆PS since no cost information is disclosed by the supplier. In consequence, there is no more need for the supplier to subdivide his real increase to estimates per buyer as suggested in (142) within the original scheme for one supplier and multiple buyers. Moreover, in contrast to the original scheme265 no central agent is required any longer to determine the total cost effect of a supplier proposal, since this is done by the supplier himself once each buyer reports his local cost effect. Therefore, not only the amount of exchanged cost data is reduced, but the entire collaborative planning scheme is significantly simplified by the novel approach. The situation is different with a single buyer but multiple suppliers. Principally, the same approach as for the previous scenarios could be applied again, i.e. the buyer could report compensation needs to the suppliers. However, realizing such a scheme would require a central agent at the supplier side to collect and consolidate cost benefits of individual suppliers. Furthermore, a new solution, which proves superior from a total SC perspective, does not necessarily bring cost benefits to all suppliers; some could in fact be worse off than in the initial Upstream solution. Therefore, a possibility of transfer payments between the suppliers would need to be installed. In summary, it seems more appropriate to use a different approach in this situation. An obvious choice herein is to reverse the perspective taken in the preceding scenarios, such that cost data is communicated from the suppliers to the buyer but not in the opposite direction. The resulting process flow corresponds to that in Fig. 28 except for the centralized improvement check at the supplier tier, which is again omitted. Each supplier evaluates the buyer proposal, determines a new compromise, and transmits the compromise pattern together with the local cost effect of the buyer’s proposal ∆CS,ki,1 and of his new proposal ∆CS,ki,2 to the buyer. The buyer evaluates the proposals received from the suppliers, and determines the total cost effect of his last and the supplier’s current proposals according to (126) and (143). Based on this knowledge he can perform the improvement checks to decide whether to continue the scheme or not. In result, no central agent is needed at the supplier tier any longer, as each supplier separately undertakes the various process steps. The communication of cost savings (or eventually hurts) vs. the initial Upstream outcome by the suppliers can be interpreted as the announcement of a maximum “bid” which the supplier is
264 265
See p. 106, p.109. See Fig. 27, p. 105.
5.3. Limited Exchange of Cost Information
129
willing to pay for the buyer’s commitment to a compromise proposal. By paying the entire bid, he would end up with the same cost position as in the initial solution. However, assuming that the buyer shares resulting net savings, he can expect to keep a part of the bid and hence to achieve a better result than in the initial situation. If a compromise yields higher costs at a supplier than the Upstream solution, he can submit a negative bid, i.e. compensation claim, necessary to accept the compromise. In general two-tier SCs with multiple buyers and suppliers, a unidirectional communication of cost data is possible in either one way, i.e. from the buyers to the suppliers or vice-versa. A central agent however must still be in place at the tier which receives the cost information in order to determine total cost effects. Finally, in multi-tier SCs the approach as described for a single buyer and supplier can be easily applied, when bilateral negotiations are carried out at various interfaces as discussed in section 5.1.2.266 Here too the disclosure of cost effects can be restricted to compensation claims announced by the buyer within any one supply relation. 5.3.3
Limited exchange in planning on a rolling basis
The concept of limited exchange of cost information can also be transferred to collaborative planning on a rolling basis. In discussing that matter, we restrict ourselves to the two-partner situation and assume that the modified scheme for planning on a rolling basis as described in section 5.2 is available as the starting point. In this scenario we can make use of the approach as developed for one-time planning between two SC partners in 5.3.1. Basically, the buyer can again claim compensation needs for accepting a compromise solution and leave it up to the supplier to ultimately select the best solution based upon local savings and compensation payments. In result, again no improvement check and no termination of the planning scheme takes place at the buyer. Instead, he always generates compromise proposals and transmits all information to the supplier. The resulting process flow chart corresponds to that of Fig. 33267 without the improvement and new compromise checks at the buyer side. A difference however arises here when the buyer uses the results of the preceding planning cycle as initial supply quantities in periods 1 to TN-TF. Then, as argued in 5.3.1 the initial plan is not necessarily cost-optimal for the buyer. Thus, the buyer himself can eventually realize cost improvements in the course of negotiations with the supplier. In such a case, he should announce his cost benefit as a “bid” for having the corresponding compromise selected as ultimate solution in that planning cycle. In that way the supplier is notified that the compromise is ad-
266 267
See p. 112. See p. 120.
130
5. Extensions to the Basic Collaborative Planning Scheme
vantageous for the buyer too, and can determine the corresponding total cost effect by adding the buyer’s and his local savings.268 In this chapter we developed various extensions to the basic negotiation-based scheme for collaborative planning between a single buyer and supplier. First, in section 5.1 we demonstrated how the scheme can be modified in order to support collaborative planning in more complex SC settings embracing general two-tier SCs as well as SCs with multiple tiers. Section 5.2 dealt with adaptations to the scheme when planning is repeated on a rolling basis. Finally, we have shown how the amount of cost information exchanged between collaboration partners can be farther reduced in order to weaken potential objections for joining in collaborative planning. Next, we turn out attention to the consequences of the collaborative planning scheme on financial flows, i.e. terms of supply contracts, and issues of opportunistic behavior. Recommended readings • Troßmann, E. (1992): “Prinzipien der rollenden Planung”, in: WiSt, Vol. 31992, 123-156. • De Matta, R. / Guignard, M. (1995): “The performance of rolling production schedules in a process industry”, in: IIE Transactions, Vol. 27, 564-573.
268
Alternatively, the buyer could simply refrain from requesting a compensation without disclosing his benefit. However, he would then risk that the supplier chooses another solution which yields higher savings locally.
6 Implications on Supply Contracts and Partner Incentives Content Chapters 4 and 5 describe the negotiation-based scheme for collaborative planning. Thereby the emphasis is laid on conceptual and algorithmic aspects. However, as collaborative planning affects the cost outcomes of involved SC partners, issues relating to the financial flow between the partners need to be considered as well. In particular, the objective is to adapt payments between the parties in such a way that all partners benefit from collaborative planning and hence have an incentive to cooperate with their SC partners. This is dealt with in the following section. Finally, in developing the collaborative planning scheme we have implicitly assumed that cost effects are communicated truthfully by each partner. This might be a very optimistic assumption given that individual partners are self-interested, i.e. follow their individual objectives in the first place. Therefore, we analyze cheating incentives of individual partners and describe potential counter-actions as a final aspect in section 6.2. Key points • In order to give all partners clear incentives to participate in collaborative planning, resulting net savings have to be shared – each partner should receive a significant share of savings. • Compensation and savings share can be added to a base contract existing between buyer(s) and supplier(s) as a bonus, rendered to the buyer(s) after implementation of the resulting plan. A limited flexibility to deviate from agreed to order volumes should however be in place for the buyer(s). • The negotiation scheme and contractual consequences proposed here offer cheating incentives for selfish collaboration partners. They can be lowered by the SC relation itself (i.e. need for a long-term, trustful partnership), controlling and auditing measures and – if needed – by additional modifications to the negotiation scheme.
6.1
Contractual Consequences
As mentioned above in 3.3.1269 supply contracts are the major means to regulate how SC partners intend to do business together and are financially rewarded or penalized. To ensure that all partners benefit from collaborative planning therefore requires to adapt contract terms appropriately. For doing so we first discuss which
269
See p. 42.
G. Dudek, Collaborative Planning in Supply Chains, 2nd edn., DOI 10.1007/978-3-540-92176-9_6, © Springer-Verlag Berlin Heidelberg 2009
6. Implications on Supply Contracts and Partner Incentives
132
additional payments should be granted based on the result of collaborative planning, and secondly how supply contracts can be adjusted for that purpose. 6.1.1
Compensation and savings sharing
Adapting pricing and corresponding payments rendered by one SC partner to another is a regular means to achieve coordination between independent partners as discussed in the literature on SC coordination by contracts. To demonstrate the approach typically proposed there, let us reconsider the basic model by Monahan (1984) to align cost incentives in a two-party lot-sizing situation. As explained above,270 here a buyer faces a single-item lot sizing problem with constant demand, and the supplier produces lot-for-lot whenever an order arrives and bears fixed setup costs. When all information is common knowledge, Monahan shows that the supplier can offer a price discount for orders of the jointly optimal lotsize. In that way, the buyer receives a compensation for ordering a larger quantity than his locally optimal lot-size. By changing to the larger order size and receiving the discount, the buyer is equally well off in terms of total costs, so that no disadvantage accrues to him. The supplier on the other hand realizes true cost savings and thus greater profits. The question with such a purely compensation-oriented approach is whether the buyer accepts to switch his ordering policy or not. After all, he “knows” or least can expect that his SC partner realizes true benefits, otherwise the supplier would not offer the discount in question. Based on a notion of completely rational decision makers as often assumed in economics literature, the resolution is to offer the buyer an additional amount ε>0. No matter how small ε is, it gives the buyer a true financial incentive to switch to the larger order size. However as already noted by Monahan, a potential difficulty with this solution is that “while the proposed price discount may be mutually beneficial to both buyer and supplier, it is certainly not equally beneficial”.271 Experiments in economics research suggest that it is unlikely that human decision makers accept such an outcome. Studies of the bargaining behavior of human beings by experimental economists are usually based on a simple decision problem called “Splitting a Pie” or “Ultimatum Game”. It assumes the following situation:272 A total amount c of monetary units can be split between two players. For doing so, player one demands an amount x (0≤x≤c) for himself, which leaves an amount y=c-x for player two. Now, player two can accept or reject the outcome. If he accepts, the players receive payments x and y, respectively. If not, no payments at all are granted and the game ends.
270 271 272
See p. 42 and Monahan (1984), pp. 721. Monahan (1984), p. 723. C.f. Rasmusen (1994), pp. 275, Güth (1995), p. 330.
6.1. Contractual Consequences
133
When this situation is analyzed by game theory (assuming purely rational, utility maximizing, players273) the outcome is equivalent to the supplier’s discount offer in the model by Monahan. Namely, player one demands x=c-ε where ε is the smallest monetary unit, e.g. one cent, and player two accepts for he receives a benefit, too.274 Experiments with human beings however reveal strikingly different outcomes. Ahlert (1999) reports that, among others, • the most frequent outcome is c/2 for both players, • player one rarely dares to demand the maximal amount c-ε, • player two is willing to sacrifice a payment in order to punish player one for “unfair” behavior.275
Experiments have been conducted by various researchers to get an understanding of determinants of the players’ behavior. For example, effects of anonymity of the players (whether players meet in person or play with anonymous counterparts), gender (behavior of female and male players), or cultural background (effects of geographic or social origins) have been analyzed. Although results indeed show some variations,276 all experiments suggest that “fairness matters but that it is only one of several competing incentives”.277 An interesting observation herein is that both parties may believe that one player deserves a larger or smaller payment depending on his contribution to the fact that an amount c can be shared between the players. Güth / Tietz (1985), for example, auction the position to be player one among a group of individuals. In this constellation, players one feel entitled to receive more since they have paid for being in this position. In result, the average outcome observed is indeed 2c/3 for player one and c/3 for two, showing that players two now accept the strategic advantage of players one.278 Fairness therefore does not seem to be simply perceived as “an equal share to everyone”, but as a share which is linked to the achievements of individual players. Coming back to savings sharing in SCs, the following implications can be drawn from the above discussion. For one, an offer of a small portion of net savings can be rejected by the SC partner even though it brings a financial reward, if the partner believes that benefits are distributed inadequately. Second, one way to determine “objectively appropriate” or fair shares is by considering the efforts or achievements of individual partners. Of course, many more factors can come into play here, for instance the power and leadership structure of the relationship or the dependence of one partner on the other, and vice versa. Nonetheless, it is surprising that the literature on contracts and SC coordination hardly offers quantifiable proposals for savings shar-
273 274 275 276 277 278
C.f. Jost (2001), p. 12, Rasmusen (1994), p. 10. C.f. Rasmusen (1994), p. 276. C.f. Ahlert (1999), pp. 2. See Ahlert (1999), pp. 5, for a brief overview. Güth (1995), p. 332. C.f. Güth / Tietz (1985), pp. 129. The average result is however still far from the outcome predicted by game theory.
134
6. Implications on Supply Contracts and Partner Incentives
ing. For example, in discussing consequences of shared savings contracts on the consumption of indirect materials Corbett / DeCroix (2001) simply state that the supplier receives a fraction λ of net savings, but omit to comment which values λ could or should take or how these could be determined.279 One noteworthy exception from this general trend is offered by Fleischmann (1999) and is briefly introduced in the following. Fleischmann studies the cooperation of two consumer goods manufacturers in distributing their products. The idea is to (partly) combine shipments to identical customers, e.g. warehouses of retail chains, thereby reducing total mileage and duration of transports. The determination of combined shipments and synergy potentials is a complex process which comprises among others a careful analysis of the status-quo and the design of a combined distribution system.280 When a cooperation is beneficial and implemented, it yields cost savings which can be expressed as S = K1 + K 2 − K ′ (155) i.e. as the difference between costs prior to cooperating (K1, K2) and costs of combined distribution (K’). The question then is how to split the savings among the partners. Fleischmann proposes four rules for savings sharing and compares them with respect to consequences on the partners’ total and per unit costs. Candidate rules are: • • • •
a simple 50-50% split of savings, a split of savings proportional to the total shipping quantity per partner, a split of resulting costs (K’) proportional to total quantity per partner, and a split of savings according to the ratio of initial costs K1/K2.
In result, he recommends the last rule (split based on ratio of initial costs) since it is the only rule which guarantees that each partner receives an identical percentage reduction of total and per unit shipping costs.281 This is particularly important, as the partners may in fact be competing companies. Hence, the cooperation in transport should not affect their competitive position one vs. the other. How can the above findings be transferred to the collaborative planning scheme considered here? For discussing that matter, it is again useful to start with the basic two-partner scenario (one buyer / one supplier) and one-time planning. Thereafter, planning on a rolling basis and multiple partners are dealt with subsequently.
279
280 281
C.f. Corbett / DeCroix (2001), p. 885. One should note that the efficiency analysis of the contract in question as conducted in the article is in fact irrespective of the value of λ; hence there is no strict need for the authors to specify how savings are shared. See Fleischmann (1999), pp. 176, for more details. C.f. Fleischmann (1999), p. 184. The other candidate rules can yield odd results such as higher per unit shipping costs than initially (based on rule one), or no savings at all to one partner (based on rule three).
6.1. Contractual Consequences 6.1.1.1
135
Compensation and savings sharing between two partners
First of all, it should be clear that, just as in the model by Monahan (1984), the buyer has to be compensated for any cost increases. Since the negotiation scheme begins with Upstream Planning, i.e. the buyer’s locally optimal plan, the buyer is always confronted with additional costs through the course of negotiations as described in 4.3.2.282 Receiving a compensation for the additional costs associated with the final solution of the negotiation scheme is therefore a minimum requirement for the buyer. Otherwise he could simply refuse being involved in collaborative planning and stick to the initial plan. Secondly, one can ask how to go about the true, net savings that accrue to the supplier. Generally speaking, an acceptable savings sharing arrangement here too depends on the individual SC setting and the relationship of the two partners. A single best arrangement therefore can hardly be presented from a general perspective. Nonetheless, two potential approaches are set forth and discussed in the following. The first represents an even 50-50% split of savings, the second a fixed “collaboration fee” granted by the supplier to the buyer. An equal distribution of savings among the partners as also discussed by Fleischmann (1999) can be justified on grounds of the contribution of each partner. As we have seen above, one result of experimental studies of the ultimatum bargaining game is that players link expectations on appropriate shares to the achievements or contributions of individual parties; e.g. player one deserves a higher share when he has auctioned his position, to recite the example above. If one recaps how each partner contributes to the negotiation-based scheme, an equal distribution of savings appears to be fair. For one, the buyer shows willingness to cooperate instead of just staying with his initial solution. Second, both partners essentially take the same efforts to bring the scheme to work. That is, both have to set up means to exchange necessary data and carry out the respective planning steps as described in chapter 4. Hence, the result of collaborative planning can be equally attributed to both partners, and the natural “focal point” solution based on this line of argument is to share the benefits equally. Of course, individual circumstances come into play here as well, and each partner’s share can be subject to negotiations prior to formally implementing collaborative planning. Still, it is important to note that each partner deserves a substantial share based on the effort and contribution to the planning scheme and should indeed receive it, if the cooperation is intended to be trustful and lasting. A potential drawback of this approach is that the supplier discloses the total amount of savings to the buyer by granting agreed to x%. This is obviously no obstacle as long as cost effects are disclosed by both partners anyway, as it is the case in the original scheme described in chapter 4. However, it might be unattractive to the supplier when the communication of cost effects is limited to the buyer as discussed in section 5.3.283
282 283
See pp. 94. The example of Table 9, p. 97, gives a demonstrative impression. See pp. 125.
136
6. Implications on Supply Contracts and Partner Incentives
This consideration brings us to the second approach to savings sharing which consists of a fixed payment rendered to the buyer. The idea here is to reward the buyer for his cooperation by a “flat rate” regardless of the specific outcome of the negotiation scheme. The introduction of fixed payments is a common way to align incentives between SC partners, for instance in the form of franchising agreements.284 The major question concerning this arrangement is how to specify the amount to be paid. Determinants of an appropriate amount are the efforts in terms of costs or investments undertaken by the buyer on the one hand and expected benefits, i.e. savings, to the supplier on the other. It should be apparent that the costs of setting up the collaborative planning scheme usually need to be smaller than expected benefits, otherwise the whole venture does not pay off. It might however be difficult for the parties to quantify associated efforts and to determine the amount being paid in this way. The alternate approach is to consider expected savings to the supplier and pay the buyer a portion of the expected benefit. Expected savings are neither easy to specify, however their magnitude might be estimated based on e.g. past experience or simulation studies.285 Given the discussion above, the buyer “deserves” a substantial share of expected savings. However, the situation is now insofar different as the buyer receives the agreed amount with certainty, no matter what the outcome of the negotiation scheme actually brings about. The supplier on the other hand bears the risk that actual savings after collaborative planning are smaller than expected. Therefore, the share of savings offered to the buyer can be smaller than with the first approach where the buyer’s reward follows from actual savings. The precise percentage will again be subject to negotiations, but the supplier can justify to offer a share well below 50% of expected net savings. In summary, the fixed payment solution brings an advantage to the supplier in that he does not need to disclose actual savings and can justifiably offer a smaller portion of expected savings to the buyer. The buyer in turn benefits from receiving a guaranteed fixed payment next to the compensation of cost increases. A difficulty can however remain concerning the estimation of expected savings which forms the basis for agreeing to a fixed amount. Table 11 shows a comparative overview of the two approaches to savings sharing as just presented. Of course, still other schemes can be developed. One should however keep in mind that sharing rules should be based only on information that is common knowledge to both partners. Due to that reason, for example, savings sharing proportional to total costs of individual partners as also suggested by Fleischmann (1999) cannot be implemented, since total costs are not disclosed in the collaboration.
284 285
C.f. Lariviere (1999), p. 246, Corbett / DeCroix (2001), p. 885. Fleischmann (1999) too uses simulation analyses in order to determine expected savings (c.f. Fleischmann (1999), p. 178).
6.1. Contractual Consequences
137
Table 11. Savings sharing arrangements
Rule Percentage Sharing (±50%)
Fixed Payment
Characteristics + fair agreement + risk to obtain benefits shared evenly - actual benefits known only after collaborative planning - supplier discloses total savings + supplier can keep total savings private + guaranteed benefit to buyer - risk borne solely by supplier - difficulty to determine appropriate fixed payment
The proposed agreement does not need to be changed substantially when collaborative planning between two partners is repeated on a rolling basis. When the negotiation scheme is adapted for that purpose as laid out in 5.2,286 the only difference concerns the fact that the buyer does not necessarily face cost increases, but might as well realize savings compared to his initial solution.287 Therefore, a compensation payment might not be required, and only supplier savings above the savings realized by the buyer have to be shared. To make the last point clear, let us consider a simple example. Suppose, the buyer realizes savings of 50 MU and the supplier of 100 MU. Then, only 50 MU of supplier savings are subject to a sharing agreement, since the buyer already realizes savings of 50 MU himself. In fact, even a situation can occur where only the buyer obtains savings, while the supplier faces cost increases compared to the initial solution. In this case, the perspective needs to be reversed such that the buyer compensates the supplier for additional costs and shares net savings. Of course, these changes only relate to the percentage sharing rule. When a fixed payment is granted to the buyer, no changes are required. All the above also holds true when bilateral negotiations take place in any arbitrary multi-tier SC structure as described in 5.1.2.288 Since in such a scenario cost improvements are generated at interfaces between two distinct SC partners, savings can be attributed to the two respective partners and be shared between them just as in the basic two-partner situation dealt with thus far. This applies equally to one-time planning and to planning repeated on a rolling basis.
286 287
288
See pp. 115. Because the starting point of the CP scheme is the negotiation outcome of the previous planning cycle. See pp. 112.
6. Implications on Supply Contracts and Partner Incentives
138
6.1.1.2
Compensation and savings sharing in general two-tier supply chains
The situation becomes more complex when several partners are present at one or both tiers of the SC. To investigate how savings sharing can be accomplished here, we pursue the same approach as taken in describing the negotiation scheme for general two-tier SCs in 5.1.1:289 we first consider a scenario with one supplier but several buyers, secondly one with several suppliers and one buyer, and finally multiple partners at both tiers. In all these scenarios we utilize the same sharing rules as described above for two SC partners, i.e. percentage sharing of savings and fixed payments for the buyer(s). However, the presence of several partners at one tier requires some additional thoughts. In a situation where collaborative planning takes place between a single supplier and several buyers, each buyer faces cost increases in the course of negotiations while the supplier realizes savings. Just as in the case of two partners, the foremost consequence hence is for the supplier to render compensation payments to each buyer. Remaining are net savings held by the supplier. When percentage sharing is used to split savings among the partners, we apply the argument that each partner contributes equally by setting up and implementing collaborative planning, so that an equal sharing can be justified again. In result, each partner receives N-1 % of savings when there is a total of N partners (supplier plus buyers). Equal sharing of this kind will most likely be accepted by the partners, if all buyers purchase similar total volumes. If, on the contrary, some buyers purchase significantly more and others significantly less, then this arrangement might not appear fair any longer. This is because large order volumes (on average) contribute more strongly to cost improvements as they offer greater “room for maneuver” in the negotiation process.290 In such a situation a more acceptable sharing scheme would be one which accounts for the total order volume of individual buyers. The percentage sharing rule can be enhanced for this purpose to a two-step sharing scheme. First, percentage sharing can be used to split savings between the supplier and the buyers (e.g. 50-50%). In a second step, the total buyer share can be subdivided proportionally to the total order volume per buyer.291 Thus, when total savings accumulate to S, each buyer k receives a share
289 290
291
See the overview of Fig. 26, p. 104. As an example imagine an extreme case where one buyer orders 1000 units and the other, say, 10. Granting equal savings to each buyer then is a questionable solution. When multiple items are present this obviously requires that these can be measured in common units. An alternative distribution, which avoids a summation across items, could be based on shares of total order volumes per item, or mathematically Sk =
1 x% S 100% JS
∑
j∈JS k
XO k , j
∑ XOl , j
l =1..K
∀k = 1..K
6.1. Contractual Consequences
Sk =
⎛ ⎞ ∑ XO k , j ∑ ∑ XO l , j ⎟ ∀k = 1..K ⎟ l =1..K j∈JSl 100% ⎜⎝ j∈JSk ⎠ x%
S⎜
139
(156)
proportional to his contribution to the total volume ordered by all buyers (x% represents the total share rendered to the buyers). The sharing rule of (156) has the side-effect that each buyer receives an identical discount per unit purchased. This is insofar interesting as the buyers may be competing companies. Since identical discounts per unit do not alter their margins, each buyer’s competitive position relative to other collaborating buyers remains unchanged. As noticed by Fleischmann (1999), this is an important property for getting acceptance by partnering companies that actually are competitors.292 If the fixed payment scheme is utilized, the situation is similar from the angle that payments rendered to individual buyers can be related to their total order volumes in a way as expressed in (156). Of course, the amount actually paid can be negotiated with each buyer individually and his contribution to total volume may only represent a benchmark or orientation point. In a scenario with one buyer but several suppliers the situation differs in some aspects. The buyer is confronted with cost increases as in all the scenarios considered before. Savings accrue to all suppliers in conjunction, but whether individual suppliers realize savings at all and which amount is only known after implementing the negotiation scheme. So who should then compensate the buyer and how to share savings? The easiest way to answer these questions is by pooling the savings obtained by individual suppliers to total, gross savings. The buyer and all suppliers facing cost increases can then be compensated from this total amount. Remaining net savings can now be split among the partners. Percentage sharing can again be either based on fixed percentage values for all partners or, at the supplier side, be proportional to total supplied volumes in analogy to (156). If fixed payments shall be rendered to the buyer, the amount needs to be accumulated across all suppliers. This can again be best handled by pooling gross savings of individual suppliers and paying from the available amount. Of course, the total amount can in some occasions be less than what is promised to the buyer. In these cases each supplier needs to pay an additional, proportional fee. A potential solution for general two-tier SCs with multiple buyers and suppliers can finally be obtained by combining the above schemes for single supplier / several buyers and several suppliers / single buyer. In essence, gross savings of suppliers should be pooled and the total amount be first used to compensate all buyers (and possibly suppliers) for cost increases. Secondly, net savings can be shared according to fixed percentage sharing or based upon total supply and order volumes by individual partners.
292
It yields however shares that are not linked to order volumes, when each buyer purchases distinct items (e.g. when one buyer order 1000 units of item 1 and the other 10 units of item 2, then both still receive equal savings shares of x/2 %). C.f. Fleischmann (1999), p. 184.
140
6. Implications on Supply Contracts and Partner Incentives
6.1.2
Adaptation of supply contracts
In the previous section we discussed which payments should be rendered by the supplier(s) to the buyer(s) in order to ensure that a “fair” win-win situation results for all parties. The main result is that the buyer(s) should receive a compensation for his (their) cost increases and a share of net savings. Now we consider how the contractual setting can be enhanced such that both parties indeed have incentives to implement this result of collaborative planning. As a starting point we assume that, as stated at the beginning of chapter 4, a basic wholesale price contract exists between the partners, i.e. a contract which specifies fixed per unit prices for all items irrespective of total purchasing volumes or quantities by period.293 According to such a basic agreement and given a buyer’s order volume over the planning interval, the buyer so far expects to pay an amount P = ∑ p j ⎛⎜ ∑ XOt , j ⎞⎟ (157) ⎠ ⎝ t∈T j∈JS to the supplier (pj refers to the wholesale price of item j). The objective of modifying the contract terms is to ensure that the result of collaborative planning is implemented and brings the expected benefits to both partners. This means that the buyer should adhere to the order quantities as determined in the planning process, while the supplier should in return reward the buyer by paying the compensation and savings sharing amount associated with the planning result. An appropriate enhancement of the supply contract can consist of a quantity commitment which, generally speaking, specifies that a buyer needs to comply to some pre-defined order quantities. Quantity commitment contracts are discussed and analyzed in the literature. In the following we therefore briefly introduce these contributions and thereafter comment on how to treat the specific situation considered here by quantity commitment contracts. Anupindi / Bassok (1999) describe and analyze several commitment-type contracts as observed in practice. Their major distinction is between contracts with total minimum commitment on the one hand and contracts with periodical commitments on the other.294 Only periodical commitments are regarded in the following, since these are of actual relevance here. Regarding periodical commitments, they farther distinguish two contract types, namely rolling-horizon flexibility and commitments with options. The first case applies to a rolling horizon environment where the buyer commits to purchase certain quantities per period in each planning cycle. In subsequent planning cycles he has a chance to update the quantities within given limits. The magnitude of allowable changes usually grows with in-
293 294
C.f. Lariviere / Porteus (2001), p. 294. C.f. Anupindi / Bassok (1999), pp. 200. Total commitment refers to a minimum purchasing quantity over a given time interval, periodical commitments to certain quantities by period.
6.1. Contractual Consequences
141
creasing horizon. A contract with options too requires the buyer to specify purchasing quantities by period. Here, the buyer can in addition buy options which allow him to adjust the quantities upward on short notice. Anupindi / Bassok assess rolling horizon flexibility contracts in a multi-period news vendor problem. That is, the buyer faces random demand and places orders with the supplier prior to realization of demand.295 Excess inventory at the end of a period forms starting inventory of the next. Based on the commitment contract, the buyer not only places orders for the current period, but also forecasts his order quantities of coming periods. Subsequently, he can deviate from forecasted values within the specified limits. Based on this contract setting Anupindi / Bassok find, among others, that a relatively low flexibility is sufficient for the buyer to come close (within 1%) to his locally optimal performance, whereas the order variability faced by the supplier is significantly reduced.296 Tsay (1999) studies a similar situation in a single period news vendor problem. Here, the buyer first forecasts his order quantity, and the supplier plans production based on the forecast. The buyer can then update his actual order within given bounds after receiving a “signal” of what actual market demand is likely to be. Tsay shows that this commitment contract with flexibility can coordinate the SC, i.e. yields globally optimal performance. In particular, for any given wholesale price paid by the buyer to the supplier, there exists a unique flexibility (deviation bounds) such that the total SC performance is identical to central coordination.297 Also, greater flexibility can be offered for a higher wholesale price, and vice versa; a result in line with intuitive expectation. Finally, Moinzadeh / Nahmias (2000) deal with a contract where the buyer receives fixed deliveries of Q units every T periods in a multi-period news vendor problem. The buyer can increase delivery quantities on short notice without limits, but has to pay a fixed adjustment fee and additional per unit order costs. For this scenario the authors approximately determine the optimal delivery quantity Q, which coordinates the SC, from a central planner’s perspective. As Anupindi / Bassok above, they show that the agreement yields a reduced variance in buyer orders compared to a basic wholesale price contract. However, since the buyer faces cost increases due to the fixed deliveries, the supplier needs to offer an appropriate price discount in order to create a win-win situation.298 In conclusion, the above contributions deal with quantity commitment in news vendor type problems. Commitments here result in lower variance of buyer orders and hence bring in the first place benefits to the supplier. In order to make the arrangement attractive for the buyer too, price discounts are offered. In Anupindi /
295 296
297 298
See 3.3.1, pp. 42, for a brief description of the news vendor problem. C.f. Anupindi / Bassok (1999), p. 221. For example, the buyer requires a flexibility of 10% (25%) when demand coefficient of variation is 0.25 (0.5). Based on a demand coefficient of variation of 0.5 and a flexibility of 5%, the coefficient of variation of buyer orders is only 0.12. C.f. Tsay (1999), p. 1350. C.f. Moinzadeh / Nahmias (2000), p. 419.
142
6. Implications on Supply Contracts and Partner Incentives
Bassok and Tsay, adjustments of order quantities are allowed within given limits. The authors thereby assume that the buyer accepts the bounds and do not comment on what happens, if this is not the case. In Moinzadeh / Nahmias unlimited adjustments can be made, but come at a considerable extra cost to the buyer. This in effect distracts him from deviations unless they are strictly required to cover final demand. To comment on how these observations relate to the situation considered here, we again first consider one-time planning and later broaden the perspective to planning on a rolling basis. Basically, the application of quantity commitments is straightforward. In onetime planning the buyer is asked to comply to negotiated order quantities for all items and over the entire planning interval. In return, he receives a reward which corresponds to the compensation and savings sharing payment. A translation of the total payment to item- and (potentially) period-dependent price discounts is not even required for that purpose. Much rather, the entire payment can be granted as a single (end of time interval) bonus to the buyer. Thus based on (157) above, the total amount paid by the buyer is reduced according to P ′ = P − ∆C − S B (158) where ∆C refers to the compensation and SB to the savings component rendered to the buyer. The question then is how to go about the bonus when the buyer does not fully stick to negotiated quantities. After all, the buyer faces uncertainty of demand forecasts and internal processes. Hence, even when he is principally willing to cooperate, he might at times need to deviate from negotiated orders to some extent. Similarly as with savings sharing, a universal and precise solution for how to deal with such deviations can hardly be given from a general perspective and is instead subject to negotiations of contract terms between SC partners. In order to give some orientation, two potential approaches are nonetheless outlined in the following. Let us start by considering two “extreme” solutions. To one end, the supplier could be asked to pay the bonus, even if the buyer literally ignored the negotiation solution and placed orders in full self-interest. Clearly, this arrangement makes little sense, because it does not give the buyer incentives to comply to negotiated quantities and will not be accepted by the supplier. At the other extreme, imagine the buyer would not receive any bonus at all as soon as he deviated from any one order quantity. This appears to be overly restrictive from the buyer’s point of view. An implementable solution will therefore lie somewhere between these extremes such that the interests of both buyer and supplier are balanced. One approach, which in fact leads to an adjustment of the bonus payment according to the true cost effects of updated orders, is by reevaluating the buyer’s actual order pattern with the supplier’s planning model. Suppose the buyer announces his actual, possibly adjusted, order quantities some time after collaborative planning was completed. This could happen at a single point in time or, more likely, gradually from period to period until the planning horizon is reached. If the supplier solves his planning model based on these actual orders, he obtains a new
6.1. Contractual Consequences
143
cost outcome CS*,adj. which can principally be higher or lower than his original cost outcome of collaborative planning C S* . The cost difference (CS*,adj. − CS* ) can be used to adjust the bonus payment. If the order adjustments increase resulting costs at the supplier, the bonus payment needs to be reduced accordingly. If the opposite is true, it can even be enlarged. In order to fully capture the effect on the bonus payment, the change to the buyer’s compensation also has to be taken into account. As the order adjustments in most cases bring a cost advantage to the buyer, i.e. he introduces changes to his favor, his compensation declines by (C B* − C B*,adj. ) . The above approach may be appealing as the adjustment of the bonus payment is quantified by applying the planning models used in collaborative planning to actual order quantities. However, it is not without difficulties. First, the above cost comparisons are only meaningful, if, by adjusting orders, the buyer only shifts quantities from one period to another without changing the total order volume just as in the collaborative planning scheme. Otherwise the adjustment of the bonus payment based on the difference between original and updated cost outcomes is inappropriate. To highlight this point, imagine the buyer orders only half of the original volume, and the supplier in consequence obtains roughly half of original costs. This obviously does not mean that the new order pattern is more favorable to the supplier and that the buyer’s bonus should be increased by 25% or so. Similarly, changes to other input data can as well cause differences between original and updated cost outcomes, e.g. updated information on demand by other customers of the supplier, changes in available capacities etc. Second, one may argue that the above approach gives a too high degree of freedom to the buyer, since he can principally adjust orders in any desired way, instead of truly committing to negotiated orders. Also, in introducing order adjustments the buyer cannot directly incorporate likely effects on his bonus payment, as he has no information at hand for this purpose. This would however be helpful for trading-off desired adjustments in orders with the associated loss of bonus. To overcome these drawbacks, another, heuristic approach is introduced in the following which gives the buyer orientation on the effects of order adjustments on his bonus and thereby more incentive to comply to negotiated quantities. The approach draws from the above literature in two aspects: quantity flexibility as proposed by Anupindi / Bassok and Tsay and cost penalties for order adjustments as discussed by Moinzadeh / Nahmias. The idea is to split the total bonus to bonus payments by item and period. Each item-period bonus is then granted only, if the buyer complies to the corresponding negotiated order quantity. Obviously, this approach is heuristic as fixed shares are deducted from the total bonus, instead of evaluating actual cost effects of order adjustments. However, it gives both partners a clear perspective on the consequences of deviations from negotiated quantities. In particular, the buyer can incorporate the resulting bonus reductions into internal considerations on adjusting order quantities. To further specify the approach, we first consider in more detail how to split the total bonus to
144
6. Implications on Supply Contracts and Partner Incentives
“sub-boni” by item and period. Secondly, we deal with the flexibility that should be offered to the buyer. We use a simple rule to split the total bonus. Basically, the overall bonus is first divided to total boni per item. In order to account for the importance of individual items, this can be accomplished in analogy to the computation of deviation measures in 4.2.3.2,299 i.e. based on each items share in the total order volume. The total per item bonus can be split to item and period dependent boni in a second step. Here, an even split of the total payment across all periods is used. The resulting calculation of the bonus Bj,t per item and period then follows as B j ,t =
1 XO j (∆C + S B ) T ∑ XOl
∀j ∈ JS , t
(159)
l∈JS
In consequence, the buyer is granted the bonus per item and period Bj,t, if the corresponding order XO adj. j, t is equivalent to the result of collaborative planning. Concerning deviations between negotiated and actual order quantities, it appears appropriate to offer a limited flexibility for order adjustments as in Anupindi / Bassok and Tsay due to the uncertainties faced by the buyer. A straightforward possibility is by including flexibility bands as proposed by these authors. Flexibility bands mean that the buyer receives the bonus as long as adjusted orders stay within given limits, usually expressed as some percent of the original order quantity. Only when the limits are exceeded, no bonus is granted any more. Also as implied by Anupindi / Bassok, tighter bands can be specified for the first number of periods, but can be broadened towards the planning horizon when uncertainty of demand and other information increases. Clearly, specific values need to be agreed to by the partners based on individual problem settings. However, assuming that adjusted orders should not alter the supplier’s planning results and costs significantly (otherwise payment of the bonus is no longer justified), no more than 2 to 5% of flexibility will be accepted from the supplier’s perspective. Fig. 35 a) shows an example of the item- and period-dependent bonus payment as a function of the adjusted order quantity and flexibility band (the percentage flexibility limit is referred to as α). As can be seen, the buyer receives the full bonus for small deviations from the original quantity, while the bonus drops to zero as soon as the order quantity grows above or decreases below the flexibility band. This property can be perceived as the major drawback of this simple scheme. Therefore, an alternative adjustment scheme, which too is easily manageable for the partners, is presented in Fig. 35 b). Here, the buyer’s bonus declines linearly with increasing deviation and the flexibility limit marks those points where no bonus is granted any more. Since the buyer is penalized as soon as he adjusts an order, the flexibility limits can usually be set wider than in a) as implied in the sketch. The per-unit reduction of the bonus can be calculated by dividing the itemperiod bonus Bj,t by the flexibility limit (measured in total units) αXO j, t .
299
See pp. 75.
6.1. Contractual Consequences
145
One exception from allowing some flexibility to the buyer can however be appropriate in periods where orders are negotiated to zero. If binary setup decisions are triggered at the supplier by the order quantities, as it is the case with the lotsizing model considered here, then even small adjustments upwards from zero can cause additional setups and hence considerable extra cost to the supplier. This can in consequence justify zero flexibility to the buyer in such periods, i.e. a situation where the buyer loses the entire item-period bonus as soon as he places an order greater than zero.
Bonus
Bonus
B
B
(1-α)XO
XO (1+α)XO
XO adj.
(1-α)XO
a)
XO
(1+α)XO
XO adj.
b)
Fig. 35. Flexibility and bonus payment schemes
Besides limits to order adjustments in single periods it is useful, not to say necessary from the supplier’s point of view, to add an upper limit on the allowable total adjustment per item. This is because, based on period-dependent flexibility only, the buyer could increase an order to any arbitrary size, once he realized that we would not receive the item-period bonus Bj,t any more. One way to counteract this is by limiting the total adjustment per item, too. With this extension, the buyer loses the entire bonus per item, when he exceeds an item-specific total limit. The allowable quantity can be determined based on an item’s total order volume and, e.g., the per-period flexibility limit α. In consequence, an additional check is carried out prior to granting the resulting boni by item and period, namely the supplier checks whether the inequalities α ∑ XO j ,t ≤ t∈T
. ∑ XO j ,t − XO adj j ,t
t∈T
∀j ∈ JS
(160)
hold. Where this is not the case, resulting item-specific boni should not be granted. In order to give a comparative overview of the two bonus adjustment schemes, i.e. fixed flexibility band and linear adjustment, an example is presented in Table 12. Only a single item is considered. The item-period bonus is assumed to be 100 MU. The top rows show the original negotiated pattern of orders and adjusted orders as placed by the buyer. The flexibility limit is 2% for scheme a) (fixed flexibility band) and 4% for scheme b) (linear bonus adjustment). As can be seen, with scheme a) the full bonus is granted as long as the adjusted order remains within the flexibility band (periods 2,3,5,6,7). The total bonus hence comes to 500 MU. With scheme b) in contrast, the bonus is only partly granted in
6. Implications on Supply Contracts and Partner Incentives
146
periods with tolerated adjustments (periods 2,4,7) so that the total bonus only adds up to 456 MU. Also, as indicated in the rightmost column, the total adjustments stay within tolerated limits as defined in (160). So far the perspective was on one-time planning where the partners implement all planning results up to the planning horizon. Both approaches to bonus adjustments, i.e. re-evaluation by planning models and the heuristic item-period bonus adjustment as just described, can however be applied, too, when planning is repeated on a rolling basis. Table 12. Example of period-dependent bonus payment schemes
1
2
3
4
5
6
7
XO1,t XOadj.1,t Adjustment Absolute Adj.
Period
168 175 -7 7
230 228 2 2
0 0 0 0
397 385 12 12
0 0 0 0
239 239 0 0
375 382 -7 7
Total 1409 1409
Scheme a) Flex. Limit Bonus
3.4 0
4.6 100
0 100
7.9 0
0 100
4.8 100
7.5 100
28.2 500
Scheme b) Flex. Limit Bonus
6.8 0
9.2 78.3
0 100
15.8 24.4
0 100
9.6 100
15 53.3
56.4 456
28
As described above in 5.2, in planning on a rolling basis results of one planning cycle are implemented only up to the frozen horizon TF. Also, when the negotiation horizon TN exceeds TF, results of the periods between TF and TN are supposed to be used as a starting solution by the buyer in his initial plan.300 Hence, the assessment of order adjustments can be restricted to actual orders up to TF and the buyer’s initial orders of the subsequent planning cycle regarding periods TF+1 to TN. Since the bonus payment is based on these planning results up to TN, the bonus can be fully granted, if the buyer complies to all original order quantities. Otherwise, an adjustment can be made in full analogy to the approaches laid out above, but by only considering orders up to TN. In SC settings with several buyers (and potentially several suppliers), the concepts just presented can too be used with respect to each buyer and his negotiated and actual pattern of orders. Thereby adjustments to agreed upon compensation and savings sharing payments can be made in the same way as described for the two-party situation.
300
See pp. 115 for details.
6.2. Potentials of Opportunistic Behavior and Counteractions
6.2
147
Potentials of Opportunistic Behavior and Counteractions
If not the description of the collaborative planning scheme in chapters 4 and 5, then on the latest the preceding section makes apparent, that a truthful communication of cost effects, i.e. savings to the supplier(s) and cost increases faced by the buyer(s), is imperative for the successful implementation of negotiation-based collaborative planning. Without correct announcement of cost effects, the negotiation-based search process for improved solutions can be misled and possibly directed towards inferior solutions that are actually outperformed by other known solutions in terms of resulting SC costs. Even worse, compensation and net savings associated with the solution ultimately chosen can be determined incorrectly, resulting in inappropriate bonus payments. Therefore, the final aspect of concern here is to analyze the incentives for such “opportunistic behavior”301 potentially underlying the negotiation-based scheme and to outline counteractions that can be deployed in order to reduce cheating opportunities. The following section tries to identify the cheating incentives existing for opportunistic decision makers based on a game-theoretic perspective on the collaborative planning scheme. In section 6.2.2 we discuss whether SC partners indeed behave as presumed in game-theoretic analyses, and introduce means that reduce opportunistic behavior. 6.2.1
Game-theoretic analysis
For analyzing the collaboration partners’ incentives to communicate incorrect cost effects, a game-theoretic perspective can be taken. Gamy theory was already mentioned above in the context of the ultimatum bargaining game discussed in 6.1.1.302 It is concerned with the analysis of so-called strategic situations in which the ultimate outcome depends on decisions by several parties who are conscious that their actions affect each other.303 The objective herein is to identify the most advantageous behavior of each decision maker and, based on that, to predict the likely outcome of the decision situation studied.304 The crucial assumption is that decision makers act individually rational, i.e. only maximize their own utility. They however do this by taking into account the actions and reactions of the other decision makers involved.
301 302 303 304
Williamson (1975), p. 26. See p. 132. C.f. Holler / Illing (1996), p. 1, Rasmusen (1994), p. 9. C.f. Güth (1999), p. 1.
148
6. Implications on Supply Contracts and Partner Incentives
According to Rasmusen (1994) such a strategic situation, i.e. a game, can be described and analyzed by specifying the players, their potential actions, the state of information, player strategies, payoffs, and the game’s equilibria.305 Identifying the players is the obvious first step in tackling a strategic situation. Similarly, the players’ alternative action sets must be clarified. The information state consists of information sets of individual players which represent the player’s knowledge of relevant variables or parameters at a particular point of the game. A player’s strategies are the rules that tell him which action to choose at each instant of the game. The payoff refers to the (expected) utility a player receives in a particular outcome. Finally, the equilibrium (or in some games multiple equilibria) represents a set of the best strategies for each individual player. While the players, their action and information sets usually are given parameters of the situation studied, it is up to the analyst to determine the player’s strategies and associated payoffs, and, based on that, to obtain the game’s equilibrium. Two major distinctions of games which are of relevance here are for one between non-cooperative and cooperative games and second between games with discrete and continuous action sets. The major characteristic of cooperative games is that the players can make binding commitments, e.g. in the form of enforceable contracts. In contrast, no possibility of enforcement exists in non-cooperative games. This does not mean, that players never cooperate. In fact, they do cooperate, if this is beneficial to each player. However, cooperation is pursued voluntarily here and cannot be enforced by law.306 The difference between discrete and continuous action sets is quite obvious. In many simple games as presented in textbooks,307 players can only choose between two or three discrete alternative actions, e.g. to “confess” or “deny”. If, however, they can decide upon some real valued decision variables, their action sets are considered continuous. Not surprisingly, the second case is usually more complex and equilibria are more difficult to find.308 The importance of equilibria has been stressed above. Before we turn towards modeling the collaborative planning scheme in terms of a game, a few remarks are therefore in place on equilibria. A game’s outcome can be most easily predicted, if there is a dominant-strategy equilibrium. A strategy is a dominant strategy, if “it is a player’s strictly best response to any strategy the other players might pick”.309 That is, no matter which strategies the others pursue, the player’s payoff is highest with his dominant strategy. A dominant-strategy equilibrium is one where each player chooses his dominant strategy. Clearly, if a dominant strategy is available to each player, then the dominant-strategy equilibrium represents the game’s out-
305 306 307 308
309
C.f. Rasmusen (1994), p. 10. C.f. Holler / Illing (1996), p. 23. For example the “prisoners’ dilemma” (see e.g. Güth (1999), pp. 154). A well-known example with continuous action sets is the “Cournot game” where two competitors choose production levels sold at a common market (see e.g. Rasmusen (1994), pp. 83). Rasmusen (1994), p. 16.
6.2. Potentials of Opportunistic Behavior and Counteractions
149
come as long as all players act rationally. In consequence, predicting a game’s outcome is straightforward, if a dominant-strategy equilibrium exists. However, in many situations there is no single best strategy for each player. In order to still predict the outcome, the approach used in such situations is the socalled Nash equilibrium. It is a strategy profile where “no player has incentive to deviate from his strategy given that the other players do not deviate.”310 Identifying the Nash equilibrium is more difficult as it requires to determine each player’s response to each strategy of his counterparts. Whereas in most cases there is an incentive to change the strategy once the other players’ best responses are known, no incentive to deviate exists in the equilibrium. The Nash equilibrium only represents a game’s outcome, if the players are able to perfectly anticipate how the other players react to their actions and to choose their best strategy given these reactions. Therefore, a considerable level of rationality and analysis is assumed, if the Nash equilibrium shall indeed be the outcome of a game. Now we turn to modeling the collaborative planning scheme as a game. The analysis is limited to considering two collaboration partners and one-time planning. For doing so, we start with a most simplified situation which is then extended successively. As a starting point we consider a single generation of a counter order / supply proposal by one partner, e.g. the supplier’s first counterproposal. 6.2.1.1
Single counter-proposal and perfect information
There are two players in this basic game, the initiator of the proposal, referred to as the leader in the following, and the SC partner, which we call the follower. With the counter-proposal, the leader realizes savings SL vs. his status-quo cost outcome. We suppose that the follower faces a cost increase HF from the counterproposal, but that the proposal leads to an improved outcome in total, i.e. SL>HF. Resulting net savings shall be shared between the partners as discussed in 6.1.1.1,311 with a share λ for the follower and (1-λ) for the leader. Furthermore, we assume that the leader is perfectly informed about the proposal’s cost effects. That is, he not only knows SL, but is also aware of HF. Finally, we presume that the game is non-cooperative, i.e. there is no enforceable contract telling that the players must cooperate and tell the truth. Although there usually is a legal agreement concerning the result of collaborative planning and its implementation as just discussed in 6.1.2, the assumption relates to the collaborative planning process and states that the players act freely in the course of the negotiation process. The players’ actions consist of announcing cost effects (savings sL by the leader and cost increase hF by the follower) which then serve to determine compensation and savings sharing payments rendered to the follower. This makes clear that each player has a continuous action set. The sequence of events shall be as in the basic scheme described in chapter 4, i.e. the leader first announces his savings together
310 311
Rasmusen (1994), p. 23. See p. 135.
150
6. Implications on Supply Contracts and Partner Incentives
with the proposal pattern to the follower. The follower evaluates the pattern and thereafter announces his cost increase.312 Now, which values sL and hF will be announced by the partners, if each maximizes his individual benefit? For answering this question, we consider the payoff accruing to each player. The leader realizes a payoff according to his actual savings minus compensation and savings share rendered to the follower, as long as announced savings outweigh the cost increase announced by the follower. Otherwise, the proposal appears not to bring an improved solution, the partners stick to the best outcome known so far and the payoff is zero. Put mathematically, we have ⎧S − hF − λ ( sL − hF ) ΠL = ⎨ L 0 ⎩
if h F ≤ s L ⎫ ⎬ else ⎭
(161)
Similarly, the follower’s payoff consists of the payment received from the leader minus his actual cost increase, if hF is not greater than sL, i.e. ⎧− H + h F + λ ( s L − h F ) ΠF = ⎨ F 0 ⎩
if h F ≤ s L ⎫ ⎬ else ⎭
(162)
In order to determine the savings announcement sL which maximizes the leader’s payoff, it is helpful to refer to the follower’s best response function. Best response functions are mathematical expressions which maximize a player’s payoff for given decisions of the other players and are particularly useful in games with continuous action sets.313 Here, for a given leader decision ~s L the follower realizes a maximum payoff based on his response function314 sL } = ~ s L − ε if H F ≤ ~ sL ⎫ ⎧max{ hF | hF ≤ ~ RF = ⎨ (163) ⎬ else 0 ⎩ ⎭ That is, whenever savings ~s L announced by the leader outweigh the follower’s
actual cost increase, he claims that hF is almost as large as the savings in order to receive as large a portion of ~s L as possible. This is a dominant strategy for all ~ s L ≤ H F , since (163) holds for any values of ~ sL . Based on that argument, the leader too has a dominant strategy which is to announce as little savings as possible. Therefore, he pretends to have only s *L = H F + ε in savings such that the new proposal is accepted as a new best solution. Corresponding payoffs to leader and follower are Π L = SL − (H F + ε ) ΠF = ε (164) Not surprisingly, the solution is equivalent to the game-theoretic outcome to the ultimatum bargaining game.315 Hence, given the simplifying assumptions stated above, the partners indeed have no incentive to tell the truth freely in trying to
312
313 314 315
Therefore, the game situation can be referred to as a “Stackelberg” game, where the leader moves or decides first, and the follower thereafter, being aware of the leader’s decision (c.f. Holler / Illing (1996), pp. 109). C.f. Rasmusen (1994), p. 85. ε again represents a small number. See 6.1.1, pp. 132.
6.2. Potentials of Opportunistic Behavior and Counteractions
151
maximize their respective payoffs. The resulting dominant-strategy equilibrium is an outcome with a strong first mover advantage where almost the entire benefit accrues to the leader. However, the above analysis rests on several critical assumptions. It is therefore interesting to see whether the outcome changes after dropping some of them. The farthest reaching simplifications of the above situation are for one that only the generation of a single counter-proposal is considered, and second that the leader has perfect information on the follower’s cost increase HF. Both assumptions are eliminated in turn in the following. 6.2.1.2
Sequence of counter-proposals and perfect information
First, we consider a sequence of proposal generations as it actually happens in the collaborative planning scheme. This means that both partners alternate in proposing new compromise patterns, and the roles of leader and follower switch repeatedly between buyer and supplier. As in the single-proposal case above, we assume that incremental savings SLi vs. the current status-quo outcome accrue to the originator (leader) of proposal i and an incremental cost increase HFi to the follower. Again, we presume that net savings result from each new proposal (SLi≥HFi) and that all remaining assumptions stated above are still valid. Also, perfect information is assumed available to both players regarding savings SLk and increases HFk of all future proposals (k>i). Is there any reason why the outcome with a sequence of proposals should differ from repeating the single-proposal outcome a number of times? In fact, in many non-cooperative games that take place repeatedly there is. The motivation behind changes in players’ behavior in repeated games is as follows: Realizing short-term gains by selfish behavior in a single round is often penalized by long-term losses due to other players’ reactions to the selfish strategy in a previous round. Therefore, when expected long-term losses weigh higher than the short-term gain, there is an incentive to change to a cooperative strategy.316 To illustrate this, take e.g. the “prisoners’ dilemma”. If the prisoners are interrogated a single time, both confess that their counter-part was involved in the crime and are convicted. When they are however interrogated repeatedly, then both have an incentive not to confess, as long as the other has not confessed either. Only when one player is convicted, he knows that the other confessed and will then “punish” the other by revealing his involvement in the crime, too. Hence, both cooperate as long as their counterpart cooperates. Resulting is a so-called “tit for tat” strategy which rewards cooperate behavior with cooperation and punishes selfish decisions with non-cooperation.317
316 317
C.f. Holler / Illing (1996), p. 21. C.f. Holler / Illing (1996), p. 21. From a theoretical viewpoint this result only holds true, if the game is repeated infinitely long. Otherwise, the last round lacks an incentive to cooperate and both will act selfish here. Given that, they however do not have in-
152
6. Implications on Supply Contracts and Partner Incentives
Now, just as in the “prisoners’ dilemma” the players’ individually rational behavior might change in the collaborative planning situation considered here due to the repetition of the single-round game. A change towards more cooperative decisions can however only take place, if this opens chances of higher benefits. Therefore, we first analyze the players’ payoffs with a sequence of proposals under the equilibrium behavior of a single round, and secondly try to determine whether cooperative behavior promises additional benefits. Assuming that a sequence of I proposals is generated in total and that proposals with an odd index originate from the supplier and those with an even index from the buyer, the supplier receives payoffs based on the single-round equilibrium behavior according to Π S NonC =
⎡I / 2 ⎤
∑
i =0
(S
2i +1 L
)
− ( H F2i +1 + ε ) + ⎡I / 2⎤ ε
(165)
where SLi refers to the leader’s savings and HFi to the follower’s cost increase associated with proposal i. Similarly, the buyer receives Π B NonC =
⎡I / 2 ⎤
∑
i =1
(S
2i L
)
− ( H F2i + ε ) + ⎡I / 2⎤ ε
(166)
Put in words, each partner essentially obtains the sum of net savings accruing from the counter-proposals which he generates. In contrast, based on cooperative behavior where a part of net savings is shared, shared savings originating from the respective player are subtracted from the payoffs in (165) / (166) and shared savings originating from the counterpart are added. Resulting are payoffs318 ΠSC = Π BC =
⎡I / 2 ⎤
(
)
∑
(1 − λ ) S L2i +1 − H F2i +1 +
∑
(1 − λ ) S L2i − H F2i +
i =0 ⎡I / 2 ⎤ i =1
(
)
⎡I / 2 ⎤
∑
i =0
λ S L2i − H F2i
)
(167)
λ S L2i +1 − H F2i +1
)
(168)
⎡I / 2 ⎤
∑
i =1
(
(
Comparing (165) to (167) and (166) to (168), respectively, each partner can determine whether cooperative behavior is beneficial, given that he has perfect information available, including payoffs of coming rounds. This is demonstrated by an example in Table 13. It shows three proposals generated by each partner, savings to the leader and cost increases to the follower, as well as associated payoffs to leader and follower based on non-cooperative and cooperative behavior (with ε=0, λ=0.5). A characteristic of the example is that the proposals generated by the supplier are decisively more beneficial, i.e. result in higher savings. Therefore, based on non-cooperative behavior which leaves all net savings to the leader, the supplier can keep most of total savings (15,001 of 17,758 MU) whereas the buyer only gets 2,757 MU. In contrast, both partners end up with identical payoffs of 8,879 MU
318
centives to cooperate in the second last round either, and so forth up to the very first round (so called backward-induction principle, c.f. Holler / Illing (1996), p. 134). ε is assumed to be zero for simplicity.
6.2. Potentials of Opportunistic Behavior and Counteractions
153
assuming cooperative behavior and equal sharing of net savings (λ=0.5). Hence, the buyer might have an incentive to cooperate, as his payoff can increase. The underlying reasoning is that by acting cooperatively he might induce cooperative behavior of the supplier, and by that receive a higher total payoff. Table 13. Example payoffs with cooperative and non-cooperative behavior
Leader
Actual Cost Effects SL
S B S B S B
9452 2048 14231 1840 727 1555
Payoffs Non-Cooperative
Payoffs Cooperative (λ=0.5)
HF
ΠL
4060 337 4772 1671 577 678
5392 1711 9459 169 150 877
ΠF 0 0 0 0 0 0
ΠL 2696 855.5 4729.5 84.5 75 438.5
ΠF 2696 855.5 4729.5 84.5 75 438.5
Total
ΠS
15001
(165)
8879
(167)
Payoffs
ΠB
2757
(166)
8879
(168)
However, the supplier lacks any incentive to cooperate since he can only decrease his payoff by cooperation. This is because, although the portion received by each partner can alter, the total payoff across both partners does not change, no matter whether they act cooperatively or not.319 Thus, only one partner can profit from cooperation here, the one who receives the smaller payoff from non-cooperative behavior. Since this partner however can anticipate that his counterpart will refrain from cooperating anyway, there is no reason for him to cooperate either. Therefore, unlike the “prisoners’ dilemma” the players’ behavior and the game’s outcome does not change here when several i i proposal generations take place. The leader still announces savings s*, L = HF + ε in each round i and the payoffs are as given in (165) and (166) above. In case that some proposals do not bring net savings, i.e. SLi
319
The situation represents a so-called zero-sum game where one player can only earn more, when the other loses a corresponding amount (c.f. Güth (1999), p. 153).
6. Implications on Supply Contracts and Partner Incentives
154
6.2.1.3
Asymmetric information
How may the outcome be influenced when no perfect information is available to the partners? Generally, player strategies and outcomes of games can change, when the information sets of individual players are altered, similarly as players can act differently when a game takes place repeatedly. This is particularly the case when players possess hidden, i.e. private, information regarding their preferences and utilities.320 The challenge with hidden information is that a player can no longer perfectly anticipate the reactions of his counterparts. This can in consequence lead to a change in his strategy as compared to a situation with perfect information. Take e.g. the game situation shown in Table 14 with two players and two alternate actions for each one. Table 14. Example game
A1,1 A1,2
A2,1
A2,2
(5,5) (10,5)
(7,1) (0,1)
Based on perfect information player one’s equilibrium strategy is to choose action two, since he knows that player two’s dominant strategy is to select action one (payoff 5). Now, in absence of knowledge on player two’s payoffs, it might however be more attractive for player one to go with action one, as it guarantees an average payoff of 6 no matter what player two decides to do. The example not only demonstrates how a player’s behavior can change in absence of perfect information, but also makes obvious that the type and amount of (imperfect) information available to him plays a crucial role in determining a player’s best strategy. Typically in games with hidden information and discrete action sets, it is assumed that players can be of several “types” with known probabilities. In the example above, player two may e.g. have action one as dominant strategy with probability 0.75 or action two with probability 0.25. In order to obtain a player’s best strategy, the expected payoffs of his potential actions are considered based on a summation across all types of other players and associated probabilities.321 Regarding the collaborative planning scheme, how does the initiator, i.e. leader, of a proposal act without perfect information? For answering this question we again just consider the generation of a single proposal and rely on the same assumptions as in the initial single-proposal case, except that the leader does not possess knowledge of the follower’s cost increase HF.
320 321
C.f. Holler / Illing (1996), p. 45. C.f. Holler / Illing (1996), p. 78. In the example, if player two chooses action one with probability 0.75 and action two with probability 0.25, then player one’s best strategy is selecting action two as it yields an expected payoff of 7.5, whereas action one yields 5.5.
6.2. Potentials of Opportunistic Behavior and Counteractions
155
What the leader however does know in this situation, is that once he announces savings sL, the follower maximizes his payoff by announcing a cost increase hF=sL-ε, whenever sL is greater than his actual cost increase HF. Therefore, the leader is in a conflicting situation for he wishes to announce as little savings sL as possible, while running into the risk that his payoff drops to zero, if announced savings are smaller than the follower’s actual cost increase HF. Given the probability density p(HF) of the follower’s cost increase, the leader’s expected payoff calculates to E{Π L } = (S L − ( s L + ε ) ) × P( H F ≤ s L ) + 0 × P ( H F > s L ) sL
(169)
= (S L − ( s L + ε ) ) ∫ p (H F )dH F 0
Knowing the probability density p(HF) allows to maximize the expected payoff according to (169). Hence, for realizing the first mover advantage as with perfect information, it is crucial for the leader to predict the cost increase accruing to the follower as accurately as possible. Suppose for example, the leader can state that the follower’s cost increase takes values between zero and an upper limit HFmax with equal probabilities. Then, the probability that announced savings sL exceed HF equals to sL/HFmax and the expected payoff can be determined to E{Π L } = (S L − ( s L + ε ) )
sL
(170)
H Fmax
Neglecting ε, (170) takes its maximum at sL=0.5SL.322 Thus, in this case the leader announces savings (171) s *L = min 0.5S L , H Fmax The minimum operator in (171) is required since there is no use for the leader to announce savings higher than HFmax. Correspondingly, the maximum expected payoff takes values
{
}
⎧⎪ S L − H Fmax E {Π L }* = ⎨ ⎪⎩(0.5S L ) 2 / H Fmax
if H max < 0.5S L ⎫⎪ F ⎬ ⎪⎭ else
(172)
Given announced savings sL*, the follower reacts as in the case of perfect information by stating a cost increase hf equivalent to the leader’s announced savings, if sL* outweighs his actual cost increase HF. Therefore, he now potentially faces a payoff greater than zero according to (173) ⎧⎪− H + s * if H ≤ s * ⎫⎪ ΠF = ⎨ ⎪⎩
F
F
L
0
else
L
⎬ ⎪⎭
Based on (173), his expected payoff can be determined to E{Π F } =
s*L
∫
0
322
(− H F + s *L ) p (H F
)dH F =
1 H Fmax
s *L
* ∫ (− H F + s L )dH F =
0
( s *L ) 2 2 H Fmax
(174)
The extreme point can be found by setting the first order derivative to zero. The second order derivative is negative, i.e. the point represents a maximum.
156
6. Implications on Supply Contracts and Partner Incentives
With sL* from (171) we obtain ⎧⎪ 0.5H Fmax if H max < 0.5S L ⎫⎪ F E {Π F }* = ⎨ ⎬ 2 max ⎪⎩(0.5S L ) / 2 H F ⎪⎭ else
(175)
Fig. 36 shows announced savings and expected payoffs to leader and follower as functions of actual savings SL (based on a maximum cost increase HFmax of 100 MU). It can be seen that the leader announces savings of 0.5SL until this term reaches the value of HFmax. From that on, he announces HFmax which guarantees a positive payoff and is smaller than 0.5SL. Although expected payoffs are positive for both leader and follower for all values of SL greater than zero, they are higher for the leader indicating that there is still a “first mover advantage”. Nonetheless, the leader is forced to share net savings due to the lack of perfect information. For example, when his actual savings SL are 100 MU, he announces savings of 50 MU to the follower. The follower faces a cost increase of less than 50 MU with a probability of 50% and his expected payoff is 12.5 MU in that case. In consequence, there is a 50% chance for the leader to realize a payoff of 50 MU yielding an expected payoff of 25 MU. The above example shows that the lack of perfect information induces the leader to act more cooperatively and to share a part of savings. The actual amount offered to the follower highly depends on the degree to which the leader can predict the follower’s cost increase. The more accurate predictions he can make, the more he can return to the outcome with perfect information, where he only announces high enough savings to cover the follower’s cost increase. For the follower, the situation does not change. Since he is aware of the actual cost increase accruing to him and knows the savings announced by the leader, he can still claim that his cost increase almost equals to the leader’s savings. Therefore, while the absence of perfect information strongly affects the leader’s decisions, the follower remains reluctant to cooperative behavior. As a consequence, the leader still announces as few savings as possible. The analysis just carried out only considers the generation of a single counterproposal. However, on grounds of the arguments as presented above for the case of perfect information, it also remains valid when several proposals are generated by the buyer and supplier in turn. Each time a proposal is generated, the leader determines announced savings sLi which maximize his payoff by taking into account his knowledge of the follower’s cost increase. A potential new feature which can come into play here, is that each partner can “learn” about the other’s cost increases based on the experience gathered with former proposals. In that way, the partners may be able to increase the accuracy of their predictions of partner cost increases and approach the perfect information situation with a growing number of proposals.
6.2. Potentials of Opportunistic Behavior and Counteractions
157
Announced savings sl
120 100
HF=100
[MU]
80 60 40 20 0 0
50
100
150
200
250
actual savings SL [MU]
a) Expected payoffs 200
[MU]
150 100
Leader
50 Follower
0 -50 0
50
100
150
200
250
actual savings SL [MU]
b) Fig. 36. Example curves of announced savings and expected payoffs
Finally, in all the above considerations we have assumed that net savings are shared between buyer and supplier based on a portion λ rendered to the follower of a proposal. However, the outcomes do not change when a fixed payment is rendered to the buyer based on the result of collaborative planning as also discussed as a sharing agreement in 6.1.1.323 The reason why the players’ behavior and associated outcomes do not alter is that with this sharing agreement the buyer also receives a compensation for his cost increase above the initial Upstream Planning result. Hence, when the buyer is the follower in a proposal generation, he still has an incentive to pretend facing a cost increase hF equivalent to the savings sL as announced by the supplier.
323
See pp. 132.
6. Implications on Supply Contracts and Partner Incentives
158
One may argue that both players have no cheating incentive here, when the buyer generates a proposal, i.e. has the leader role. Since the buyer receives a fixed payment in the end, he can announce actual savings of a proposal without hesitation. The supplier neither needs to cheat, since neither the compensation nor the fixed payment are affected by the cost increase he announces. However, we can assume that the net savings over the entire sequence of proposals indirectly influence the fixed amount rendered to the buyer. That is, in agreeing fixed payments rendered to the buyer, the partners will usually utilize typical net savings accruing to the supplier. Therefore, even here the supplier has an incentive to report as little savings as possible or, being the follower in a proposal generation, as high a cost increase as possible. In conclusion, from a game-theoretic viewpoint the partners can profit from not communicating cost effects truthfully. What remains to assess is whether SC partners as considered here indeed behave in the way presumed for individually rational players or whether some of the assumptions underlying game theoretic analyses do not hold in a SC setting. Finally, one may consider counter-actions that can be deployed to reduce cheating incentives, in case opportunistic behavior of the partners is still expected. Both aspects are described in the following section. 6.2.2
Means preventing opportunistic behavior
The attractiveness of fully selfish behavior aimed to exploit the strategic first mover advantage inherent in the collaborative planning scheme and to realize short-term gains can be curtailed by the type and nature of the SC relationship between buyer and supplier. This aspect is discussed in the following. Moreover, the SC partnership and collaboration can embrace other elements than collaborative planning, either to support the operations planning process or with respect to other, independent business processes. Such elements are additional means to underpin cooperative, truthful behavior, in particular when they include SC costing and auditing activities, and are regarded subsequently. Finally, when such measures are not in place or the partners feel that the danger of opportunistic behavior still remains, further design changes can be undertaken in the collaborative planning scheme which help to limit opportunism. Such further modifications are briefly introduced as a final point. 6.2.2.1
Effects of supply chain partnerships
It is stressed in the literature that the concept of SCs and the engagement in SCM relies on mid- to long-term, trustful relationships to SC partners, which are initiated because they lead to a business performance higher than could be reached by the involved partners individually.324 According to Ellram / Cooper (1990), a SC
324
See e.g. Stadtler (2005), p. 11, Simatupang / Sridharan (2002), p. 19.
6.2. Potentials of Opportunistic Behavior and Counteractions
159
relationship is “forward looking, takes place over an extended time period, and involves trust and the associated sharing of information, risks and rewards”.325 It should also be clear that not all SC links require close and long-term partnering. Lambert et al. (1996) therefore suggest to differentiate between three types of SC partnerships. Type one is a limited, rather short-term engagement which usually includes the coordination of a small set of activities. In type two partnerships, activities are not just coordinated, but integrated across company borders. They typically embrace more complex business processes and involve several business functions. Finally, in type three partnerships organizations share significant levels of operational integration. The SC partner is perceived as an extension of the own firm, and the partnership is intended for an indefinite time.326 Usually, only a few type three partnerships are pursued, reserved for suppliers and customers who are critical for a firm’s long-term success. Regardless of the level of intensity, SC relationships can generally rest on three dimensions or modes of control: power, contracts, and trust.327 Power stems from differences in resources and impact on the SC’s environment. Contracts contain agreed to terms and responsibilities with respect to the transactions made between the partners. Finally and of particular relevance in our context, trust represents a less formal mode of control which often develops through a series of past interactions. Despite the formal control by contracts and the exertion of power, Sydow (2002) argues that integrated SCs heavily rely on trust and trustful cooperation, e.g. due to the problem of hidden action and information possessed by individual SC partners.328 Trust is however not simply present in a SC relationship. Rather, it develops over time based on the expectations and actual actions of the SC partners. According to Smeltzer (1997), the more ethical SC partners behave and the better ex-ante expectations are covered by actual partner action, be more trustful a SC relationship can become.329 An often observed side effect of increasing trust and good experiences made by the partners is that the relationship intensifies not only on the social dimension, but also in terms of the scope of the transactions and the volume of business. E.g. when a buyer perceives a supplier as acting reliably, i.e. keeping promises etc., he is attracted towards shifting additional purchasing volume or even entirely other services, such as involvement in product development, to this SC partner. This trend however increases the mutual dependence of the partners on each other, and by that also the threat or damage of terminating the relationship.330 In effect partners become increasingly dependent on each other and have growing interest in sustaining a trustful cooperation.
325 326 327 328 329 330
Ellram / Cooper (1990), p. 4. C.f. Lambert et al. (1996), pp. 2. C.f. Peck / Jüttner (2000), p. 37. C.f. Sydow (2002), p. 13. C.f. Smeltzer (1997), p. 41. C.f. Stump / Heide (1996), p. 432.
160
6. Implications on Supply Contracts and Partner Incentives
A good example of how a SC relationship can develop is reported by Boddy et al. (2000) in a case study of a computer manufacturer and one of its plastics suppliers.331 It makes apparent how positive experiences by the partners lead to intensifying the relationship and encourage further cooperative initiatives. Also, growing (informal) trust leads to constructing formal institutions such as monthly cross-company meetings. The scope of the relationship is extended from supply of standard components to more complex sub-systems and engagements in research and development. These findings on SC relationships and trust building as reported in the literature have implications on the collaborative planning scheme in several respects. First, drawing from Lambert et al. (1996) we can assume that SC partners who implement collaborative planning are usually in a type two or three partnership. This is due to the fact that considerable process alignment and information exchange is required which will typically only be realized in a long-term relationship with substantial importance to both partners. Secondly, based on the same reasoning one can expect that the relationship is intended for a considerable time. Also, partners who agree to cooperatively plan their operations have developed a close, trustful relationship. Otherwise they would shy away from making relationshipspecific investments and concessions to the SC partner. In such a situation, the partners are however likely to be led by other considerations than present in the game-theoretic perspective discussed above. Essentially, the partners may attribute high value to ethical behavior. That is, given positive experiences gathered so far and the trust offered by the partner in that he is willing to join in collaborative planning, each partner may have a preference to reward the counterpart by acting cooperatively. This is further amplified by the fact that each partner also expects truthful behavior of the other. In addition to “ethical reasons”, even purely rational, utility maximizing, decision makers can come to a different conclusion than presented in the gametheoretic model and prefer to act cooperatively. This originates in the potential loss of goodwill or reputation that would follow, if non-cooperative behavior is noticed by the partner. This result can be obtained with the same line of argument as used in the game-theoretic model with a sequence of proposal generations. There we argued that in “repeated games” players have incentive to cooperate, if the long-term effects of cooperating outweigh short-term payoffs of selfish behavior. The long-term gains considered in the analysis are the payoffs of succeeding proposals within the current collaborative planning cycle. Based on this perspective, cooperative behavior does not pay off. However, this viewpoint ignores the underlying relationship between the SC partners. I.e., if the long-term loss from non-cooperating is a serious damage to the relationship or even its termination, then there are chances that long-term aspects outweigh the additional payoffs realizable in a single planning cycle. In this case, the partners indeed have an incentive to cooperate in order to support the relationship established with the collaboration partner.
331
See Boddy et al. (2000), pp. 1003.
6.2. Potentials of Opportunistic Behavior and Counteractions
161
Obviously, this result depends on the likelihood that non-cooperative behavior is noticed by the partner. Nonetheless, it suggests that given a close relationship and dependence on the SC partner, there is a strong case for cooperating, even if that means to give up parts of the payoffs realizable in the negotiation scheme. 6.2.2.2
Controlling and auditing measures
In the introduction of chapter 2 we have stressed that SCM can embrace various business processes and go beyond core processes of logistics, operations, and order fulfillment. One such further, supportive, process which receives increasing attention in literature is the area of controlling and auditing. Controlling is generally concerned with providing performance- and decisionrelevant information to decision makers and supporting planning, control, and coordination tasks of management.332 In light of SCs, it is confronted with several new challenges, for example in that traditional cost accounting principles do not yield precise enough cost data for effective decision making in SCs.333 In addition, relevant information is spread across the SC and data relating to specific processes within the SC often lack common measurement principles and bases.334 According to Stölzle (2002), one major purpose of controlling in SCs consists of reducing potentials of opportunistic behavior, e.g. by extending the information basis available to all decision makers or by designing appropriate control mechanisms.335 Kummer (2001) develops a “box of instruments” which can be used for achieving that purpose.336 At the core it rests on a value chain analysis which serves to describe the processes under way in the SC, their performance and resource consumption. Relevant cost information can then by aggregated and summarized in a SC costing module. Since traditional principles are of little help in devising meaningful logistics and SCM costs, concepts such as target costing, activity-based costing, or total cost of ownership can be deployed here.337 In addition, Kummer proposes to use a separate system of performance indicators in order to capture relevant measures other than costs. Data of SC costing and performance indicators can then be further used in two ways. For one, he recommends to define a SC-wide (balanced) score card intended to give an overview of the overall performance. Secondly, benchmarking can be applied to compare the performance of processes within the SC as well as to that of other, external, parties. The above concepts relate to the collaborative planning scheme as follows. First of all, SC partners implementing collaborative planning are well advised to engage in common SC controlling at least to some degree. This is for example
332 333 334 335 336 337
C.f. Horvath (2001), p. 25. C.f. LaLonde / Pohlen (1996), p. 1. C.f. Kummer (2001), p. 82. C.f. Stölzle (2002), p. 11. For details see Kummer (2001), pp. 83. C.f. LaLonde / Pohlen (1996), pp. 3.
6. Implications on Supply Contracts and Partner Incentives
162
useful since each partner uses a set of cost rates in his planning models. In order to ensure that planning decisions are traded-off appropriately between the partners, it is therefore important that consistent cost measures are in place. This however suggests that common cost calculations and accounting principles are used. When such activities are supported by common controlling processes established between the SC partners, e.g. comprising the calculation and reporting of cost figures, then cost effects realized in the collaborative planning process, or at least their likely magnitudes, can also become common knowledge. In that way an “indirect control” of the cost effects as reported in the collaborative planning process can be carried out. Beyond such indirect inspection the partners can agree to establish some formal audits of the results produced in collaborative planning. Generally, audits e.g. in the form of site visits, process observations, etc. are a commonly used practice in the selection and ongoing assessment of suppliers.338 Collaboration partners can for instance agree that planning results, or at least the cost effects communicated in the collaborative planning process, are stored in the planning systems, and might be inspected by a cross-company auditing team or a neutral third party (e.g. public accountants). According to Sydow (2002), the willingness to open files for ex-post or ongoing monitoring notably increases trust between SC partners, even if actual controls hardly take place. What matters is the fact that the partner is not reluctant to share the information.339 Shared cost reporting or monitoring of planning results in conjunction with the risk to damage the reputation and to lose goodwill in the SC relationship as discussed in the preceding section provide compelling reasons to act cooperatively and to truthfully communicate cost effects in the collaborative planning scheme. The essential argument is that the potential long-term damage to the SC partnership will usually outweigh additional short-term gains realizable by opportunistic behavior in collaborative planning. 6.2.2.3
Modifications to the collaborative planning scheme
The final set of counteractions to avoid opportunism that is dealt with here, is by introducing further modifications to the collaborative planning scheme. These measures are particularly appropriate when the underlying SC relationship is less established and important to the collaboration partners, and when monitoring mechanisms as discussed above are not available. The game-theoretic treatment of the collaborative planning scheme above has unveiled that the partners have incentives to cheat in order to (try to) receive as large a piece of the “savings cake” as possible. This is because announcements of savings and cost increases affect the payoffs which they obtain at the end of the scheme. Therefore, one approach to eliminate cheating incentives is by decoupling the payoff of at least one partner from reported cost effects.
338 339
Stump / Heide (1996), p. 433. C.f. Sydow (2002), p. 13.
6.2. Potentials of Opportunistic Behavior and Counteractions
163
In particular, the buyer could be paid a fixed sum for joining collaborative planning regardless of the actual compensation and savings generated. By receiving a fixed amount independent of the cost effects reported during the scheme, the buyer principally lacks incentives not to tell the truth. One disadvantage of this solution is however that the supplier needs to render the payment irrespective of the actual outcome to the collaborative planning process. To share the risk more evenly between the partners, the arrangement can be enhanced such that the buyer is only paid when an improved solution is indeed found from the supplier’s perspective. That is, the supplier can ultimately decide whether to stay with the Upstream solution or whether to implement a compromise plan and pay the fixed sum to the buyer. The risk borne in this setting by the buyer concerns outcomes where the fixed sum does not fully cover the cost increase faced with the ultimate outcome. Realizing that the buyer would be worse off than initially in such a case, underpins his interest to claim as large a fixed sum as possible. This highlights the major difficulty of the fixed payment approach, i.e. to determine an appropriate amount paid to the buyer.340 For example, the buyer may be tempted to announce higher cost increases than are actually occurring during the negotiation scheme, based on the argument that he might indirectly influence the fixed amount the supplier is willing to pay. Due to these difficulties, another resolution can be proposed based on a different reasoning. We have seen above in the case of asymmetric information341 that without knowledge of the partner’s cost increase the initiator of a proposal is willing to offer as much of savings accruing to him as he sees necessary to maximize his expected payoff. He however expects that the follower acts selfish and claims that his cost increase is equivalent to the savings announced by the leader, as soon as the savings announcement outweighs his actual cost increase. Now, if these decisions represent the partners’ preferred “mode of operation” in the case of asymmetric information, then the negotiation scheme can be adapted such that the above becomes the official compensation and savings sharing rule. Namely, when a partner generates a proposal with savings x but unknown cost increase to the partner, he may offer some amount y which he is willing to pay for the partner’s acceptance of the new solution. The partner can then either accept the proposal and receive amount y regardless of his actual cost increase or deny the proposal (typically, when y is smaller than his cost increase). In result, the situation for both partners is almost equivalent to the case of asymmetric information described above, with the difference that their decisions do no longer represent opportunistic behavior, but the agreed to and expected process. As discussed above, the amount offered by the leader to the follower strongly depends on his ability to predict the follower’s cost increase. In conse-
340
341
This problem is analogous to difficulties of determining appropriate fixed payments in the compensation plus fixed payment scheme discussed above in 6.1.1.1, pp. 135. See 6.2.1.3, pp. 154.
164
6. Implications on Supply Contracts and Partner Incentives
quence, the leader offers as much of his savings as he believes to be required for compensating the partner. The disadvantage of this approach is that the negotiation scheme’s performance in terms of realizing improvements in total SC costs can be hampered. It occurs, since proposals which actually yield an improved outcome for the SC as a whole can be discarded by the follower, when the leader’s offer is to small to outweigh the follower’s cost increase. The focus of this chapter was to lay out financial implications from the collaborative planning scheme developed above in chapter 4 and 5 and to analyze incentives of opportunistic behavior of collaboration partners. Concerning financial issues we have first seen that parties facing cost increases from collaborative planning have to be compensated in order to create a win-win situation. Also, based on experimental studies of bargaining situations, resulting net savings should be shared between the partners to ensure each partner’s willingness to participate. Compensation and savings sharing can be incorporated into supply contracts in the form of a bonus granted when the buyer’s actual orders comply to the results of collaborative planning. A simple heuristic scheme was proposed for situations where actual and agreed to order quantities deviate from each other. In essence, the idea is to subtract a part of the total bonus depending on the degree of deviation. Potentials of opportunistic behavior underlying the negotiation scheme were studied by applying a game-theoretic analysis. Its result suggests that cheating incentives indeed exist as they can increase the payoffs accruing to individual partners. However as discussed at the end of the chapter, opportunistic behavior bears the risk of damaging the SC relationship established with the collaboration partner, and to suffer considerable long-term losses in consequence. Therefore, cheating is usually less attractive in trustful, long-term relationships to SC partners. This is particularly the case, when the communication of cost effects is controlled by collaborative SC costing or by auditing activities supporting collaborative planning. Recommended readings • Anupindi, R. / Bassok, Y. (1999): “Supply contracts with quantity commitments and stochastic demand”, in: Tayur, S. / Ganeshan, R. / Magazine, M. (Eds.): Quantitative Models for Supply Chain Management, Boston et al., 1999, 197-232. • Rasmusen, E. (1994): Games and Information – An Introduction to Game Theory, 2nd ed., Cambridge / Oxford, 1994. • LaLonde, D.M. / Pohlen, T.L. (1996): “Issues in supply chain costing”, in: International Journal of Logistics Management, Vol. 7(1), 1-12.
7 Computational Evaluation Content This final chapter deals with the evaluation of the collaborative planning scheme developed in chapters 4 and 5 by computational tests. The purpose is to determine the quality of solutions attainable with the scheme on the one hand and the computational efforts necessary to achieve these solutions on the other. The focus of the computational analysis is on the basic version of the scheme as described in chapter 4, i.e. one-time planning between a single buyer and supplier. However, a smaller number of tests also considers a more general SC structure with a single supplier but several buyers, as well as planning on a rolling basis between two SC partners. Before discussing the computational results, section 7.1 outlines the implementation of the collaborative planning scheme used to carry out the computational analysis. Also, characteristics of the test instances and input parameters are introduced in 7.2. The computational results are presented thereafter in sections 7.3 through 7.5. Key points • Overall, the negotiation scheme closes approximately 70% of the gap of upstream to central planning results. • Across 756 test problems for a single buyer and supplier with systematically varied input parameters, Upstream Planning yields in 94 cases insufficient capacity at the supplier and an average cost gap to central planning of 23% for the remaining 662 cases. In contrast, results of the negotiation scheme are on average 1.7% above central planning, reached within an average of 4.6 iterations. • In test problems with 2 or 3 buyers, Upstream Planning results in a gap to central planning of 40% which is reduced to 5% by negotiation-based collaborative planning. • In planning on a rolling basis, the negotiation scheme clearly improves upstream results, even with a negotiation horizon of only 1 or 3 periods.
7.1
Implementation of the Collaborative Planning Scheme
The negotiation-based collaborative planning scheme was implemented under the Microsoft Windows XP operating system by the use of standard software. In particular, the implementation rests on Microsoft Excel, Visual Basic for Excel, and ILOG OPL Studio (Optimization Programming Language) and Cplex 7.0 matheG. Dudek, Collaborative Planning in Supply Chains, 2nd edn., DOI 10.1007/978-3-540-92176-9_7, © Springer-Verlag Berlin Heidelberg 2009
166
7. Computational Evaluation
matical programming solver. This approach was chosen because results can be easily accessed and, being available in spreadsheets, are ready for further analyses and visualization. Visual Basic can be directly used in Excel to extend the program’s functionality beyond standard routines and functions. It is easy to comprehend and allows the implementation of the scheme without in-depth programming skills. Also, OPL Studio is distributed with a so-called component library which enables to interface OPL directly from Visual Basic.342 In that way Visual Basic can be used to generate and solve MIP models with OPL and CPlex. A conceptual diagram of the software components and their interactions is shown in Fig. 37. The core element is made up by the Visual Basic code which contains the process flow and control associated with the negotiation scheme as described in chapter 4343 for the basic version and chapter 5 for the various extensions. Excel spreadsheets serve as a database. They carry some basic input parameters required by the Visual Basic routines (e.g. number of items included in the order / supply pattern). In the first place they are however used to store the computational results in terms of cost effects by partner and category (e.g. setup, inventory holding) and corresponding order / supply patterns. Text files represent an auxiliary means to incorporate input data into the MIP models and are created by Visual Basic procedures. Required input data comprise two categories: data describing the current test instance and data relating to the negotiation scheme itself. The first type relates to information such as the bill-ofmaterial, available capacities, and cost rates and is created once at the start of the negotiation scheme. Data items of the second category are updated continuously during the negotiation scheme. They represent the various parameters needed by the distinct planning models, such as the current order / supply pattern proposed by the collaboration partner or the cost parameters Cmax and Cmin used in the goal programming models.344 OPL and CPlex generate and solve the MIP models described in chapters 4 and 5. As mentioned above, the MIP solver is executed directly from Visual Basic via the component library. When OPL is called, it generates the coefficient matrix of the current model using a general model formulation and the input data given in the respective text files. It then runs Simplex and Branch-and-Bound algorithms of the CPlex solver to obtain the optimal solution to the model. Once the solution is available, output data can be retrieved via the interface directly to Visual Basic and Excel. Although eight distinct models are formulated in chapter 4 (four for each partner), only two model formulations (one for the buyer and one for the supplier) are implemented in OPL. This is possible since all four models pertaining to one partner have a majority of constraints in common and only differ by a few, specific constraints and the objective function.
342 343 344
C.f. ILOG (2000), p. 17. See in particular section 4.3, pp. 91. See e.g. Model 6, p. 73.
7.1. Implementation of the Collaborative Planning Scheme
167
Excel Spreadsheet : Data Storage read write
Text files: Input data
write
Visual Basic : Process Control
execute read
data
retrieve data
OPL/Cplex: Mathematical Programming
Fig. 37. Software components and interactions
Therefore, one common formulation is used in OPL which contains “switches” that allow to specify which distinctive constraints and objective shall be used, e.g. for evaluating the partner proposal, determining the most preferred outcome, or generating a compromise. The “switch” is simply one of the input parameters written by Visual Basic to a text file and obtained from there by OPL as described above. A final remark is in place on the organizational perspective of how the collaborative planning scheme is implemented here. According to the description in chapter 4,345 each collaboration partner acts as an independent entity and controls a part of the total process flow associated with the negotiation scheme. In contrast, the implementation just presented lacks a distinction between responsibilities of individual partners. However, the responsibility or ownership aspect is irrelevant for testing the negotiation scheme’s performance in terms of solution quality and computational effort. Therefore, the easiest way to implement the scheme is by a single program that covers all process steps as in the implementation here with Visual Basic. Since the planning models are solved by calls from Visual Basic to the OPL engine, the implementation can actually be interpreted such that a central coordinator (Visual Basic) owns the coordination process and logic, but leaves it up to the decentralized units (planning models implemented in OPL) to solve their respective planning problems and report the results back to the coordinator.
345
See especially 4.3.2, pp.94.
168
7.2
7. Computational Evaluation
Generation of Test Instances
Recapping the modeling framework developed in chapter 3.1, we assume that the planning situation of each collaboration partner can be described as a multi-level, capacitated lot-sizing problem (MLCLSP).346 In order to create test instances we therefore adapt a concept developed by Derstroff (1995) for generating test problems for the MLCLSP.347 This design concept and resulting test problems have been used by various authors dealing with multi-level, capacitated lot-sizing.348 In the following we discuss which parameters have to be specified and how they are used in order to obtain a full description of a test problem (comprising all input data needed by the planning models). Also, we specify values or sets of values for basic parameters, if these are identical across all test instances used in the computational study. Values of parameters that are changed from some test instances to others are introduced in the succeeding sections prior to the actual discussion of test results. The following parameters have to be available in order to fully describe a test problem: • • • •
the problem’s dimensions the structure of operations and demand (forecast) series of final products resource requirements and available capacities, and relevant cost rates.
Problem dimensions represent basic characteristics of a test instance. They comprise the length of the planning interval and the number of items and resources per collaboration partner. The planning interval is set to 12 periods across most of the test instances. The only exception is made up by one test class where just 10 periods are considered. In tests with planning on a rolling basis, each planning cycle too covers 12 periods and a total of 23 periods is regarded. The number of items and resources per collaboration partner varies depending on the SC structure studied (single buyer and supplier or multiple partners) and the test class. For each SC structure several test classes are defined, each with a certain number of items and resources. The structure of operations is too specified for each test class separately. One commonality at this point is however that secondary demand coefficients rj,k349 are set to one across all test classes and items.
346 347 348
349
See pp. 25. C.f. Derstroff (1995), pp. 90. See e.g. Tempelmeier / Derstroff (1993), pp. 68, Tempelmeier / Derstroff (1996), pp. 750, Ertogral / Wu (2000), pp. 937, Stadtler (2003), pp. 487. I.e. units of item j required to produce one unit of a successor item k (see Model 1, p. 33).
7.2. Generation of Test Instances
169
Concerning demand forecasts, primary demand by external customers is only considered for end products. Six demand series are generated for each test class. Although actual values are class dependent, their generation follows a common logic. It rests on given average demand per final product, a seasonal curve, and a random component. The seasonal curve consists of a cosine oscillation with an amplitude of 0, 0.3, or 0.5 relative to the item’s average demand.350 The random component is drawn from a normal distribution with zero mean and a coefficient of variation of 0.1 or 0.2. Combining the three seasonal curves with the two coefficients of variation results in six demand series for each test class and final product. The number of resources as well as the specification of resource needs by individual items is again described separately for each test class. However, two properties concerning resource needs are common across all test instances. Namely, each item is only processed at a single resource and item-resource coefficients ar,j351 are set to unity for all items and resources. Available resource capacities are not directly used as input parameters. Instead, average capacity utilization is specified for each collaboration partner. Available resource capacity is then calculated from average capacity needs and given utilization. Capacity needs in turn are computed from a bill-of-material explosion of average final demand and each item’s unit resource requirements. Given average (primary and secondary) demand E j for all items j and utilization Ur,t per resource and period, available capacity is obtained for all resources as Cr , t =
1 U r ,t
∑ ar , j E j
j∈J r
∀r , t
(176)
(where Jr is the set of items processed at resource r). Seven capacity utilization profiles are considered for each test class as given in Table 15. The underlying idea is to combine varying utilization levels at the buyer and supplier stage. In profiles 3 and 4 utilization varies over time, the numbers in brackets show the corresponding time intervals.352 Finally, cost rates are required for directing planning decisions. Given the planning situation underlying multi-level, capacitated lot-sizing, data on inventory holding, setup, variable production and capacity expansion (overtime) cost must be available.353
350 351
352
353
C.f. Stadtler (2003), pp. 487. I.e. capacity units of resource r required to process one unit of item j (see Model 1, p. 33). In test class L, where the planning interval is limited to 10 periods, available capacity changes in periods 3 and 9 rather than 4 and 10 as shown in the table. See Model 1, p. 33. Variable production costs are neglected, assuming that unit production costs per item do not change during the planning interval and hence do not affect planning results.
170
7. Computational Evaluation
Table 15. Capacity utilization profiles Profile
Supplier(s)
Buyer(s)
cap-1 cap-2 cap-3 cap-4 cap-5 cap-6 cap-7
90 % 70 % 70 % (1-3,10-12), 90 % (4-9) 90 % (1-3,10-12), 70 % (4-9) 70 % 90 % 50 %
90 % 70 % 90 % (1-3,10-12), 70 % (4-9) 70 % (1-3,10-12), 90 % (4-9) 90 % 70 % 50 %
Capacity expansion is considered in two “modes”. The first, “allowable” mode refers to actual overtime that can be planned for at given costs per unit of capacity. It is restricted to 20% of the resource’s regular period capacity in all computational tests. The second, “expediting” mode does not represent capacity expansion that could as such be put into practice. Instead, it serves as a last resort to ensure that feasible solutions can be found for all test instances in mathematical programming. If the optimal solution to a planning model contains overtime in expediting mode, then it is actually impossible to realize the desired production volume within given resource capacities and allowable overtime. Thus, unit costs of the expediting mode are significantly higher than those of the allowable mode as well as all other cost rates, so that the expediting mode is only planned for when no other choice exists to fulfill demand.354 The various cost rates needed for specifying a test problem are not all together generated as independent input parameters. Rather, only two basic data items are used: a marginal holding cost rate per item and each item’s average cycle time or time-between-orders (TBO). Marginal (or echelon) holding costs can be defined as the difference between an item’s holding cost and the sum of holding costs of all direct predecessor items.355 TBO represents an average production frequency that would result, if the item’s marginal holding and setup costs were optimally balanced with an isolated view of the item in question and by neglecting capacity restrictions.356 Given marginal holding costs and TBO’s of each item, the actual cost rates needed for the planning models can be deducted. This concept of calculating all cost rates from marginal holding costs and TBO’s has two advantages. First, the number of input parameters that have to be specified is significantly reduced compared to the number of cost rates needed by the planning models. Second and most important, all cost rates are reasonably scaled and coherent with each other. This
354
355 356
With respect to capacity expansion, the concept used here differs from Derstroff (1995) who does not foresee capacity expansion at all. Stadtler (2003) allows for overtime only in the prohibitive expediting mode (c.f. Stadtler (2003), pp. 487). C.f. Tempelmeier (2003), p. 213. C.f. Derstroff (1995), p. 92.
7.2. Generation of Test Instances
171
is important, because by independently specifying values for cost parameters, there is a danger that values are chosen such that some “extreme” solutions result. For example, strict lot-for-lot production may result, if setup costs are chosen too small relative to inventory carrying costs. Given marginal holding costs, total holding costs can be calculated recursively, starting at the “bottom” of the bill-of-material, by subsuming each item’s marginal holding costs and the total holding costs of all direct predecessor items according to357 ch j = cmh j +
∑ rl , j chl
∀j
l∈Pj
(177)
(cmhj refers to the item’s marginal holding costs and Pj is the set of direct predecessor items). Setup costs can be obtained from each item’s marginal holding cost and TBO. The underlying assumption is that the TBO was determined based on the item’s marginal holding cost, setup cost, and average demand by use of the classical EOQ formula for single-item lot-sizing with stationary demand. Thus, an item’s setup cost follows from given TBO and average demand E j to:358 cf j =
1 cmh j (TBO j ) 2 E j 2
∀j
(178)
Finally, costs of allowable overtime are expressed as costs of operating the resource for some additional time. They are too calculated from marginal holding costs of the items processed at the respective resource. This becomes possible by assuming that holding costs only represent (opportunity) costs of capital, i.e. interest. In such a situation, marginal holding costs can be calculated from the valueadded in production (abbreviated by vj in the following) according to cmh j = v j
i 52
∀j
(179)
(i refers to the yearly interest rate and is divided by 52 assuming that weekly periods are considered – an interest rate i of 10% is used in all test instances). Now, if we further assume that the added value vj is completely generated by processing the item at the resource with limited capacity, vj can be expressed as the product of resource cost per capacity unit crr and the amount of capacity needed to process one unit of item j (ar,j), i.e. v j = ar , j crr ∀r , j ∈ J r (180) Combining (179) with (180) and rearranging the term, we get crr ( j ) =
cmh j 52 ar , j i
∀r , j ∈ J r
(181)
The resource cost rate depends on j, since several items are processed at one resource. In order to obtain a single value of resource operating costs, a weighted average is finally calculated based on each item’s average demand:
357 358
The abbreviations of cost rates follow the definitions laid out in Model 1, p. 33. See e.g. Silver et al. (1998), pp. 151, Chase et al. (1998), pp. 587.
172
7. Computational Evaluation
crr =
1
∑E j
j∈J r
∑
j∈J r
cmh j 52 Ej ar , j i
∀r
(182)
Resulting are resource costs crr that are used as overtime cost rates cor, so that we finally obtain359 cor = crr ∀r (183) E The cost rate of the expediting mode cor is derived from allowable overtime costs by simply multiplying the respective values by ten: (184) cor E = 10cor ∀r E In that way we ensure that cor are large enough to avoid the expediting mode whenever possible. Now, concerning the specification of the basic input parameters, one set of marginal holding costs and three TBO-profiles are defined for each test class. Marginal holding costs per item are generated randomly based on a rectangular distribution. Their values originate from the interval [0.5;1] with regard to items processed by the buyer, whereas values of supplier items are drawn from the interval [1.5;2]. The reason behind this differentiation lies in the fact that, in this way, the supplier’s portion of total SC costs tends to be higher than that of the buyer. As observed by Simpson / Erengüc (2001), this property in turn hinders that initial Upstream solutions already come close to the global SC cost optimum.360 Similarly, TBO’s influence the magnitude of setup costs and hence too affect the costs accruing to each collaboration partner. Therefore, three profiles are used for each test class. In a basic profile, all TBO’s take one identical value (usually 4 periods). In a second profile, TBO’s of buyer items are reduced by 25% while TBO’s of supplier items are increased by 25% (e.g. 3 periods at the buyer and 5 periods at the supplier). In the third profile, the situation is reversed, i.e. TBO’s are higher at the buyer (+25% vs. profile one) and lower at the supplier (-25%). A summarizing overview of input parameters and value specifications is given in Table 16. Resulting is a total of 126 test problems for each test class which follows from combining the six demand series, seven capacity utilization profiles, and three TBO profiles.
359
360
Of course, a (percentage) surplus could be added for overtime operation due to higher overtime wages etc. This is however omitted for the sake of simplicity. C.f. Simpson / Erengüc (2001), p. 123. Since the negotiation scheme is intended to “close the cost gap” between Upstream Planning and centralized optimization, significant initial gaps are desired.
7.3. Tests with a Single Buyer and Supplier
173
Table 16. Overview of input parameters for test problems Parameter
Specification
planning interval secondary demand coefficients rj,k item-resource coefficients ar,j interest rate of capital
12 (10 in test class L) 1 for all items
Defined per test class
marginal holding costs number of items / resources bill-of-material resource needs by items
one set per test class (defined below) (defined below) (defined below)
Systematically varied
demand series capacity utilization
six per test class seven profiles as given in Table 15 three profiles per test class
Deducted
inventory / setup / overtime costs
Pre-set for all test instances
TBO’s
resource capacities
7.3
1 for all items and resources 10% in all test instances
calculated from marginal holding costs and TBO’s as given in (177) to (184) calculated from cap. utilization as given in (182)
Tests with a Single Buyer and Supplier
In this section we analyze the performance of the negotiation-based scheme between two SC partners, one buyer and one supplier. We first introduce the test classes generated for this SC structure and the test program, i.e. the types of computations carried out. Various aspects of the test results obtained with the basic scheme as developed in chapter 4 are then laid out and discussed in sections 7.3.2 and 7.3.3. In section 7.3.4 we describe results obtained for a subset of the test classes by applying the collaborative planning scheme with limited exchange of cost information as described in 5.3. 7.3.1
Test classes and test program
The objective of generating test classes is to create a “representative” and large enough sample of test problems, so that the computational results give a sound implication on the general solution quality that is attainable with the collaborative planning scheme. Furthermore, the scheme’s sensitivity to specific parameter values and their combinations can be tested. Six test classes are generated for that purpose.
174
7. Computational Evaluation
Table 17. Test classes for single buyer and supplier
small
S1
S
S2
B
S
1
5
4
2
6
S
B
6
B
4
2
5
3
7
S3
1 2
6
1
5
3
3
4
medium
M1
S
M2
S
B
8
5
9
6
10
7
1
8
2
9
3
10
B
7
1 3
6
4
large
2
5
L
S
4
B
22 23
15
24
16
10
25
17
11
7
3
26
18
12
8
4
27
19
13
9
28
20
29
21
1
14
2
5 6
30
They mainly differ by the problem dimensions in terms of number of items (total and per SC partner) and number of constrained resources. An overview is given in Table 17 (items are visualized by boxed numbers and resources by frames enclosing all items processed at the respective resource).
7.3. Tests with a Single Buyer and Supplier
175
Test classes with small problem structures comprise 6 or 7 items and 2 or 3 resources. Class S1 has a two-level bill-of-material and a single constrained resource at each collaboration partner. In classes S2 and S3 there are three-level bills-ofmaterial (BOM) and 3 resources. In S2 a convergent BOM structure prevails such that all component items are ultimately used in a single end product. The buyer controls the first two BOM-levels and resources. S3 contains a divergent structure where all end products are based on a single common component. Here the supplier governs two levels of the BOM and two constrained resources. Medium-sized test classes contain 10 items and 3 resources. There are 4 end products and the BOM is identical for both M1 and M2.361 In M1 the buyer is in charge of only the end products which are processed at a single constrained resource. In M2, the buyer produces end products and components 5 and 6, each (end products and components) at a dedicated resource. The supplier manufactures items 7 to 10 at a single resource. Finally, the large test class L contains 30 items and 4 resources. The BOM structure mainly converges to components 7,8,9 which are then differently combined to six end products. The buyer produces items 1 to 14 at two constrained resources. The supplier is in charge of items 15 to 30, also by utilizing two resources as shown in Table 17. The average demands of the various end products of each test class are given in Table 18. It can be seen that a mix of different values is typically used. Recapping that 126 instances are defined within each test class by combining six demand series, seven capacity utilization profiles and three cost structures as described in the previous section, the entire test set comprises 756 planning problems. As stated above, the major distinction between small, medium and large test classes are the problems’ dimensions. To underscore that point we therefore take a look at how the problem structures affect the numbers of variables and constraints that have to be planned for and obeyed, respectively, in the planning task. To do this we consider a single MLCLSP model which covers the entire SC as it is used in centralized planning. Reciting Model 1,362 planning decisions are drawn with respect to output xj,t and inventory levels ij,t per item and period, overtime or,t per resource and period, and binary setups yj,t per item and period. Also, we need to take into account that overtime can be planned for in two modes (allowable and expediting) as described above,363 so that the number of overtime variables doubles. In terms of constraints, balance equations and setup relationships must be obeyed for each item and period and capacity restrictions are imposed on each resource and period. Thus, there is a total of 2× J × T + 2× R × T (185)
361
362 363
The problem structures considered here are identical to test set A+ used by Stadtler (2003) (see Stadtler / Sürie (2000), p. 5). See p. 33. See 7.2, pp. 168.
176
7. Computational Evaluation
continuous variables, J × T
(186)
binary variables, and 2× J × T + R × T
(187)
constraints.364 Table 18. Average demand of end products
Test class S1 S2 S3 M1 M2 L
Item 1
2
3
4
5
6
70 100 70 70 70 40
30 30 30 30 20
50 50 50 50 30
100 100 100 60
20
30
Based on a planning interval of 12 periods for small and medium test classes and 10 periods for class L, as used in the computational study, the resulting numbers of continuous and binary variables as well as constraints per test class are given in Table 19. Classes S2, S3 and M1, M2 only differ by the structure of the BOM and assignment of items to resources. Since this does not influence the problem dimensions, corresponding problem sizes are identical. As can be seen, the problem sizes grow considerably from small to medium, and from medium to large test classes. The critical element herein is obviously the number of binary setup variables, since these trigger the size of the search tree and average computational time of the branch-and-bound process. As the number of binary variables increases by almost 43% from class S1 to M1/M2, and by another 150% from M1/M2 to L, it becomes obvious that the computational effort and solution time grows rapidly from the small to the large test classes. Table 19. Problem dimensions by test class
Test class
364
S1
S2,S3
M1,M2
L
Variables cont. binary
216 84
216 72
312 120
680 300
Constraints
192
180
300
640
C.f. Stadtler (1996), p. 572, (non-negativity restrictions on variable values are ignored).
7.3. Tests with a Single Buyer and Supplier
177
Regarding the test program, that is the type of computations carried out, the negotiation-based scheme obviously must be executed for each test instance and corresponding planning results be stored. However, in order to have comparison bases, i.e. benchmark solutions, for negotiation outcomes, results obtained with other planning approaches also have to be available. Two benchmarks are used here to evaluate the negotiation scheme. For one, Upstream Planning results are considered. They represent an upper bound on total SC costs as the Upstream solution forms the starting point of the negotiation scheme. Secondly, results obtained with a single MLCLSP model covering the entire SC are regarded. Since cost-optimal planning results for the SC as a whole can be found in that way, these results can be used as lower bounds on total costs. Upstream Planning solutions can be directly gathered when the negotiation scheme is executed, where they correspond to the initial outcome of iteration one. Concerning the global planning model, a pure MLCLSP is also implemented in OPL and run from Visual Basic similarly as the planning models pertaining to the negotiation scheme. The formulation used for the global MLCLSP corresponds to a “shortest route” model representation of the MLCLSP.365 It was chosen because the initial LP relaxation is tighter here, average quality of first integer solutions is better and optimality proven in shorter time than with the basic I&L formulation as given in Model 1.366 A final aspect concerning the test runs is the definition of limits on the maximum computational time given to the CPlex solver. This is particularly important with respect to the global MLCLSP model, as optimal integer solutions, even in small test classes, can only be found with notable computational time. In medium and large test classes, time limits are also required, or at least useful, in the negotiation scheme itself. This especially regards to Model 4 and 5 as used for determining the most preferred outcome associated with the current order / supply proposal. This is due to the fact that, by introducing modifications to the order / supply pattern, the set of feasible solutions is enlarged considerably and the models’ solution time increases. Therefore, restrictions on the computational time are defined as shown in Table 20 based on a series of preliminary test runs. The time limit for the negotiation scheme is meant as maximum time per planning model. Concerning small test classes, the model solution time during the negotiation scheme is usually within a few seconds, and the limit only restricts the computational time of some exceptional cases. This situation however changes as of the medium test classes. Here, as well as for the large test class, the time limit is chosen such that Model 2 and 3 as used to determine the current proposal’s outcome are solved optimally (or nearly optimally) prior to reaching the time limit. Also, optimal solutions to the goal programming models are available within the time limit in many test instances, while the time limit truly applies to finding the most preferred solution (Model 4 / 5) as mentioned above. Finding only sub-optimal preferred outcomes
365 366
See Stadtler (1996), p. 570. C.f. Stadtler (1996), pp. 574.
7. Computational Evaluation
178
can however be tolerated, since these are only used as an orientation point for generating the actual comprise proposals. Table 20. Limits on the computational time
Test class Time Limits [sec.] global MLCLSP negotiation scheme
S1/2/3
M1/2
L
600 60
1200 120
1800 180
With regard to centralized planning with a single, global MLCLSP model, the situation is similar. In test classes S1/2/3 optimal solutions can be obtained within the time frame for almost all test instances. For medium-sized problems of classes M1/2, the time limit of 1200 sec. is sufficient to find the optimal solution in a majority of test problems, but by far not for all. Concerning class L, optimal solutions can however hardly be found. Still, the time limit is not farther increased, because even by increasing the limit the quality of solutions (in terms of best integer solution vs. best LP bound at the end of the branch-and-bound process) rises only slowly. In order to potentially find better benchmark solutions than the best integer solution to the global MLCLSP model after 1800 sec., a heuristic solution procedure to the MLCLSP based on internallyrolling schedules as developed by Stadtler (2003) was additionally applied to the test problems of class L.367 Based on the heuristic, which decomposes the global problem to a sequence of sub-problems with shorter planning intervals, solutions can be found to class L problems within a short time frame (100 sec. where used in the computations). The negotiation results are then compared to the best solution found, i.e. either the best solution to the global MLCLSP model or the outcome to the heuristic.368 7.3.2
Overview of test results
All computational results presented in this and subsequent sections are obtained at a PC with Intel Pentium IV CPU (2.4 GHz). As a starting point, we consider the benchmark solutions to central planning by a single, global MLCLSP model. Table 21 contains an overview of results obtained across the six test classes and based on the time limits as given above in Table 20. The first row (‘”Total”) shows that in 529 of 756 test instances optimal solutions are found and optimality is proven. Concerning the other 227 test problems, the maximum remaining integrality gap, i.e. the difference between the best
367 368
C.f. Stadtler (2003), pp. 487. Strictly speaking, without optimal solution to the global MLCLSP, the best known solution no longer represents a lower bound on total SC costs. Nonetheless, best solutions are still used as comparison benchmarks in all test cases.
7.3. Tests with a Single Buyer and Supplier
179
integer solution and the best LP bound, is on average 5.4%. The average solution time comes to 642 sec. Table 21. Central planning results
Optimal solutions
Total
# 529
S1 S2 S3 M1 M2 L
126 102 116 72 112 1
Not-optimal solutions % gap vs. best LP bound av. 5.4% 3.7% 6.0% 3.8% 4.2% 6.5% (only MIP: 7.1%)
Av. comp. time (sec.) 641.9 56.9 425.8 265.0 720.9 585.1 1797.4
Looking at the breakdown by test class, we see that the number of optimal solutions is highest for small test classes and decreases with growing problem complexity. This effect is offset to some degree by the extension of the time limit from small to medium and large test classes. The enlargement of the computational time to 1200 sec. is particularly successful in test class M2, where 112 of 126 instances are solved optimally within the time limit. Not surprisingly, the situation is worst with respect to class L. Here, the time limit of 1800 sec. is insufficient to prove optimality (except in one case). Also, the maximum remaining integrality gap is largest with an average of 6.5%. The results shown in Table 21 already include outcomes obtained with the internally-rolling schedule heuristic. If only best solutions to the global MIP are regarded, the average gap comes to 7.1% as also stated in the table. This indicates that improved solutions can be found with the heuristic in some cases, but the situation does not change drastically. Next, we consider the other, upper limit, benchmark solutions of Upstream Planning. Table 22 shows an overview of the Upstream Planning results in total and by test class. The major distinction with regard to Upstream results is made between solutions which include overtime in expediting mode at the supplier’s domain and those where feasible solutions are found with given capacity and allowable overtime (maximal 20% of period capacity). Based on the framework described above,369 the first case indicates that the supplier is not able to cover buyer orders within given capacity limits. In result, he would either need to outsource some of the orders to another (external) supplier or fulfill the orders only in part or delayed. This (unsatisfying) situation results from the fact that the buyer does not account for the supplier’s capacity situation in Upstream Planning. Central planning results, in contrast, contain at most overtime in
369
See 7.2, pp. 168.
180
7. Computational Evaluation
allowable mode, which shows that capacity-feasible solutions can be obtained for all test instances. Table 22. Upstream Planning results
Insufficient capacity
Total
# 94
S1 S2 S3 M1 M2 L
25 4 22 6 7 30
Sufficient capacity (incl. allowable overtime) % cost gap vs. central planning Average Std. Dev. Min 23.0% 42.8% -2.2% 25.6% 33.9% 18.3% 18.8% 15.3% 26.9%
32.6% 61.7% 32.7% 38.7% 21.7% 52.4%
0.8% 0.0% 0.0% 0.5% 0.2% -2.2%
Av. comp. time Max 358.0% 150.5% 333.2% 198.6% 213.4% 103.8% 358.0%
(sec.) 52.2 1.0 1.0 1.0 16.8 4.4 289.1
As shown in the first column of Table 22, there are in total 94 test instances where capacity and allowable overtime are exceeded at the supplier domain. The number of such outcomes largely varies from test class to test class with most cases originating from classes S1, S3, and L (presumably due to the corresponding, randomly generated demand series). The middle section of Table 22 serves to assess the solution quality of the remaining 662 test instances. The performance indicator used here is the percentage gap of resulting total costs vs. associated central planning solutions, i.e. (188) (C res,UP − C res,CENT ) / C res,CENT Average of the gaps, standard deviation, minimum, and maximum values are listed for the total and by test class. As can be seen, the gap averages to 23% showing that Upstream Planning mostly yields costs which deviate significantly from the global optimum. Also, the standard deviation of 42.8% indicates that the gap varies strongly across individual instances. This is farther supported by the range between the minimum of – 2.2% (Upstream Planning outperforms the best integer solution to central planning here) and a maximum value of 358%. Although average values and standard deviations fluctuate across test classes, the order of magnitude is comparable in all cases. The highest deviation from central planning can be observed for test class S2. Upstream results outperform central planning in nine test instances of class L. This is in line with one’s expectations, since optimal solutions to central planning are not available here and maximum integrality gaps are still relatively large. Finally, the rightmost column of Table 22 underscores that the single dimension in which Upstream Planning clearly tops central planning is the computational effort required to obtain results for the entire SC. Notable computational times only occur in medium and large test instances. With an average of 4.4 and 16.8 sec., respectively, the total time limit of 240 sec. (120 sec. times two model
7.3. Tests with a Single Buyer and Supplier
181
solutions) is never required in medium test classes. Only in class L, the time limit (360 sec. in total) indeed terminates the computations in some test instances.370 Now we turn to results realized with the negotiation-based scheme. First, it should be noted that, unlike Upstream Planning, the negotiation scheme yields results without overtime in expediting mode in all test cases. This means, that capacity shortages present in Upstream Planning results are successfully resolved in every instance by rearranging the order / supply pattern. This initial observation already demonstrates the improvement potential brought about by the modelbased negotiation process. The overview of results of the negotiation scheme is presented in Table 23. The first columns refer to the same performance indicator as used for assessing Upstream results, i.e. the solutions’ percentage gap vs. central planning. Again, average, standard deviation, minimum, and maximum values are listed. Table 23. Negotiation scheme results
% cost gap vs. central planning
Iterations
Total
Average 1.7%
Std. Dev. 2.0%
Min -2.2%
Max 12.0%
Av. 4.6
Av. comp. time Total Per model (sec.) (sec.) 674.5 26.5
S1 S2 S3 M1 M2 L
2.4% 1.5% 0.9% 1.5% 1.6% 2.0%
2.4% 1.8% 1.2% 1.7% 1.8% 2.5%
0.0% 0.0% 0.0% 0.0% -0.7% -2.2%
12.0% 9.6% 5.6% 8.8% 9.8% 12.0%
5.3 3.7 4.4 4.7 4.3 5.1
35.8 24.6 66.4 1425.2 276.3 2218.5
1.2 1.2 2.7 54.2 11.6 79.2
On average, negotiation results deviate from the best integer solution to the global MLCLSP model by 1.7%. Also, the standard deviation of 2% implies that the majority of outcomes lies in the vicinity of the average value. The minimum value is identical to Upstream Planning at –2.2%. The maximum value, that is the maximum deviation from central planning observed across all test instances, however comes to only 12% as opposed to 358% in Upstream Planning. Concerning outcomes by test class, some variation in the average values can be observed. To some degree this correlates with average gaps of the initial Upstream solutions, i.e. best results are obtained for classes S3, M1, and M2 where the average gaps of Upstream solutions are smallest. Standard deviations are all of a similar magnitude, indicating that most results are relatively close to average values in all test classes. Maximum values are 12% for classes S1 and L, and even lie below 10% in the remainder. In total, test class S3 offers most favorable results regarding all measures average gap, standard deviation, and maximum value.
370
This information is not taken from Table 22, but from the detailed records available to the author.
182
7. Computational Evaluation
As shown in the middle column, 4.6 iterations take place on average. This means that a moderate number of about nine order / supply proposals (one per partner and iteration) is generated and exchanged. It must however be noted that, even though the number of iterations is relatively small, the negotiation scheme consumes considerable computational time. This is not unexpected, since (at least) three MIP models are solved per iteration and partner. The resulting average total time elapsing during the negotiation scheme comes to 674.5 sec., the corresponding average time per planning model lies at 26.5 sec. Inspecting the times by test class, we can see that the relatively high average value is mainly caused by test problems of classes M1 and L. While average times of small test classes are in the range of 25 to 66 sec. with an average time per model of 1 to 3 sec., it grows to 276 sec. (or 11.6 sec. per model) in class M2, and even to 1425 and 2218 sec., respectively, in classes M1 and L. All in a whole, the gain in solution quality as compared to Upstream Planning comes at a considerable computational effort, especially in complex problem structures. One conclusion of this finding can be to further reduce the number of iterations carried out in the scheme, particularly when good improvements vs. Upstream Planning can already be achieved in the first iteration(s). This aspect is, among others, considered in more detail in the next section 7.3.3. Apart from the computational effort, we can however note that, based on the computational results, solutions of a quality close to central planning are achieved with the negotiation scheme in most instances. In order to get insight on the solution quality beyond average and standard deviation and thus a more detailed comparison to Upstream Planning, Fig. 38 exhibits frequency distributions of test results as functions of the percentage gap to central planning. Fig. 38 a) refers to test classes S1 to M2, whereas results of class L are shown in part b). Class L is analyzed separately, since the benchmark solutions to central planning are of a lower quality. Also, as test problems of class L possess the highest complexity and are most difficult to deal with, it is particularly interesting to see how the negotiation scheme performs here. In both diagrams, the x-axis represents intervals of the percentage gap to central planning, e.g. 2-3%, 3-5% etc. The y-axis shows relative frequencies, i.e. percentages of test instances. Thus, concerning small and medium test classes (Fig. 38 a)) the bars indicate that in Upstream Planning gaps to central planning between 3 and 12% are most frequent. More than 20% of test results have gaps of 3 to 5%, almost 20% of 5 to 8% and another 15% of 8 to 12%. It can also be seen that a noteworthy number of test problems exhibits gaps of 0 to 1% or 1 to 2%, respectively. This shows that Upstream Planning can yield good solutions in some problem structures, an observation in line with Simpson / Erengüc (2001).371 On the other hand, arguably weak results with gaps of 30% and beyond are too obtained in some 20% of test instances.
371
C.f. Simpson / Erengüc (2001), p. 123.
7.3. Tests with a Single Buyer and Supplier
percentage test instances [%]
100%
183
Upstream & Negotiation Gaps vs. Central cumulated
80% 60%
negotiation upstream
40% 20% 0% <1%
<2%
<3%
<5%
<8%
<12% <20% <30% <50% <80% <130% >130%
gap vs. central pl. solution [%]
a) test classes S1 to M2 Upstream & Negotiation Gaps vs. Central (Class L) 100% percentage test instances [%]
cumulate d 80% 60%
ne gotiation upstre am
40% 20% 0% <-2%
<-1%
<0%
<1%
<2%
<3%
<5%
<8%
<12%
<20%
<30% <50%
<80% <130% >130%
gap vs. central pl. solution [%]
b) test class L Fig. 38. Frequency distributions of gaps vs. central planning
The picture drastically changes with the negotiation scheme. Here, the majority of test results (more than 50%) has gaps to central planning of less than 1%. Another 20% of test problems yield a gap of 1 to 2%, and the worst outcome falls into the interval of 8 to 12%. Looking at the cumulated frequency curves, one can see how the negotiations literally shift the Upstream Planning curve to the left, towards significantly lower gaps to central planning. In result, almost 90% of test results after negotiations have a gap to central planning of less than 5%. These observations apply similarly to results pertaining to class L (Fig. 38 b)). The major difference is that a larger number of Upstream results already comes close to central solutions or even outperforms them. In total, about 30% of the test results have gaps of less then 1%. Since small gaps between Upstream and central planning are less frequent in other test classes, we can assume that this result is
184
7. Computational Evaluation
due to the lower quality of central solutions rather than to a better performance of Upstream Planning. Regarding remaining test instances (with gaps higher than 1%), gaps of Upstream results are widely spread across the x-axis with similar frequencies of better and worse solutions. With the negotiation scheme, on the other hand, again about 45% of test problems have gaps below 1% and about 85% of no more than 5%. The worst outcome falls again into the range of 8 to 12%. The final aspect of test results discussed in this section is what we will call “remaining gaps”. The discussion of gaps vs. central planning just laid out suggests that the negotiation scheme comes close to central planning solutions in a vast majority of test cases. Another, though related, question in this context is to which degree the negotiation scheme is able to “close the gap” to central planning which is present in Upstream outcomes. For getting some insight on this issue, we consider another performance indicator, namely the remaining gap after negotiations defined as the ratio between the gap vs. central planning after negotiations and prior to negotiations, i.e. in Upstream Planning. Mathematically, this is expressed based on resulting total costs as (189) (C res, NEGO − C res,CENT ) /(C res,UP − C res,CENT ) An overview with average and standard deviation values in total and by test class is shown in Table 24. It should however be noted that the analysis is limited to those 662 test instances without expediting overtime in the Upstream solutions. Test instances with overtime in expediting mode in Upstream Planning yield extremely high total costs due to the penalties included in the objective function. Corresponding remaining gaps after negotiations are therefore very small and depend on the values (arbitrarily) assigned to the penalty cost rates. As we can see from Table 24, remaining gaps average to 31.8% across all test problems. That is, about 68% of the cost gap between Upstream solution and central planning can be eliminated by the negotiation scheme on average. However, the standard deviation of 40.3% indicates that individual values vary strongly from some test instances to others. Table 24. Remaining gaps of negotiation outcomes
Total
Average 31.8%
Std. Dev. 40.3%
S1 S2 S3 M1 M2 L
28.6% 38.3% 28.7% 30.9% 23.9% 41.3%
35.2% 39.9% 38.0% 35.1% 38.9% 51.3%
As with the percentage gaps vs. central planning, results by test class vary to some degree, but are all of a similar magnitude. The largest remaining gaps are
7.3. Tests with a Single Buyer and Supplier
185
observed in test results of class L with an average of 41.3%. I.e., the negotiation scheme is least successful here in bringing total costs down towards the global optimum. This is not surprising, given that the most complex problem structures are dealt with here. Similarly as above, we can inspect the remaining gaps more closely by considering their frequency distribution. The corresponding diagram is exhibited in Fig. 39. It can be seen that test results with very small remaining gaps (less than 1%) are most frequent (almost 20% of test instances). Beyond that, remaining gaps are considerably spread across the interval of 1 to 100%, an observation which is backed by the high value of the standard deviation. One should however note that the interval size shown in the diagram increases steadily with growing remaining gaps.
Remaining Gaps (all test classes)
percentage test instances [%]
100% 80%
cumula ted
60% 40% 20% 0% <1%
<2%
<3%
<5%
<8%
<12%
<20%
<30%
<50%
<80%
>80%
remaining gap [%]
Fig. 39. Frequency distribution of remaining gaps
Looking at the cumulated frequency curve, we see that more than 40% of the tests have remaining gaps of below 8%, and about 60% of below 30%. On the other hand, a gap of more than 80% remains in a substantial number of test problems (about 20%). This means, that the negotiation scheme is less successful here in decreasing total costs down from the Upstream result. A potential explanation for this result are those test instances where the initial gap between Upstream and central planning is already relatively tight. In these cases, additional improvements are obviously more difficult to find as compared to tests with significant improvement potentials in Upstream Planning results. In order to test the hypothesis, that remaining gaps are particularly large when the gap of Upstream vs. central planning is small, the average percentage gap between Upstream and central planning was determined for test instances with a remaining gap of 80% and higher. Resulting is indeed an average gap of 2.6% which strongly supports the hypothesis. I.e. we can conclude that large remaining gaps
7. Computational Evaluation
186
go primarily back to test instances where the initial Upstream results is already close to the global optimum. 7.3.3
Results by cost structure, utilization profile, and iteration
So far we have dealt with total outcomes across all test problems or results by test class. For getting a better understanding of the effects of some input parameters, results are in addition categorized by such parameters in the following, namely by the cost structure and capacity profile underlying the test problem. Also, we analyze how the quality of solutions develops with a growing number of iterations. First, we consider how test results are influenced by the cost structure underlying a test problem. As explained above, all cost parameters used in the planning models are deducted from marginal holding costs per item and each item’s timebetween-orders (TBO).372 Whereas only a single set of marginal holding cost rates is used in each test class, three TBO-profiles are defined: equal TBO’s for all items, increased TBO’s for supplier (+25%) with decreased TBO’s for buyer (25%) items, and vice versa. In order to give an indication on how the different TBO-profiles affect resulting costs, Table 25 shows which portions of total costs accrue to buyer and supplier in Upstream Planning based on test class S1 (only test instances without expediting overtime are included). With equal TBO’s, the buyer covers on average 33% of total (SC-wide) costs, while 67% fall back to the supplier. This might astonish given that TBO’s are identical across all items, but we need to keep in mind that marginal holding costs and average (secondary) demands of supplier items are higher. Table 25. Division of total costs by TBO profile
TBO-profile
Supplier
Buyer
s-b S-b s-B
67% 77% 57%
33% 23% 43%
With increased TBO’s on supplier items (abbreviated by an upper case “S”), the imbalance naturally shifts even further towards a higher portion to the supplier and lower to the buyer (77 vs. 23%.). Based on increased TBO’s to the buyer, the effect is just reverse and a higher portion of total costs accrues to the buyer and a lower to the supplier (57 vs. 43%). An overview of test results by TBO-profile is given in Table 26 based on the total of 756 test instances. Total results across all test instances are listed next to results by TBO for better orientation. The table contains Upstream and negotiation results. Concerning Upstream Planning, first the number of capacity-infeasible so372
See 7.2, pp. 168.
7.3. Tests with a Single Buyer and Supplier
187
lutions, i.e. with expediting overtime, is shown, followed by average and standard deviation of the percentage gap vs. central planning of test instances without capacity overrun. Similarly, average and standard deviation of gaps vs. central planning are presented for negotiation solutions. In addition, average and standard deviation of remaining gaps as well as the average number of iterations is shown with respect to the negotiation scheme. Table 26. Computational results by cost structure
Negotiations Upstream Planning cost insuff. cap. gap vs. central gap vs. central structure # av. std. dev. av. std. dev.
remaining gap iterations av. std. dev. av.
Total
94
23.0%
42.8%
1.7%
2.0%
31.8%
40.3%
4.6
s-b S-b s-B
30 47 17
24.8% 29.0% 16.1%
42.6% 53.8% 28.9%
1.6% 2.1% 1.2%
1.9% 2.1% 2.0%
30.3% 38.3% 27.6%
28.8% 36.3% 26.4%
4.6 4.6 4.5
The results presented in Table 26 indeed display some variations which can be backed by intuitive reasoning. The first TBO-profile yields results that are close to the total across all test problems. The number of capacity-infeasible solutions to Upstream Planning is roughly one third of the total number (30 of 94), and average as well as standard deviations pertaining to gaps vs. central planing, remaining gaps, and the number of iterations are similar as over the total sample of 756 test instances. The second TBO-profile with higher TBO’s to the supplier and lower ones to the buyer causes a further shift towards the supplier in the portions of total costs as indicated in Table 25. Therefore, it is not surprising that the average gap of Upstream vs. central planning observed with this cost structure is higher than in profile one. Obviously, the new cost structure even leads to an increase in the number of capacity-infeasible solutions to Upstream Planning (47), although this is not directly influenced by the magnitude of cost rates. The performance of the negotiation scheme does not overly suffer. However, since initial Upstream solutions are farther off from global optimum, a somewhat higher average gap vs. central planning of 2.1% is obtained. Counter-intuitive is the increased average value of the remaining gap (38.3%). Based on larger initial Upstream gaps vs. central planning and a similar quality of negotiation results, one would expect smaller remaining gaps. Finally, the average number of iterations is again unchanged compared to the total average value. In the third TBO-profile the changes to TBO’s and thus setup cost rates are opposite to profile two, and the situation is reversed such that the buyer carries an increased portion of total costs. In result, the average gap of Upstream vs. central planning is smaller, since the supplier contributes a smaller part to total costs. Resulting is an average gap of just 16.1%. Also opposite to profile two is the effect on the number of capacity overruns so that overtime in expediting mode is only included in 17 test problems. Given the improved initial Upstream outcomes, the negotiation scheme performs slightly better and comes to an average gap vs. cen-
7. Computational Evaluation
188
tral planning of 1.2%. The number of iterations is again similar, and thus seems generally not to be affected by TBO-profiles or setup cost rates. Another interesting question is to see which impact available capacity has on the solution quality of Upstream Planning and the negotiation scheme. One obvious effect on Upstream Planning is that the likelihood of outcomes containing overtime at the supplier domain grows with increasing capacity utilization. Whether the performance of the negotiation scheme is also affected by available capacity, is however difficult to predict. An overview of test results by capacity utilization profile is presented in Table 27. The average capacity utilization faced by buyer and supplier in each profile corresponds to Table 15 above.373 Table 27 contains an overview of Upstream and negotiation results and is structured identically to Table 26. The first interesting insight refers to the number of capacity-infeasible solutions to Upstream Planning. As can be seen, all these outcomes originate in utilization profiles cap-4 and cap-6. The characteristic of these profiles is that the buyer has sufficient capacity (70% utilization) over the entire planning interval (cap-6) or during the first number of periods (cap-4), while the supplier faces a high utilization of 90%. Average gaps of (capacity-feasible) Upstream solutions vs. central planning are also by far highest in profiles four and six. The third largest average gap is obtained for profile one where both buyer and supplier face a high utilization of 90%. The smallest average gaps, and hence the best performance of Upstream Planning, is realized when capacity is tight at the buyer and uncritical at the supplier. In result, average gaps vs. central planning of only 2.4% occur in profile cap-5 and 7.1% in profile three (here, the buyer has 90% utilization only in the first and last periods). Table 27. Computational results by capacity profile
Negotiations Upstream Planning capacity insuff. cap. gap vs. central gap vs. central profile # av. std. dev. av. std. dev.
373
remaining gap iterations av. std. dev. av.
Total
94
23.0%
42.8%
1.7%
2.0%
31.8%
40.3%
4.6
cap-1 cap-2 cap-3 cap-4 cap-5 cap-6 cap-7
0 0 0 37 0 57 0
35.2% 10.3% 7.1% 56.6% 2.4% 85.7% 8.5%
38.5% 19.3% 14.9% 49.6% 1.9% 86.8% 12.8%
2.5% 1.1% 1.2% 2.8% 1.4% 1.0% 1.6%
2.5% 1.4% 1.5% 2.9% 1.5% 1.2% 1.6%
19.6% 28.8% 31.8% 22.0% 66.7% 9.2% 29.4%
17.3% 27.7% 30.6% 19.6% 65.3% 8.3% 27.8%
4.4 4.3 3.4 5.8 2.8 6.8 4.4
See p. 170.
7.3. Tests with a Single Buyer and Supplier
189
Compared to Upstream Planning, the negotiation scheme proves relatively insensitive to changes in available capacity. Some variations in average gaps vs. central planning can be observed, too. In particular, the worst performance relates to capacity profiles one and four with average gaps of 2.5 and 2.8%, respectively. However, with an average gap in the range of 1 to 2.8% good results are obtained for all capacity utilization profiles. The weakest performance observed with profiles one and four might be linked to the high capacity utilization faced by the buyer. Due to the tight capacity at the buyer, the supplier’s compromise proposals can be more harmful than in situations with sufficient slack capacity. Hence, chances are smaller to find overall cost improvements. This can in turn lead to a lower average solution quality. Nonetheless, with an average gap of 2.8% and a corresponding standard deviation of 2.9% the performance degradation is only limited and the negotiation scheme still delivers satisfying results. The average number of iterations is also influenced by the capacity situation. Here, the average gap vs. central planning present in Upstream solutions seems to correlate with the average number of iterations carried out by the negotiation scheme. The maximum values of 6.8 and 5.8 pertain to capacity profiles four and six with highest average gaps in Upstream outcomes. On the other hand, the smallest number of iterations is observed in profiles three and five where Upstream Planning performs best. This interdependence seems logical, since the effort (in terms of the number of iterations) required to bring resulting costs close to the global optimum can be expected to increase with a growing initial gap. Finally we analyze how the quality of solutions obtained with the negotiation scheme develops from iteration to iteration. Above we have seen that the negotiation scheme yields results close to central planning with an average gap of 1.7% across all test instances and a maximum average gap per test class of 2.4% (class S1). However, this performance is accompanied by considerable computational times of 675 sec. as total average and values of 1425 sec. and 2219 sec. in test classes M1 and L, respectively. On the other hand, one advantage of the negotiation scheme as stated at the beginning of chapter 4 is that a consistent overall plan can be obtained from each compromise proposal in every iteration. Thus, the negotiation process can be terminated prior to when this happened in the computational tests based on the stopping criteria described in chapter 4. For example, the procedure can be aborted after a predefined number of iterations or a preset maximum computational time. Especially for complex, computationally expensive problem structures, it is therefore interesting to see how the quality of solutions develops in the course of the negotiation process. For that purpose Table 28 shows an overview of average gaps vs. central planning by iteration. Two columns are given for each iteration, as two proposals (one by each partner) are generated. As in the analyses above, the total average across all test problems as well as value per test class are given. The rightmost column contains the final average gaps based on the end results to the negotiation scheme. First it should be noted that the values presented in Table 28 are derived from all 126 instances per test class, including those cases where overtime in expediting
7. Computational Evaluation
190
mode and associated penalty costs occur in the Upstream outcome. For this reason the average values of the first outcome in iteration one take relatively large values (133% for total). The average gaps of Upstream Planning presented in Table 22 above are in contrast based only on capacity-feasible solutions, and hence by far lower (total average of 23%). Taking the total results across all test classes, one can see that the final average gap vs. central planning of 1.7% is available as of iteration six. Inspecting the results backwards from iteration six shows that average gaps close to the final outcome are already obtained in iteration four (1.8%). Even results of iteration three come fairly close to the final gap with 2.0%. In fact, one can observe that the solution quality makes a substantial leap forward with the second outcome of iteration two, already resulting in an average gap of just 3.2%. Table 28. Average gaps vs. central planning by iteration Iteration 1
Final 2
3
Total 133.0% 14.7% 11.3% 3.2% S1
4
5
6
2.2%
2.0%
1.9%
1.8%
1.8% 1.8% 1.7% 1.7% 1.7%
3.4%
2.9%
2.8%
2.7%
2.7% 2.6% 2.6% 2.6% 2.4%
1.6%
1.6%
1.0%
1.0%
1.6% 1.6% 1.6% 1.6% 1.5% 1.0% 0.9% 0.9% 0.9% 0.9%
86.4%
6.2%
5.6%
3.7%
S2
44.8%
7.6%
4.8%
2.4%
1.9%
1.9%
S3
180.7% 14.0% 13.1% 1.8%
1.3%
1.1%
M1
134.5% 8.2%
6.7%
2.2%
2.0%
1.8%
1.7%
1.7%
1.6% 1.6% 1.6% 1.6% 1.5%
M2
35.2%
5.2%
2.2%
1.9%
1.7%
1.7%
1.6%
1.6% 1.6% 1.6% 1.6% 1.6%
316.3% 44.9% 32.7% 7.1%
2.7%
2.6%
2.5%
2.4%
2.2% 2.2% 2.1% 2.1% 2.0%
L
7.1%
These characteristics also apply to the results per test class. Generally, a notable improvement is realized at the end of iteration two. In the succeeding iterations three to six, additional, but smaller improvements are obtained and the average gap converges to the final outcome. In result one can see that even if the negotiation scheme is aborted at the end of iteration two, substantial improvements vs. Upstream Planning can be realized on average. Continuing the negotiation process for one additional (third) iteration already brings results close to final, best outcomes. Based on these observations one could e.g. consider to limit the negotiation scheme to three iterations in test class L. In that way, results with an average gap vs. central planning of 2.6% could still be achieved. At the same time, the average computational time would be reduced to a factor 3/5.1 (5.1 is the average number of iterations in class L), roughly yielding a time consumption of only 1305 sec. as compared to 2219 sec. without early termination. 7.3.4
Results with limited exchange of cost information
In 5.3 a modified version of the negotiation-based collaborative planning scheme is presented aimed to limit the amount of cost information exchanged between buyer and supplier. Whereas the original version of the negotiation scheme con-
7.3. Tests with a Single Buyer and Supplier
191
tains communication of cost effects in both directions, from buyer to supplier and vice versa, it is only unidirectional in the modified version. Namely, the buyer still announces compensation needs associated with compromise solutions. The supplier however does not disclose local savings. Instead, he determines privately which cost improvements result from compromise solutions by adding the buyer’s compensation and his savings.374 We have argued above that the modified scheme can yield a performance similar to the original version. The only difference which might affect planning results is that the buyer cannot make use of cost anticipation in his goal programming models. In order to get an impression of the results attainable with limited exchange of cost information, the modified version of the collaborative planning scheme was too implemented in Visual Basic. Computational tests covering the small test classes S1 to S3, i.e. a total of 378 test problems, were rerun. An overview of the results is presented in Table 29. It shows gaps vs. central planning and the average number of iterations as obtained with the original scheme and corresponding results with limited exchange of cost information. The average gap vs. central planning across all three test classes comes to 1.8% with the modification in place and thus is slightly higher than the original 1.6%. The standard deviation is in total 2.2%, implying that here too most results fall into the vicinity of the average. Similar to the average, the maximum value of 13.7% compares to 12% in the original scheme. The number of iterations is notably smaller with an average of 3.6 vs. an original value of 4.6. It indicates that more degraded solutions occur without cost anticipation at the buyer side which on average causes an earlier termination of the scheme. Table 29. Negotiation results with limited exchange of cost information
iterations av. 4.6
Limited cost gap av. 1.8%
Exchange
Total
Original cost gap av. 1.6%
std. dev. 2.2%
min 0.0%
max 13.7%
iterations av. 3.6
S1 S2 S3
2.4% 1.5% 0.9%
5.3 3.7 4.4
2.7% 1.6% 1.2%
2.6% 2.0% 1.6%
0.0% 0.0% 0.0%
13.7% 13.6% 10.4%
3.8 3.2 3.7
Results by test class display a similar pattern. Average and standard deviation of gaps vs. central planning are slightly higher in all cases, and the average number of iterations is lower. Significant increases can however be observed for the maximum gaps vs. central planning in test classes S2 (from 9.6 to 13.6%) and S3 (from 5.6 to 10.4%). This suggests that in some test problems the outcome can degrade notably due to the lack of cost anticipation at the buyer domain.
374
See pp. 125 for details.
7. Computational Evaluation
192
In conclusion, a certain performance loss can indeed be observed, as one would expect. However, the results demonstrate that a good performance in terms of resulting costs can still be realized. Thus, limited exchange of cost information can be a promising solution when the supplier shies away from disclosing savings. As stated above, the major difference between the scheme with limited exchange of cost information and the original version stems from the absences of cost anticipation at the buyer side. Since the resulting performance loss is rather small as just discussed, one may ask whether the concept of cost anticipation in goal programming is required at all or whether similar results can be obtained when it is simply omitted. Therefore, the computational tests based on the scheme with limited exchange of cost information were repeated, this time without cost anticipation at both buyer and supplier, in order to analyze whether the cost anticipation brings any value, i.e. result improvement, at all. Corresponding results are shown in Table 30 which has the same format as Table 29. Table 30. Negotiation results without cost anticipation
Total
Original cost gap av. 1.6%
iterations av. 4.6
S1 S2 S3
2.4% 1.5% 0.9%
5.3 3.7 4.4
No Anticipation cost gap av. std. dev. 3.8% 7.5% 4.4% 2.6% 4.4%
2.9% 3.2% 12.2%
min 0.0%
max 99.6%
iterations av. 3.2
0.4% 0.0% 0.0%
18.7% 21.4% 99.6%
3.4 2.8 3.3
In essence, one can observe that, this time, more significant increases in average and standard deviation of the gaps vs. central planning are obtained. Overall, the average gap is more than twice as high as with the original scheme (3.6 vs. 1.6%). The standard deviation too increases considerably from 2.0 to 7.5%. Even worse, the maximum gap observed across all test instances grows to 99.6% from 12% with the original scheme and 13.7% with limit exchange of cost data. This maximum value implies that at least in one instance the negotiation scheme is no longer able to eliminate all overtime present in the initial Upstream outcome, a situation not observed in the results presented so far. The average number of iterations has farther decreased, presumably due to more frequent cost degradations already occurring in early iterations. Results by test class are in line with the general trend in that average and standard deviation of gaps vs. central planning are significantly higher now. Only with regard to their maximum values, test classes S1 and S2 yield better results than S3. A final, more detailed, comparative overview of results obtained with the original version and the modified scheme with limited exchange of cost data, with and without cost anticipation at the supplier domain, is given in Fig. 40. It contains a diagram with cumulated frequencies of gaps vs. central planning of the three test runs. It can be seen that the original version and the scheme with limited exchange including cost anticipation by the supplier perform similarly well also in terms of
7.4. Tests with One Supplier and Several Buyers
193
frequency distributions of gaps vs. central planning. In both cases, roughly 50% of test results have a gap of less than 1%, about 70% of at most 2%, and more than 80% of 0 to 3%. In contrast, results obtained with the modified scheme without cost anticipation are clearly inferior. Here, only 22% of test instances possess gaps of up to 1%, about 40% gaps of up to 2%, and less than 60% of up to 3%. In conclusion, the final set of computational tests shows that cost anticipation as it is proposed here indeed pays off. Resulting is a performance improvement of the negotiation scheme which leads to average gaps vs. central planning that are about 50% smaller than without cost anticipation. On the other hand, tests performed with the modified scheme and including cost anticipation at the supplier side display similar results as the original negotiation scheme. Cumulated Frequencies of Gaps vs. Central
percentage test instances [%]
100% 80%
Original Limited Exchange
60%
No Anticipation
40% 20% 0% <1%
<2%
<3%
<5%
<8%
<12%
<20%
<30%
<50%
<80% <130% >130%
gap vs. central planning [%]
Fig. 40. Cumulated frequencies of gaps vs. central planning
7.4
Tests with One Supplier and Several Buyers
In this section we analyze the performance of the negotiation scheme in SC settings, where one supplier serves several buyers. This setting is of particular relevance from suppliers’ viewpoint, as these often have several customers with whom they develop close relationships. In the following we first describe the test classes defined for this scenario and the test program carried out. Test results and their characteristics are discussed thereafter in section 7.4.2. 7.4.1
Test classes and test program
Four test classes are generated for the single supplier – multiple buyers scenario. The major focus here is laid on a setting with two buyers which underlies three of
194
7. Computational Evaluation
the test classes. Test class four represents a case where the scope is farther extended to three buyers cooperating with the supplier. The test structures used in this section are exhibited in Table 31. Test classes 2B-1 to 2B-3 are based on the small classes used in the single buyer and supplier setting and were essentially obtained by doubling the problem structure pertaining to the buyer. In case of 2B-1, the fourth buyer item present in S1 is eliminated in order to obtain the same problem dimensions as underlying 2B-2/3. In 2B-2 and 2B-3 on the other hand the number of resources present at the buyer domain is reduced from two (in S2/S3) to one. In result, each SC partner is in charge of three items that are processed at a single resource, yielding a total of nine items and three resources in all test classes. Table 31. Test classes for multiple buyers and one supplier 2 Buyers
2B-1
S
2B-2
S
S
1 2
1
2
3
7
3
8
8 9
B1
2
1
7
2B-3
B1
B1
5
8
4 5
4
5
6
6
6
B2
B2
B2 3 Buyers
3
9
9
4
7
3B 2
S
1
B1
4
B2
7
B3
3 10
5
11 12
6 8 9
Test class 3B rests on class 2B-2 and is obtained by copying the buyer problem yet another time. Resulting is a structure with three buyers, each processing three
7.4. Tests with One Supplier and Several Buyers
195
items (but only a single end product) at one resource. Corresponding test problems contain twelve items and four resources in total. Average demands of end products are also based on related two-partner scenarios. However, permutations are introduced vs. the original data in order to generate differing item-demand characteristics for each buyer. An overview is given in Table 32. The number of binary variables present in problems of test classes 2B-1 to 3B shall be considered, in order to give an impression of the complexity of the test instances. As the number of binary variables follows from the product of the number of items and planning periods, we only need to differentiate between test classes 2B-1 to 2B-3 on the one hand and 3B on the other. Given nine items as present in the two-buyer settings, the corresponding (global) MLCLSP model contains 108 binary variables (12 planning periods are considered as in the two-partner case). Test class 3B in contrast covers 12 items, yielding a total of 144 binary variables. Comparing these results with the numbers of binary variables present in the test problems with a single buyer and supplier, we see that the problem complexity faced here is similar to that of the medium sized two-partner test classes M1/M2 (120 binary variables). With respect to the negotiation scheme one should however bear in mind that the total problem structure now is split to three or four subproblems by partner, i.e. applying the negotiation scheme is computationally less complex here than in test classes M1/M2 above. Table 32. Average demand of end products with multiple buyers
Test class
Item 1
2
3
4
5
6
7
8
9
2B-1 2B-2 2B-3 3B
70 100 70 100
30 30 -
50 50 -
50 100 50 100
30 30 -
70 70 -
100
-
-
Concerning the test program, the same set of computations is performed here as in the two-partner setting described in 7.3.1. First, the negotiation scheme is carried out with each test instance, also yielding corresponding Upstream Planning results as a by-product. Of course, running the negotiation scheme with several buyers requires extensions to its basic form as laid out above in 5.1.1.375 The Visual Basic implementation used for the computational tests is therefore enhanced accordingly. In result, the distinct process steps of the negotiation scheme, i.e. evaluating the partner proposal, determining the preferred outcome, and generating a counter-proposal, are carried out by each buyer in turn before the respective order patterns and cost effects are submitted to the supplier. Also, as explained in 5.3.2 it is particularly compelling to combine the multiple buyer setting with the extension to limited exchange of cost information, as it avoids a centralized cost
375
See pp. 103.
7. Computational Evaluation
196
improvement check at the buyers’ side.376 On the other hand limited exchange of cost data can result in loss of some performance due to the lack of cost anticipation as investigated above in 7.3.4. Therefore, computational tests are run with both versions of the negotiation scheme, the original multiple-buyer form of 5.1.1 and the version with unidirectional exchange of cost data described in 5.3.2. In addition to the negotiation scheme, global MLCLSP models (central planning) are solved for each test problem to make up the lower bound, benchmark solutions. As in the two-partner case above, “shortest route” representation models are used for that purpose. Also in analogy to 7.3.1, time limits are defined for the various computations. Regarding the negotiation scheme, limits of 60 sec. per planning model are used in all test classes. These maximum times are fully sufficient as the sub-problems per SC partner are identical to those of the small test classes of the two-partner setting. With respect to global MLCLSP models, time limits of 1200 sec. are applied, chosen in analogy to medium test classes M1/M2 of the two partner scenario, as the global problems faced here are of similar dimensions. 7.4.2
Overview of test results
As in 7.3.2 we start by considering solutions to central planning. Table 33 contains an overview of the results based on a time limit of 1200 sec. It can be seen that 314 of the total of 504 (4×126) test instances could be solved to (proven) optimality. The maximum integrality gap of the remaining test problems averages to 2.9% and the average computational time comes to 557 sec. Inspecting the results by test class, one can observe that, not surprisingly, most optimal solutions were obtained in two-buyer test problems (especially in classes 2B-1/3 –the average computational time is also well below the total average here). In test class 3B, on the other hand, only 12 test instances are solved optimally and the remaining integrality gap averages to a relatively high 6.1%. Table 33. Multiple partners - central planning results
Total 2B-1 2B-2 2B-3 3B
376
See pp. 127.
Optimal solutions # 314 117 81 104 12
Not-optimal solutions % cost gap vs. best LP bound av. 2.9% 1.4% 4.1% 1.8% 6.1%
Av. comp. time (sec.) 557.4 266.3 573.9 241.6 1147.9
7.4. Tests with One Supplier and Several Buyers
197
Second, results to Upstream Planning are regarded which are shown in total and by test class in Table 34. The number of capacity-infeasible solutions comes in total to 104 instances, representing more than 20% of all test problems.377 Also, the average gap vs. central planning occurring in the remainder of 400 instances is significantly higher here with a value of 40.3% (compared to 23% in the twopartner setting). Given the standard deviation of 64%, the high average value is presumably due to a large number of test instances with (allowable) overtime at the supplier domain. Results by test class display a similar pattern. The highest numbers of capacity-infeasible solutions are observed in classes 2B-2 and 3B where the average gap vs. central planning is also largest with 52.7 and 47.8%, respectively. Computational times are not included in Table 34, since a significant time consumption does not occur. Given the small sizes of planning models per partner, Upstream Planning results are generated in an instant of time in all cases. Table 34. Multiple partners - Upstream Planning results
Insufficient capacity
Sufficient capacity (incl. allowable overtime) % cost gap vs. central planning Std. Dev. Min Max
#
Average
Total
104
40.3%
64.0%
0.0%
382.8%
2B-1 2B-2 2B-3 3B
20 33 16 35
34.6% 52.7% 29.1% 47.8%
60.2% 79.3% 52.0% 64.7%
0.4% 0.0% 0.0% 0.0%
294.4% 382.8% 284.0% 318.1%
Finally, we turn to results obtained with the negotiation scheme. Table 35 contains an overview of results realized with the original negotiation scheme for multiple buyers as described in 5.1.1.378 The first number of columns refers to gaps vs. central planning. Their average is 5.2% across all test problems with a standard deviation of 12.8%. The minimum and maximum values of –11.6 and 128.7%, respectively, indicate that the results vary considerably across the test instances. This first impression suggests that, although the negotiation scheme here too is able to bring total costs closer towards the global optimum, it is less successful than in the two-partner scenario (average gap of 5.2 vs. 1.7%).
377
378
In the two-partner scenario, in contrast, only 94 of 756 test instances proved capacity infeasible in Upstream Planning. See pp. 103.
7. Computational Evaluation
198
Table 35. Multiple partners - negotiation results (original scheme)
% cost gap vs. central planning Average Std. Dev.
Iterations
Min
Max
Av.
Av. comp. Time Total Per model (sec.) (sec.)
Total
5.2%
12.8%
-11.6%
128.7%
5.6
118.1
2.5
2B-1 2B-2 2B-3 3B
3.2% 7.4% 2.4% 7.7%
2.7% 19.3% 2.8% 15.8%
0.0% 0.0% 0.0% -11.6%
19.8% 128.7% 20.4% 96.9%
5.0 5.7 5.0 6.5
95.2 75.9 56.1 245.2
2.2 1.5 1.3 3.3
Inspecting the results by test class however shows that favorable results are obtained in classes 2B-1/ and 2B-3 with average gaps of 3.2 and 2.4%, respectively. Standard deviations and maximum values found here support this observation. Classes 2B-2 and 3B show less successful results with average gaps of 7.4 and 7.7% and clearly higher standard deviations. Also, maximum values of 128.7 and 96.9% make apparent that solutions include considerable (allowable) overtime in some cases. In terms of the number of iterations, the average of 5.6 is also higher than what we have seen in the two-partner setting (average 4.6), although the increase in this dimension is by far less considerable. The average number of iterations varies across test classes similarly to the solution quality. That is, fewer iterations take place on average in classes 2B-1 and 2B-3 (average 5.0 in both) while more are observed in the cases of 2B-2 and 3B (5.7 and 6.5, respectively). The computational time in tests with two buyers is similar as in small test classes with a single buyer and supplier, in particular in terms of solution time per planning model. Higher total and per model computational times are observed in class 3B. This is for one due to the higher number of models solved in each iteration (at least three per partner). Secondly, with a growing number of buyers as collaboration partners, the supplier’s planning model becomes increasingly complex since there are order patterns and associated variables for each buyer. This effect presumably causes the increased computational times per planning model in class 3B (3.3 sec.). An interesting insight can be derived from the remaining gaps of negotiation outcomes, i.e. the ratio of the difference vs. central planning after and prior to negotiations (for the mathematical definition see (189)379). Table 36 shows average and standard deviations of remaining gaps in total and by test class. The interesting observation here is that average remaining gaps are similar across all test classes. Also, the corresponding total average value is even smaller than the average across two-partner test problems as given in Table 24 (29.3 vs. 31.8%).380 Hence, while the average gaps of negotiation results vs. central planning increase from two to three, and from three to four collaboration partners, corre379 380
See p. 184. See p. 184.
7.4. Tests with One Supplier and Several Buyers
199
sponding remaining gaps stay at a constant level. This however implies that the performance loss vs. central planning as observed in Table 35 goes back to the fact that the gaps of Upstream results vs. central planning grow significantly with three and four SC partners. The negotiation scheme is constantly able to close about 70% of the gap between Upstream and central planning. However, given higher initial gaps, the final outcome deviates farther from the global optimum. Table 36. Multiple partners – remaining gaps of negotiation outcomes
Average
Std. Dev.
Total
29.3%
36.5%
2B-1 2B-2 2B-3 3B
31.7% 32.5% 28.4% 24.4%
32.2% 37.8% 35.3% 41.1%
Results from the final set of computational tests are presented in Table 37, namely outcomes of the negotiation scheme with limited exchange of cost information. As discussed in 5.3.2, this version of the collaborative planning scheme is particularly easy to realize as no centralized improvement check is required at the buyers’ side. However, given that cost effects are only communicated from the buyers to the supplier, buyers lack the possibility of anticipating the supplier’s cost increases in their goal programming models. This in turn is likely to cause some degradation in solution quality as already discussed in 7.3.4 for the twopartner setting. Gaps vs. central planning shown in Table 37 support this expectation. Average values are higher than with the original scheme as reported in Table 35 both in total (6.2 vs. 5.2%) as well as individually per test class. However, the performance loss is not substantial, and thus appears acceptable given the simplifications in the process flow and logic. Also, as a side-effect, the average number of iterations decreases. Related to this, the average computational time is smaller too, offering another advantage vs. the original version discussed above. Table 37. Multiple partners - negotiation results (limited exchange)
% cost gap vs. central planning
Iterations
Av. comp. time Total Per model (sec.) (sec.)
Average
Std. Dev.
Min
Max
Av.
Total
6.2%
14.3%
-6.6%
118.4%
4.1
84.1
2.4
2B-1 2B-2 2B-3 3B
4.2% 7.9% 3.7% 9.0%
4.0% 20.9% 8.4% 16.6%
0.1% 0.0% 0.0% -6.6%
23.4% 118.4% 88.8% 96.8%
3.6 4.4 4.0 4.2
67.5 61.8 45.1 161.9
2.2 1.6 1.3 3.6
200
7. Computational Evaluation
A final comparison between Upstream Planning and negotiation results from both the original scheme as well as with limited exchange of cost data is exhibited in Fig. 41. It contains a diagram of cumulated frequency distributions based on the test problem’s gaps vs. central planning, as are already used for analyzing computational results in the preceding section. The diagram shows that in Upstream Planning only relatively few test instances display small gaps vs. central planning (about 10% have gaps of 0 to 3%). Beyond 3% the cumulated frequency curve increases steadily: roughly 50% of the test problems have gaps of less than 12% and about 75% of less than 50%. With the original negotiation scheme, in contrast, about 25% of test cases possess a gap vs. central planning of below 1%, more than 60% of 0 to 3%, and almost 80% of no more than 5%. Thus, the negotiation scheme brings significant cost improvements here, too, and compared to Upstream Planning cumulated frequencies are again notably shifted towards lower gaps vs. central planning. Cumulated Frequencies of Gaps vs. Central
percentage test instances [%]
100% 80% 60%
Original Limited Exchange
40%
"Upstream"
20% 0% <1%
<2%
<3%
<5%
<8% <12% <20% <30% <50% <80% <130%>130% gap vs. central planning [%]
Fig. 41. Multiple partners - cumulated frequencies of gaps vs. central planning
The negotiation scheme with limited exchange of cost data shows some degradation in solution quality compared to the original version as already implied by the average gap vs. central planning in Table 37. Nonetheless, it can be seen that both cumulated frequency curves are relatively close, with an average “frequency gap” of about 5 percentage points (e.g. about 20% of test problems have gaps below 1% with limited exchange, while gaps below 1% occur in about 25% based on the original version). In summary, the computational tests reported in this section suggest that the negotiation scheme can be favorably applied to SC structures with one supplier and several buyers. As in the two-partner case, it is able to bring total costs resulting from Upstream Planning considerably towards the global optimum of central planning. However, since Upstream Planning shows poorer results with an increasing number of buyers, gaps vs. central planning remaining after applying the negotiation scheme increase too. In consequence a higher average gap of negotiation results vs. central planning is observed than in the setting with two partners.
7.5. Tests with Rolling Schedules
201
Nevertheless, substantial improvements are made as compared to initial Upstream results.
7.5
Tests with Rolling Schedules
The final aspect analyzed by computational tests is the negotiation scheme’s performance in a rolling schedule environment. Since planning by mathematical programming models as considered here is often practiced on a rolling basis, this too is an important issue to investigate. In what follows we first introduce the test structures and program and thereafter report and comment on the computational results. 7.5.1
Test classes and test program
In contrast to the foregoing sections only a single test structure is considered in tests with rolling schedules. This limitation is due to the large number of computations that have to be carried out in order to simulate a rolling schedule environment. Computational tests are therefore restricted to a two-partner scenario and test class S1 embracing four and three items, respectively, and one resource per planning partner as depicted in Table 17.381 As in the previous tests, the planning horizon TP used in each planning cycle (schedule) covers 12 periods, while the frozen horizon TF, that is the period up to which results are implemented before a new planning cycle is initiated,382 is set to one period across all test problems. This means that a total of 12 schedules must be generated until implementable planning results are available with respect to the first 12 periods. Hence, the number of computations required for a single test instance is 12 times larger than in one-time planning, underscoring the computational effort associated with each test instance. Also, the six demand series defined for test class S1 are expanded to cover 23 periods such that demand forecasts over 12 future periods are available up to the last planning cycle (which covers periods 12 to 23). A major distinction is made regarding the quality of demand forecasts. In a first set of tests, future demand is assumed to be deterministically known in advance. That means that forecast and actual demand are identical and planning is based on the same series of 23 demand figures per item in all planning cycles. In a second set of tests, forecast uncertainty is introduced as an additional characteristic. In effect, forecast updates are carried out prior to initiating a new planning cycle, assuming that new, more reliable information has become available. Forecast updates refer to periods 2 to 12 of the previous schedule, but exclude the
381 382
See p. 174. For details see the description is 5.2, pp.115.
202
7. Computational Evaluation
first period where planning results are put into practice. Here we assume that forecasts correspond to actual demand, so that planning results can be implemented as expected and projected inventory at the beginning of period 2 and initial inventory levels of the next planning cycle are identical. This situation is visualized by an example in Table 38. Since forecast values match actual demand in period one, planning results of schedule one, period one can be implemented without adaptations and the initial inventory of schedule two comes to its expected value. However, demand figures are updated as of period 2, causing changes to planning decisions as compared to the previous schedule. Table 38. Example of demand forecast and schedule updates
Schedule 1
Schedule 2
Period
1
2
3
4
5
6
…
Initial inventory Demand forecast Production level Inventory level
35 48 66 53
53 10 10
61 71 20
59 39 0
66 130 64
64 30 30
… … …
53 55 7 7
58 72 21
60 39 0
63 127 64
64 23 23
…
Initial inventory Demand forecast Production level Inventory level
-
…
Since the reliability of demand forecasts affects the quality of solutions, two scenarios are considered with differing forecast accuracy. In both cases, forecast “errors”, that is changes in forecast values introduced between two succeeding planning cycles, are drawn from normal distributions with zero mean, but varying standard deviations. In the first, more accurate, case, the standard deviation is set to 5% of each item’s average demand, whereas 10% are used in the second case. Also, in order to reduce the number of computations, test instances with uncertain demand forecasts are only generated for three out of the six demand series available for class S1, namely those with a coefficient of variation in period demand of 0.1. Resulting are two times 63 test problems with uncertain demand. Altogether, computational tests with rolling schedules are carried out for a total of 252 test problems: 126 instances with deterministic demand, 63 instances with uncertain demand and higher forecast accuracy and 63 instances with uncertain demand and lower accuracy. In analogy to the previous sections, the test program comprises computations based on Upstream Planning, central planning, and the negotiation scheme. Upstream results here cannot be gathered in iteration one of the negotiation scheme, since planning cycles pertaining to one test instance have to be linked by corresponding initial inventory positions. Thus, Upstream Planning in a rolling schedule environment was implemented as a separate planning scheme in Visual Basic and run with all 252 test problems. Central planning is realized as before by global MLCLSP models covering both planning partners. The only novelty here is that,
7.5. Tests with Rolling Schedules
203
as with Upstream Planning, models associated with individual planning cycles have to be linked by initial inventory levels. Concerning the negotiation scheme, the modified version for rolling schedules as described in 5.2 above was implemented in Visual Basic and OPL.383 The major changes compared to the original scheme for one-time planning refer to the introduction of a negotiation horizon TN up to which negotiations take place and the incorporation of pre-negotiated order quantities into the buyer’s initial planning model. In 5.2.1 we argued that the negotiation horizon TN is a crucial parameter which influences the quality of solutions and should be chosen as large as possible with the given accuracy of demand forecasts. In order to analyze its impact on solution quality and the interrelation to forecast accuracy, computational tests are run with several values of TN, namely the minimum value of one period, two intermediary values of three and six periods, and finally its maximum value of 12 periods (corresponding to TP). The same time limits are used as in one-time planning with test class S1 shown in Table 20,384 i.e. 600 sec. per planning cycle in central planning and 60 sec. per planning model in upstream and negotiation-based planning. 7.5.2
Test results with deterministic demand
In this section we report results obtained with the 126 test instances of class S1 and deterministic demand series. All cost related results presented in this and the succeeding section refer to costs associated with planning decisions up to the last period of the final schedule which covers periods 12 to 23. Although planning results only up to period 12 are assumed being implemented (decisions with respect to periods 13 to 23 would be updated in the next planning cycle(s)), it is important to capture costs over the entire planning interval in order to ensure a proper comparison of the three planning schemes.385 Optimal solutions to central planning are obtained with respect to all schedules of all test instances. Thereby, the computational time averages to 616 sec. per instance or 51.6 sec. per schedule (or central planning model), which is in line with the computational times observed in one-time planning with class S1 (average time of 56.9 sec.386). The maximum time observed across all test instances comes to 2466 sec. or 205.5 sec. per schedule, a value well below the time limit of 600 sec. per schedule.
383
384 385
386
See pp. 115 (implementation and computational tests are limited to the version with full exchange of cost information as laid out in 5.2). See p. 178. Alternatively, costs only up to period 12 could be considered, but would need to be reduced by a “bonus” depending on inventory levels at the end of period 12, since production of the inventory positions leads to costs that are actually caused by demand occurring in period 13 or later. See Table 21, p. 179.
204
7. Computational Evaluation
An overview of Upstream Planning results is given in Table 39. Generally speaking, the results observed here too correspond to one-time planning with test problems of class S1 as shown above in Table 22.387 The number of test instances with insufficient capacity at the supplier comes to 26 (one-time planning: 25) and the cost gap to central planning of remaining test problems averages to 24.3% (one-time planning: 25.6%) with a standard deviation of 38.8%. The average computational time is 12.7 sec. or a bit more than one second per schedule. Table 39. Rolling schedules, deterministic demand – Upstream Planning results
Insufficient capacity # 26
Sufficient capacity (incl. allowable overtime) % cost gap vs. central planning Average Std. Dev. Min Max 24.3% 38.0% 1.7% 257.7%
Total comp. Time Av. (sec.) 12.70
Results obtained with the negotiation-based scheme and varying negotiation horizons are summarized in Table 40. Results based on the minimum negotiation horizon of one period display the lowest quality, whereas the best performance is realized with the maximum negotiation horizon of 12 periods. This is not surprising, since with a negotiation horizon of one only orders / supplies pertaining to the first period of each schedule are subject to negotiations. An extension of the negotiation horizon beyond period one enlarges the “room for maneuver” of the negotiation and hence allows to realize additional cost improvements, at least in a situation with deterministic demand as dealt with here. Even the minimum negotiation horizon already brings clear improvements over Upstream Planning. The number of test instances with capacity overruns at the supplier is reduced from 26 to two cases. Also, the average cost gap to central planning of the remaining 124 capacity feasible solutions drops to 20.2% (from 24.3% in Upstream Planning). On the other hand, the resulting average gap is still substantial and underscores that a negotiation horizon of one period is insufficient to bring total costs close to the results attainable with central planning. This is supported by the relatively small average number of iterations (per schedule) of 2.0 (compared to 5.3 in one-time planning with class S1388) which documents that the scheme is terminated very early in most cases due to the lack of additional cost improvements.
387 388
See p. 180. See Table 23, p. 181.
7.5. Tests with Rolling Schedules
205
Table 40. Rolling schedules, deterministic demand – negotiation scheme results
Nego. Insuff. horizon capacity # 2 1 3 6 12
Sufficient capacity (incl. allow. overtime) % cost gap vs. central planning Average Std. Dev. Min Max 20.2% 32.8% -4.3% 175.8% 8.7% 21.3% -7.1% 96.5% 3.7% 10.4% -6.9% 51.1% 1.1% 3.4% -10.1% 11.7%
Iter. Av. 2.0 2.4 2.6 3.1
Total comp. time Av. (sec.) 360.0 484.0 485.0 568.0
The extension of the negotiation horizon to 3 periods brings a substantial benefit in cost results. Now capacity overruns present in upstream solutions are eliminated in all instances and the average cost gap to central planning declines to 8.7%. Also, the largest gap observed across all test problems is reduced from 175.8 to 96.5%. Correspondingly, the average number of iterations carried out per schedule increases to 2.4, accompanied by a rise in the average computational time to 484 sec per test instance. The positive trend in cost results continues when the negotiation horizon is farther enlarged to 6 periods. In effect, the average cost gap to central planning drops to 3.7% and the maximum gap comes to 51.1%. The average number of iterations increases slightly to 2.6, while the average computational time is (unexpectedly) hardly affected with 485 sec. per test problem. Based on the maximum negotiation horizon of 12 periods most results are finally truly close to central planning with an average gap of 1.1% and a standard deviation of 3.4%. The maximum cost gap here comes to 11.7% and thus is of a similar magnitude as observed in one-time planning (12.0%). The scheme’s increased performance however comes at the expense of additional computational effort. The average number of iterations grows to 3.1 and the computational time averages to 568 sec. per instance. It is interesting to note that the negotiation scheme outperforms central planning in some test instances, even with a negotiation horizon of one period. This is no contradiction to the statement above that optimal solutions to central planning are obtained for all test problems and schedules, since the successive application of central planning on a rolling basis yields a heuristic solution to the overall problem of finding a cost-optimal plan covering periods 1 to 23. Thus, other (heuristic) planning schemes can yield more favorable results occasionally. Upstream Planning by itself however does not outperform central planning in any one instance tested here, leaving a cost gap of 1.7% at minimum as shown in Table 39. The negotiation scheme by contrast produces results with negative minimum cost gaps in some instances regardless of the negotiation horizon is use. The minimum gap encountered with a negotiation horizon of one comes to –4.3%, negotiation horizons of 3 and 6 periods yield about –7%, and the maximum horizon of 12 gives even – 10.1%. The wide range between minimum and maximum cost gaps to central planning as shown in Table 40 makes apparent that both very favorable as well as poor results vs. central planning are present within the sample of test problems. Therefore, we take a look at frequency distributions of cost gaps as in the foregoing sec-
206
7. Computational Evaluation
tions. Fig. 42 shows cumulated frequency distributions of cost gaps of upstream and negotiation-based solutions vs. central planning. It can be seen that with Upstream Planning (rightmost curve) the best results display gaps of 1 to 3% (about 2% of test problems). Beyond 3% the cumulated frequency grows steadily. In result, about 50% of test instances have gaps of 12% or less. Based on the negotiation scheme and a negotiation horizon of one (second rightmost curve), a notable number of instances yields cost results smaller than central planning. Almost 20% of test problems display gaps below 1% and about 60% of no more than 8%. The extension of the negotiation horizon to 3 periods brings another performance leap (middle curve). Here, almost 40% of test instances have gaps below 1% and almost 80% of 5% or less. A negotiation horizon of 6 periods brings further improvements leaving about 55% of test instances with gaps below 1% and about 80% with no more than 5%. Upstream & Negotiation Gaps vs. Central
percentage test instances [%]
100%
80%
60%
Upstream 40%
Tn=1 Tn=3
20%
Tn=6 Tn=12
0%
< -2
< -1
<0
<1
<2
<3
<5
<8
< 12
< 20
< 30
< 50
< 80
> 80
gap vs. central pl. solution [%]
Fig. 42. Rolling schedules, deterministic demand – gaps vs. central planning
The maximum negotiation horizon of 12 periods brings surprisingly no performance improvement compared to a horizon of 6 periods with respect to small cost gaps (below 3%). However, while a cost gap of 8% or higher remains in a significant percentage of test problems based on a negotiation horizon of 6 periods (about 15%), gaps of above 8% hardly occur with 12 periods (1-2%). Hence, the extension of the negotiation horizon to 12 periods has in the first place a positive impact on those instances, where a horizon of 6 is insufficient to bring total costs significantly towards central planning results. In summary, the results suggest that applying the negotiation-based scheme on a rolling basis also yields considerable cost improvements as compared to Upstream Planning. As expected, the quality of solutions is strongly affected be the negotiation horizon, since an increased negotiation interval opens more chances for cost improving quantity shifts. Using large negotiation horizons imposes no serious problems for the collaboration partners when demand is known with cer-
7.5. Tests with Rolling Schedules
207
tainty. However, it might become counter-productive when demand forecasts are updated between individual planning cycles. This aspect is considered in the following section. 7.5.3
Test results with uncertain demand
In the following we consider test results obtained for the two sets of 63 test problems of class S1 with uncertain demand forecasts. As described above, forecast “errors” of set one display a zero mean and a coefficient of variation of 0.05. In set two, the coefficient of variation is set to 0.1. Central planning here too leads to optimal solutions to all test instances and schedules. A pairwise comparison of the cost outcomes detected here to central planning solutions of corresponding test instances with deterministic demand reveals that total costs increase on average by 6.4% with a coefficient of variation of 0.05 and even by 25.6% in case of 0.1. The average computational time also rises to 825 and 858 sec., respectively (from 616 sec per instance with deterministic demand). The increase in total costs compared to the scenario with known demand is natural, since future demand is anticipated less accurately when forecast errors occur. In effect, initial inventories available in subsequent schedules do not always match to updated demand figures, causing higher costs than expected in the previous planning cycle. Upstream Planning results associated with both levels of forecast accuracy are presented in Table 41. Regarding the set with higher accuracy (coefficient of variation of 0.05), results vs. central planning are of a similar quality as with deterministic demand. Capacity overruns at the supplier occur in 12 out of 63 test cases. The cost gap to central planning averages to 27.3% (deterministic demand: 24.3%) and displays a similar standard deviation and maximum value as with known demand above. The minimum value however comes to –2.5%, indicating that, based on uncertain demand, Upstream Planning outperforms central planning in at least one test instance. Average computational times are skipped in Table 41, as they are roughly identical to those observed above with deterministic demand series. Table 41. Rolling schedules, uncertain demand – Upstream Planning results
Forecast accuracy 0.05 0.1
Insufficient capacity # 12 13
Sufficient capacity (incl. allowable overtime) % cost gap vs. central planning Average Std. Dev. Min Max 27.3% 34.7% -2.5% 212.4% 21.2% 19.9% -7.5% 75.7%
Results pertaining to set two with lower forecast accuracy (coefficient of variation of 0.1) exhibit smaller discrepancies to corresponding central planning solutions. The number of capacity infeasible outcomes of 13 shows no significant difference to the case of higher forecast accuracy. However, the average cost gap to
208
7. Computational Evaluation
central planning comes to 21.2% (compared to 27.3% with higher accuracy and 24.3% with known demand). Standard deviation, minimum, and maximum values also underline that the performance gap to central planning is smaller than in the scenarios studied so far. The declining performance gap goes presumably back to a decreasing quality of the solutions to central planning, since there is little reason to assume that Upstream Planning performs truly better here. As stated above, applying central planning on a rolling basis leads to a heuristic solution to the underlying overall problem covering the interval of 23 periods. The quality of this heuristic solution is likely to decrease with a growing inaccuracy of demand forecasts. In comparison, the quality of upstream solutions seems to be less affected by forecast errors so that the gap between central and Upstream Planning declines. Negotiation-based solutions are shown in Table 42. As above, tests are run with negotiation horizons of 1, 3, 6, and 12 periods. Computational times are again skipped in Table 42, since resulting values are largely the same as in the case of deterministic demand. Neither shown is the number of capacity-infeasible solutions. Instead, novel columns are added to the table (“Order adjustments”) referring to the average number of order quantity adjustments per test instance and their magnitude. Recapping the modifications introduced to the negotiation scheme for application on a rolling basis, we know that the buyer is requested to use pre-negotiated order quantities in his initial plan of the following planning cycle, whenever the negotiation horizon reaches beyond TF (here one period).389 Now, when demand forecasts are updated, the buyer is at times not able to adhere fully to negotiated quantities. In order to avoid lost sales, he is forced to place additional orders in his initial plan as captured by the “extra supply” variables in the modified initial buyer model.390 However, such extra orders are costly to the buyer as, by placing them, he has to abandon parts of the bonus granted by the supplier for agreeing to the order quantities negotiated in the previous planning cycle. Although the precise financial implications depend on the contract terms settled between the partners, it should be clear that deviations from agreed-to quantities are usually unattractive (to the buyer). Therefore, when uncertain demand forecasts come into play, it is important to capture the amount of such necessary order adjustments as an additional performance measure. In the computational tests, two corresponding measures are captured. For one, the average number of order adjustments per test instance and schedule is determined, that is the number of incidences where order quantities are adjusted from pre-negotiated values, averaged across the 11 planning cycles per instances where pre-negotiated quantities are present (all but the first planning cycle). The figures shown in Table 42 represent average numbers across all test instances (column “# Av.”). Second, the average magnitude of order adjustments is captured during the computations. It is measured as a percentage value relative to each item’s mean
389 390
See e.g. the schematic overview in Fig. 32, p. 119. See Model 14, p. 121.
7.5. Tests with Rolling Schedules
209
order quantity. Average percentage order adjustments across all supply items and the 11 order patterns are determined for each test problem. These values are then averaged across all test instances to give the numbers shown in the table. Table 42. Rolling schedules, uncertain demand – negotiation scheme results
Forecast accuracy
Nego. horizon
0.05
1 3 6 12
0.1
1 3 6 12
Sufficient capacity (incl. allow. overtime) % cost gap vs. central planning Average Std. Dev. Min Max 17.9% 27.0% -8.9% 114.9% 8.0% 18.2% -10.3% 99.4% 3.9% 10.5% -10.9% 56.1% 1.3% 4.6% -8.1% 13.1% 15.3% 7.8% 4.2% 1.2%
26.6% 20.9% 10.3% 6.2%
-7.1% -14.2% -9.7% -8.0%
147.6% 113.3% 47.5% 23.7%
Order adjustments # Av. % Av. 0.7 1.6% 1.8 2.8% 5.0 3.7% 1.1 2.5 6.7
4.3% 5.9% 8.0%
Iter. Av. 2.1 2.7 3.0 3.6 2.3 2.7 3.1 3.5
We first turn to results of test problems with higher forecast accuracy (coefficient of variation of 0.05). As can be seen, applying the negotiation scheme even with a minimum negotiation horizon of one period yields significant improvements compared to Upstream Planning. In result, the average cost gap to central planning drops from 27.3 to 17.9%, its maximum value from 212.4 to 114.9%, and the minimum value from –2.5 to –8.9%. Order adjustments do not occur, since negotiations only refer to order quantities of the first period of each schedule which are directly implemented. Although not shown in the table, it should be noted that capacity-infeasible solutions are neither present among the test results based on a negotiation horizon of one period, nor with larger horizons of multiple periods. Extending the negotiation horizon to 3 periods is substantially beneficial in terms of costs. The gap to central planning now only averages to 8.0% and the standard deviation decreases to 18.2%. The number of iterations grows similar to the case of deterministic demand to an average of 2.7. The average number of order adjustments per initial order pattern comes to 0.7. This seems tolerable given that the order pattern comprises 3 items and pre-negotiated quantities over 2 periods. Thus, order adjustments occur on average in 0.7 out of 6 (3×2) orders per item and period. The average magnitude of order adjustments thereby comes to 1.6% of the mean order quantity, indicating that modest adjustments are sufficient in most cases. A further extension of the negotiation horizon to 6 periods pays off, too. In effect, the cost gap to central planning is on average cut by half to 3.9% with a standard deviation of 10.5%. Its maximum value also drops notably to 56.1%. The average number of iterations increases in return to a value of 3.0. Not surprisingly, the average number of order adjustments also grows to 1.8 per initial order pattern. However, given that there is a total of 15 (3×5) pre-negotiated order quanti-
210
7. Computational Evaluation
ties, an average of 1.8 adjustments still appears tolerable, in particular since their average magnitude comes to no more than 2.8% of the mean quantity. Thus, although adjustments grow in amplitude to almost double the value present with a negotiation horizon of 3 periods (1.6%), they remain relatively small in the majority of cases. Similarly, doubling the negotiation horizon from 6 to 12 periods brings total cost outcomes once more closer to central planning solutions. Resulting is an average gap of just 1.3% with a standard deviation of 4.6% and a maximum value of 13.1%. Of course, this is accompanied by an increase in the average number of iterations to 3.6 as well as more frequent and larger order adjustments. Now, 5 order adjustments are on average present in the initial order pattern, and their average magnitude rises to 3.7%. Yet, as the initial pattern comprises a total of 33 (3×11) pre-negotiated quantities, the introduction of 5 adjustments seems justifiable given the additional gain in cost performance. Cost results obtained for test problems with lower forecast accuracy (coefficient of variation of 0.1) display a similar pattern as can be seen from Table 42 and are therefore not discussed in detail. It should however be noted that the average cost gap to central planning realized with a negotiation horizon of one period is smaller here (15.3%) than in the set with higher forecast accuracy (17.9%). This is probably linked to the fact that upstream results as presented in Table 41 too come closer to central planning here. Cost results obtained with negotiation horizons of 3, 6, and 12 periods come to similar values as in the case of higher forecast accuracy such that the performance gain vs. Upstream Planning is actually smaller than realized with a higher accuracy of forecasts. The number and amplitude of order adjustments is generally higher than in corresponding tests with higher accuracy. This is natural, since more frequent and larger forecast updates force the buyer to adjust pre-negotiated orders more often. In consequence, the average number of order adjustments per initial schedule increases to 1.1, 2.5, and 6.7 with growing negotiation horizon. The increase in the average magnitude of order adjustments is even stronger. It rises to 4.3, 5.9, and 8.0% of the mean order quantity. Thus, the question of consequences from order adjustments on payments between the planning partners becomes more important. Since order adjustments of an amplitude of 6 or 8% of the mean order quantity are likely to change the supplier’s plan compared to his expectations based on pre-negotiated quantities, financial implications such as a reduction of the payment rendered to the buyer as discussed in chapter 6 are in the supplier’s interest here. Generally, the partners may, in effect, prefer to stay with a shorter negotiation horizon of e.g. 3 or 6 periods in situations with uncertain demand such that negotiated quantities are less affected by the uncertainties. Therefore, it is interesting to have a closer look at the performance of the collaborative planning scheme with varying negotiation horizons in terms of resulting costs. For that purpose, Fig. 43 exhibits cumulated frequencies of cost gaps vs. central planning obtained for the test set with lower forecast accuracy (coefficient of variation of 0.1). Comparing the various curves, one should first note that the “upstream” curve supports the fact that upstream results here outperform those
7.5. Tests with Rolling Schedules
211
corresponding to tests with deterministic demand as shown above in Fig. 42 (there, gaps of below 3% hardly occur, while they account for about 15% of the test instances here). Second, one can obtain that the negotiation scheme applied with a negotiation horizon of one period brings clear cost advantages vs. Upstream Planning, and that another performance leap is realized when the negotiation horizon is increased from one to 3 periods. However, the curves pertaining to negotiation horizons of 3, 6, and 12 periods are relatively close to each other, particularly with respect to small gaps to central planning of 2% or below. Upstream & Negotiation Gaps vs. Central - Forecast Accuracy 0.1 100%
80%
60%
Upstream 40%
Tn=1 Tn=3
20%
Tn=6 Tn=12
0%
< -2
< -1
<0
<1
<2
<3
<5
<8
< 12
< 20
< 30
< 50
< 80
> 80
Fig. 43. Rolling schedules, uncertain demand – gaps vs. central planning
Significant performance gains, especially with the negotiation horizon of 12 periods, are only realized in test problems where shorter horizons lead to relatively large gaps to central planning, similarly as in the case of deterministic demand shown in Fig. 42. The decrease in the average cost gap to central planning from enlarging the negotiation horizon to 6 or 12 periods as reported in Table 42 hence goes back to the fact that fewer (or none) results with large cost gaps are obtained. The number of outcomes with small cost gaps on the other hand remains relatively stable. In consequence, a negotiation horizon of 3 periods is sufficient to bring resulting costs close to the central planning outcome in many, but not all, test instances. More insights on the quality of negotiation outcomes which support this observation can be drawn from inspecting results per capacity profile. Table 43 contains average values and standard deviations of cost gaps vs. central planning by capacity profile realized with varying negotiation horizons. The figures are based on all 126 test problems with uncertain demand, i.e. with higher and lower forecast accuracy.
212
7. Computational Evaluation
Table 43. Rolling schedules, uncertain demand – results by capacity profile
Negotiation horizon Capacity profile cap-1 cap-2 cap-3 cap-4 cap-5 cap-6 cap-7
1
3
av.
std. dev.
av.
8.6% 1.4% 7.0% 28.0% 2.9% 68.7% 3.3%
5.2% 5.3% 6.0% 14.0% 4.1% 36.0% 3.3%
4.5% -2.2% 2.8% 2.8% 0.9% 46.4% 0.0%
6 std. dev. 4.6% 6.0% 5.7% 4.6% 4.3% 28.0% 2.9%
12
av.
std. dev.
av.
std. dev.
3.7% 0.1% 1.0% 1.3% 0.7% 21.5% 0.2%
3.1% 4.8% 5.1%
5.5% -1.2% 1.5% 4.3% 1.4% -1.9% -0.9%
3.8% 4.5% 4.3%
4.2% 4.3% 17.1% 2.5%
7.8% 4.7% 3.9% 2.9%
Although caution is in place, since the figures are derived from a sample of just 18 test instances per capacity profile, some general trends can be extracted from the overview. Starting with a negotiation horizon of one period, one can see that by far the largest gaps to central planning occur in profile 6, followed by 4. Good results with average gaps of 1.4 to 3.3% are on the other hand obtained from profiles 2, 5, and 7. Recapping the definition of the capacity profiles as laid out in Table 15391 therefore suggests that tight capacity at the supplier as in profiles 6 (90% utilization) and 4 (90% during the first and last couple of periods) leads to a poor performance of the collaborative planning scheme with a negotiation horizon of a single period. In contrast, a negotiation horizon of one period is sufficient to achieve good results when capacity is uncritical at the supplier as in profiles 2 and 5 (70% utilization) or 7 (50% utilization). The extension of the negotiation horizon to 3 periods brings the average cost gaps close to 0% (or even lower), except for the case of profile 6. Here, the cost gap still averages to 46.4% with a standard deviation of 28%. Similarly, a farther extension of the negotiation horizon to 6 periods improves most cost gaps per capacity profile, but, concerning profile 6, still leaves an average gap to central planning of 21.5%. Only an additional enlargement of the negotiation interval to 12 periods opens enough “negotiation space” to bring total costs close to central planning results in profile 6, too (average of –1.9%). These results imply that expected capacity utilization at the supplier should be considered next to the uncertainty of demand and other data in deciding upon an “appropriate” negotiation horizon. The tighter capacity is expected at the supplier, the larger a negotiation horizon should be chosen in order to make sure that capacity bottlenecks and overtime situations can be successfully eliminated during negotiations. Summarizing the above, we can state that similar cost improvements can be obtained with the negotiation scheme with and without demand uncertainties. In the
391
See p. 170.
7.5. Tests with Rolling Schedules
213
tests considered here, a negotiation interval of 3 or 6 periods, i.e. a quarter or half of the planning interval, is sufficient to yield good cost results compared to central planning in the majority of test problems. Only in some cases a larger negotiation horizon of 12 periods is required to bring cost outcomes close to central planning solutions. As expected, the number and magnitude of adjustments to prenegotiated order quantities increases with growing demand uncertainty and negotiation horizon. Thus, a compromise is required in deciding upon the negotiation horizon which leads to satisfying cost improvements on the one hand and an acceptable rate of adjustments on the other. A factor influencing the required size of the negotiation horizon turns out to be the capacity utilization at the supplier. According to the computational tests, a large negotiation horizon is required to bring costs close to central planning solutions, when capacity is tight at the supplier. In contrast, a relatively short horizon is sufficient in situations of ample capacity. Recommended readings • Tempelmeier, H. / Derstroff, M. (1996): “A Lagrangean-based heuristic for dynamic multi-level multiitem constrained lotsizing with setup times”, in: Management Science, Vol. 42(5), 738-757. • Stadtler, H. (2003): “Multi-level lot-sizing with setup times and multiple constrained resources – Internally rolling schedules with lotsizing windows”, in: Operations Research, Vol. 51(3), 487-502.
8 Summary and Conclusions In this book we laid out a negotiation-based scheme for collaborative planning between SC partners. The discussion is initiated with an overview of SCM and two distinct approaches to operations planning in SCs: hierarchical and collaborative planning. While hierarchical planning achieves coordination by centralized decision making, and due to that can usually only be applied to parts of the SC, the idea of collaborative planning is to coordinate plans between independent partners in a nonhierarchical, horizontal way. To treat collaborative planning in greater detail, it is important to clarify how planning is realized by individual SC partners. Here, we assume that mathematical programming models, or more specifically multi-level capacitated lot-sizing problems (MLCLSP), are used to generate medium-term master plans within individual planning domains. The MLCLSP is a good representative model as it includes many characteristics of medium-term SC planning, such as a multi-level bill-ofmaterial, capacity constraints, and binary decisions. The literature review on coordination of operations planning between independent SC partners has shown that coordination cannot be achieved by specifying (static) contract terms when planning is based on mathematical programming. Known coordination mechanisms for mathematical programming models, such as Upstream Planning or the Lagrangean relaxation approach, on the other hand, suffer from the facts that they are hierarchical in nature and / or require a high degree of informational integration between the SC partners. In contrast, the negotiation-based approach to collaborative planning developed here is non-hierarchical, in that it gives a similar decision authority to all partners, and involves the exchange of few information only. The core idea is to iteratively pass order / supply proposals between buyers and suppliers. Proposals received from the SC partner are analyzed for consequences on local planning and counterproposals are generated by introducing partial modifications. The basic form of the collaborative planning scheme as developed in chapter 4 considers a setting with two SC partners, one buyer and one supplier, and onetime planning. However, as demonstrated with the extensions presented in chapter 5, the approach can also be utilized in general two-tier SCs with arbitrary numbers of buyers and suppliers, and (with limitations) in multi-tier SCs. Also, its application is possible on a rolling basis. With rolling schedules only planning results of the first few periods are actually implemented. Therefore, it is useful to extend the original scheme as also laid out in chapter 5 such that negotiations are limited to a shorter time frame than the entire planning interval. A last extension presented in chapter 5 aims to further reduce the amount of cost information exchanged between the collaboration partners. Whereas savings and cost increases accompanying each new proposal are exchanged between the partners in the original scheme, we have seen that a unidirectional announcement of compensation needs required by the buyer(s) for accepting compromise proposals is sufficient. G. Dudek, Collaborative Planning in Supply Chains, 2nd edn., DOI 10.1007/978-3-540-92176-9_8, © Springer-Verlag Berlin Heidelberg 2009
216
8. Summary and Conclusions
Financial consequences of negotiation-based collaborative planning are dealt with in chapter 6. Here, we argue that a compensation of cost increases plus a share of net savings should be rendered by the supplier(s) to the buyer(s) in order to create a win-win situation, as the collaborative planning scheme by itself typically leads to savings for supplier(s) but cost increases to buyer(s). The compensation and savings sharing payment can be incorporated into supply contracts in the form of a bonus granted to the buyer(s) at the end of the planning interval, if actual orders comply to the quantities agreed to in collaborative planning. A heuristic bonus adaptation scheme is introduced in order to deal with deviations between actual and agreed to order quantities. Also, incentives of opportunistic behavior occurring during the collaborative planning scheme are discussed. Based on a game-theoretic analysis, collaboration partners indeed have incentive to cheat in order to maximize their individual shares of total savings. However, the analysis ignores effects on the SC relationship such as loss of reputation from opportunistic behavior. When such aspects come into play too, and particularly when they are accompanied by controlling and monitoring measures which increase chances that cheating is noticed by the collaboration partner, then the additional payoffs from cheating diminish as compared to the damage to the SC partnership. On the other hand, when the SC relationship is less trusty and cheating of SC partners is expected, the collaborative planning scheme can be further modified to accommodate selfish behavior. Corresponding modifications are outlined at the end of chapter 6. The last chapter is finally concerned with a computational evaluation of the collaborative planning scheme in terms of solution quality and computational effort. For that purpose the scheme and two benchmark approaches (Upstream Planning and central planning by a single global planning model) were implemented in standard software. Numerous test problems were generated based on a wellknown structure of test problems for the MLCLSP for a two-partner as well as a multiple-partner scenario (one supplier and several buyers). The computational results demonstrate that the collaborative planning scheme is able to improve total SC costs considerably compared to Upstream Planning solutions, which form the starting point of the negotiations. On average, about 70% of the initial gap between upstream and central planning can be “closed” by the negotiation scheme. It should however be noted that these cost improvements come at the expense of considerable computational effort inherent in collaborative planning. As it requires to solve three planning models per partner and iteration and continues on average for four to five iterations, computational times can be substantial. In summary, this book offers an approach to coordinate operations planning between independent SC partners based on mathematical programming models. It only requires exchange of limited information and yields consistent plans and substantial cost improvements with a small number of iterations. Also, it should be noted that the scheme is independent of the specific planning problems and mathematical programming models used by individual SC partners. Its major limitations and drawbacks have already been mentioned above. For one, the negotiation concept has been designed for two adjacent tiers of the SC. It
8. Summary and Conclusions
217
can be applied to general multi-tier SCs by subsequent tier-by-tier negotiations or in the form of bilateral negotiations between any two partners. However, situations may appear where such an application of the negotiation scheme results in solutions which are inferior to Upstream Planning. Secondly, the coordination rests on the announcement of cost effects of modified order / supply patterns at least by partners from one tier. As such, it offers potentials for cheating and opportunistic behavior for purely selfish, opportunistically acting SC members, which have to be watched out for carefully as discussed in chapter 6. Thirdly, solutions obtained with the collaborative planning scheme are a clear improvement vs. Upstream Planning results, but globally optimal solutions cannot be fully reached. Furthermore, the scheme requires substantial computational efforts.
References Journal Abbreviations EJOR IJLM IJPR MS OR SCMR ZfB
European Journal of Operational Research International Journal of Logistics Management International Journal of Production Research Management Science Operations Research Supply Chain Management Review Zeitschrift für Betriebswirtschaft
Ahlert, M. (1999): "Normen in Verhandlungsexperimenten", manuscript of a presentation at "Herbsttagung der wissenschaftlichen Kommission Operations Research“, Halle 1999. Anupindi, R. / Bassok, Y. (1999): "Supply contracts with quantity commitments and stochastic demand", in: Tayur et al. (1999), 197-232. Aouni, B. / Kettani, O. (2001): "Goal programming model: A glorious history and a promising future", in: EJOR, Vol. 133, 225-231. Aviv, Y. (2001): "The effect of collaborative forecasting on supply chain performance", in: MS, Vol. 47(10), 1326-1343. Backhaus, K. / Erichson, B. / Plinke, W. / Weiber, R. (1996): Multivariate Analysemethoden - Eine anwendungsorientierte Einführung, 8th ed., Berlin et al. 1996. Baker, K.R. / Peterson, D.W. (1979): "An analytic framework for evaluating rolling schedules", in: MS, Vol. 25(4), 341-351. Barbarosoglu, G. / Özgür, D. (1999): "Hierarchical design of an integrated production and 2-echelon distribution system", in: EJOR, Vol. 118, 464-484. Barratt, M. (2004): “Unveiling enablers and inhibitors of collabrovative planning”, in: IJLM, Vol. 15(1), 73-90. Bartsch, H. / Bickenbach, P. (2002): Supply Chain Management mit SAP APO - SupplyChain-Modelle mit dem Advanced Planner and Optimizer 3.1, 2nd ed., Bonn 2002. Bask, A.H. / Juga, J. (2001): "Semi-integrated supply chains: Towards the new era of Supply Chain Management", in: International Journal of Logistics, Vol. 4(2), 137-152. Bechtel, C. / Jayaram, J. (1997): "Supply Chain Management: A strategic perspective", in: IJLM, Vol. 8(1), 15-34. Berens, W. / Delfmann, W. (1995): Quantitative Planung - Konzeption, Methoden und Anwendungen, 2nd ed., Stuttgart 1995. Bhatnagar, R. / Chandra, P. / Goyal, S.K. (1993): "Models for multi-plant coordination", in: EJOR, Vol. 67, 141-160. Billington, P.J. / McClain, J.O. / Thomas, L.J. (1983): "Mathematical programming approaches to capacity-constrained MRP systems: Review, formulation and problem reduction", in: MS, Vol. 29(10), 1126-1150. Boddy, D. / Macbeth, D. / Wagner, B. (2000): “Implementing collaboration between organizations: an empirical study to supply chain partnering”, in: Journal of Management Studies 37(7), 1003-1017. Bourland, K.E. / Powell, S.G. / Pyke, D.F. (1996): "Exploiting timely demand information to reduce inventories", in: EJOR, Vol. 92, 239-253.
220
References
Bowersox, D.J. / Closs, D.J. (1996): Logistical Management - The Intergrated Supply Chain Process, New York et al. 1996. Bowersox, D.J. / Closs, D.J. / Stank, T.P. (1999): "21st century logistics: making supply chain integration a reality", in: SCMR, Vol. Fall 1999, 44-49. Bowersox, D.J. / Closs, D.J. / Stank, T.P. / Keller, S.B. (2000): "How supply chain competency leads to business success", in: SCMR, Vol. Sep./Oct. 2000, 70-78. Brockhoff, K. / Hauschildt, J. (1993): "Schnittstellen-Management - Koordination ohne Hierarchie", in: Zeitschrift für Führung und Organisation, Vol. 62(6), 396-403. Buscher, U. (1999): "ZP-Stichwort: Supply Chain Management", in: Zeitschrift für Planung, Vol. 10, 449-456. Cachon, G.P. (2003): "Supply chain coordination with contracts", in: Graves S.C. / de Kok, A.G. (Eds.), Supply Chain Management – Design, Coordination and Contracts – Handbook in Operations Research and Management Science, 11, Amsterdam et al. 2003, .229-329. Cachon, G.P. / Fischer, M. (2000): "Supply chain inventory management and the value of shared information", in: MS, Vol. 46(8), 1032-1048. Calhoun, K.M. / Deckro, R.F. / Moore, J.T. / Chrissis, J.W. / Van Hove, J.C. (2002): "Planning and re-planning in project and production scheduling", in: Omega, Vol. 30, 155170. Camm, J.D. / Chorman, T.E. / Dill, F.A. / Evans, J.R. / Sweeney, D.J. / Wegryn, G.W. (1997): "Blending OR/MS, judgment, and GIS: Restructuring P&G's supply chain", in: Interfaces, Vol. 27(1), 128-142. Carlson, R.C. / Jucker, J.V. / Kropp, D.H. (1979): "Less nervous MRP systems: A dynamic economic lot-sizing approach", in: MS, Vol. 25(8), 754-761. Chand, S. / Sethi, S.P. / Sorger, G. (1992): "Forecast horizons in the discounted dynamic lot size model", in: MS, Vol. 38(7), 1034-1048. Charnes, A. / Cooper, W.W. (1961): Management Models and Industrial Applications of Linear Programming, New York et al. 1961. Chase, R.B. / Aquilano, N.J. / Jacobs, F.R. (1998): Production and Operations Management - Manufacturing and Services, 8th ed., Boston et al. 1998. Chen, F. (1998): "Echelon reorder points, installation reorder points, and the value of centralized demand information", in: MS, Vol. 44(12), 221-234. Chen, F. (1999): "Decentralized supply chains subject to information delays", in: MS, Vol. 45(8), 1076-1090. Chen, F. / Federgruen, A. / Zheng, Y.S. (2001): "Coordination mechanisms for a distribution system with one supplier and multiple retailers", in: MS, Vol. 47(5), 693-708. Chopra, S. / Meindl, P. (2001): Supply Chain Management - Strategy, Planning, and Operation, Upper Saddle River 2001. Christopher, M. (2005): Logistics and Supply Chain Management - Creating Value Adding Networks, 3rd ed., London 2005. Clark, A.J. / Scarf, H. (1960): "Optimal policies for a multi-echelon inventory problem", in: MS, Vol. 6, 475-490. Cooper, M.C. / Ellram, L.M. (1993): "Characteristics of Supply Chain Management and the implications for purchasing and logistics strategy", in: IJLM, Vol. 4(2), 13-24. Cooper, M.C. / Lambert, D.M. / Pagh, J.D. (1997): "Supply Chain Management: More than a new name for logistics", in: IJLM, Vol. 8(1), 1-13.
References
221
Cooper, W.W. (2002): "Abraham Charnes and W.W. Cooper (et al.): A brief history of a long collaboration in developing industrial uses of linear programming", in: OR, Vol. 50(1), 35-41. Copacino, W.C. (1997): Supply Chain Management - The Basics and Beyond, Boca Raton 1997. Corbett, C.J. (2001): "Stochastic inventory systems in a supply chain with asymmetric information: Cycle stocks, safety stocks, and consignment stock", in: OR, Vol. 49(4), 487-500. Corbett, C.J. / de Groote, X. (2000): "A supplier's optimal quantity discount policy under asymmetric information", in: MS, Vol. 46(3), 444-450. Corbett, C.J. / DeCroix, G.A. (2001): "Shared-savings contracts for indirect materials in supply chains: Channel profits and environmental impacts", in: MS, Vol. 47(7), 881893. Corsten, H. / Gössinger, R. (2001): "Advanced Planning Systems - Anspruch und Wirklichkeit", in: PPS Management, Vol. 6(2), 32-39. Croom, S. / Romano, P. / Giannakis, M. (2000): "Supply Chain Management: an analytical framework for critical literature review", in: European Journal of Purchasing & Supply Management, Vol. 6, 67-83. Dantzig, G.B. / Wolfe, P. (1960): „Decomposition principle for linear programs“, in: OR, Vol. 8, 101-111. de Matta, R. / Guignard, M. (1994): "Dynamic production scheduling for a process industry", in: OR, Vol. 42(3), 492-503. de Matta, R. / Guignard, M. (1995): "The performance of rolling production schedules in a process industry", in: IIE Transactions, Vol. 27, 564-573. Derstroff, M.C. (1995): Mehrstufige Losgrössenplanung mit Kapazitätsbeschränkungen, Heidelberg 1995. Domschke, W. / Drexl, A. (1998): Einführung in Operations Research, 4th ed., Berlin et al. 1998. Drexl, A. / Fleischmann, B. / Günther, H.-O. / Stadtler, H. / Tempelmeier, H. (1994): "Konzeptionelle Grundlagen kapazitätsorientierter PPS-Systeme", in: Zeitschrift für betriebswirtschaftliche Forschung, Vol. 46, 1022-1045. Ellram, L.M. / Cooper, M.C. (1990): "Supply Chain Management, partnerships, and the shipper - third party relationship", in: IJLM, Vol. 1(2), 1-10. Erengüc, S.S. / Simpson, N.C. / Vakharia, A.J. (1999): "Integrated production/distribution planning in supply chains", in: EJOR, Vol. 115, 219-236. Ertogral, K. / Wu, S.D. (2000): "Auction-theoretic coordination of production planning in the supply chain", in: IIE Transactions, Vol. 32(10), 931-940. Escudero, L.F. / Galindo, E. / Garcia, G. / Gomez, E. / Sabau, V. (1999): "Schumann, a modeling framework for Supply Chain Management under uncertainty", in: EJOR, Vol. 119, 14-34. Federgruen, A. / Tzur, M. (1994): "Minimal forecast horizons and a new planning procedure for the general dynamic lot sizing model: nervousness revisited", in: OR, Vol. 42(3), 456-468. Feuerstake, B. (2002): "Ist CPFR nur auf Marktplätzen erfolgreich ?", in: Thexis, Vol. 032002, 22-27. Fink, A. (2000): Software-Wiederverwendung bei der Lösung von Planungsproblemen mittels Meta-Heuristiken, Aachen 2000.
222
References
Fisher, M.L. (1981): "The Lagrangian Relaxation method for solving integer programming problems", in: MS, Vol. 27(1), 1-18. Fisher, M.L. (1985): "An applications oriented guide to Lagrangian Relaxation", in: Interfaces, Vol. 15(2), 10-21. Fleischmann, B. (1999): "Kooperation von Herstellern in der Konsumgüterdistribution", in: Engelhard, J. / Sinz, E.J. (Eds.): Kooperation im Wettbewerb - Neue Formen und Gestaltungskonzepte im Zeichen von Globalisierung und Informationstechnologie, Wiesbaden 1999, 169-186. Fleischmann, B. / Meyr, H. / Wagner, M. (2005): "Advanced planning", in: Stadtler / Kilger (2005), 81-106. Fox , M.S. / Barbuceanu, M. / Teigen, R. (2000): "Agent oriented supply chain management", in: International Journal of Flexible Manufacturing Systems, Vol. 12, 165-188. Friedman, M. (1982): Capitalism and Freedom, 2nd ed., Chicago 1982. Gattorna, J.L. / Walters, D.W. (1996): Managing the Supply Chain - A Strategic Perspective, Houndmill 1996. Gavirneni, S. / Kapuscinski, R. / Tayur, S. (1999): "Value of information in capacitated supply chains", in: MS, Vol. 45(1), 16-24. Gavirneni, S. (2002): "Information Flows in Capacitated Supply Chains with Fixed Ordering Costs”, in: MS, Vol. 48(5), 644-651. Glaser, H. / Geiger, W. / Rohde, V. (1992): PPS - Produktionsplanung und -steuerung, 2nd ed., Wiesbaden 1992. Griffith, R.E. / Stewart, R.A. (1961): "A nonlinear programming technique for the optimization of continuous processing systems", in: MS, Vol. 7, 379-392. Günther, H.O. / Tempelmeier, H. (1997): Produktion und Logistik, 3rd ed., Berlin et al. 1997. Güth, W. (1995): "On ultimatum bargaining experiments: A personal review", in: Journal of Economic Behavior and Organization, Vol. 27, 330-344. Güth, W. (1999): Spieltheorie und ökonomische (Bei)Spiele, 2nd ed., Berlin et al. 1999. Güth, W. / Tietz, R. (1985): "Strategic power versus distributive justice - An experimental analysis of ultimatum bargaining", in: Brandstätter, H. / Kirchler, E. (Eds.): Economic Psychology, Linz 1985, 129-137. Haehling von Lanzenauer, C. / Pilz-Glombik, K. (2000): "Coordinating supply chain decisions: an optimization model", working paper, Institut für Produktion, Wirtschaftsinformatik und Operations Research, Freie Universität Berlin, Berlin 2000. Hartung, J. / Elpelt, B. (1995): Multivariate Statistik - Lehr- und Handbuch der angewandten Statistik, 5th ed., Munich / Vienna 1995. Hax, A.C. / Meal, H.C. (1975): "Hierarchical integration of production planning and scheduling", in: Geisler, M.A. (Ed.): Studies in Management Science - Vol. I: Logistics, Amsterdam 1975, 53-69. Hewitt, F. (1994): "Supply chain redesign", in: IJLM, Vol. 5(2), 1-9. Hewitt, F. (2001): "After supply chains, think demand pipelines", in: SCMR, Vol. May/June 2001, 28-38. Hillier, F.S. / Lieberman, G.J. (2001): Introduction to Operations Research, 7th ed., Boston et al. 2001. Hirzel, J. / Stephan, A. / Klink, G. / Wagner, H. (2002): "Lieferantenanbindung: Keine Angst vor Engpässen", in: Logistik Heute, Vol. 10-2002, 64-65. Holler, M.J. / Illing, G. (1996): Einführung in die Spieltheorie, 3rd ed., Berlin et al. 1996.
References
223
Holmberg, K. (1995): "Primal and dual decomposition as organizational design: Price and/or resource directive decomposition", in: Burton, R.M. / Obel, B. (Eds.): Design Models for Hierarchical Organizations, Boston et al. 1995, 61-92. Homburg, C. (1996): Hierarchische Aushandlungen in Organisationen, Heidelberg 1996. Hopp, W.J. / Spearman, M.L. (1996): Factory Physics - Foundations of Manufacturing Management, Chicago 1996. Horvath, P. (2001): Controlling, 8th ed., Munich 2001. Houlihan, J.B. (1985): "International Supply Chain Management", in: International Journal of Physical Distribution and Materials Management, Vol. 15(1), 22-38. ILOG (2000): ILOG OPL Studio 3.1 - Component Libraries User's Manual, Paris 2000. Ireland, R. / Bruce, R. (2000): "CPFR - Only the beginning of collaboration", in: SCMR, Vol. Sept./Oct. 2000, 80-88. Jain, A.K. / Murty, M.N. / Flynn, P.J. (1999): "Data clustering: a review", in: ACM Computing Surveys, Vol. 31(3), 264-323. Jensen, T (1996): Planungsstabilität in der Material-Logistik, Heidelberg 1996. Johnson, D.S. / Aragon, C.R. / McGeoch, L.A. / Schevon, C. (1989): "Optimization by simulated annealing: An experimental evaluation; Part I, graph partitioning", in: OR, Vol. 37(6), 865-892. Jones, T.C. / Riley, D.W. (1985): "Using inventory for competitive advantage through Supply Chain Management", in: International Journal of Physical Distribution and Materials Management, Vol. 15(5), 16-26. Jost, P.-J. (2001): Die Spieltheorie in der Betriebswirtschaftslehre, Stuttgart 2001. Jung, H. / Chen, F.F. / Jeong, B. (2005): „A production-distribution coordination model for third party logistics partnerships”, IEEE International Conference on Automation Science and Engineering 2005. Kansky, D. / Weingarten, U. (1999): "Supply Chain: Fertigen, was der Kunde verlangt", in: Harvard Business Manager, Vol. 4/1999, 87-95. Karabuk, S. / Wu, D. (2002): „Decentralizing semiconductor capacity planning via internal market coordination”, in: IIE Transactions, Vol. 34, 743-759. Karmakar, U.S. (1992): "Manufacturing lead times, order release and capacity loading", in: Graves, S. / Rinnovykan, A. / Zipkin, P. (Eds.): Logistics of Production and Inventory, Amsterdam et al. 1992, 287-329. Kersten, W. (2002): "Internetgestützte Beschaffung komplexer Produktionsmaterialien – das Ende der Wertschöpfungspartnerschaft in der Automobilindustrie ?", presentation at "Herbsttagung der wissenschaftlichen Kommission Produktionswirtschaft“, Munich 2002. Kilger (2005): "The definition of a supply chain project", in: Stadtler / Kilger (2005), 281301. Kilger, C. / Reuter, B. (2005): "Collaborative planning", in: Stadtler / Kilger (2005), 259278. Kimms, A. (1998): "Stability measures for rolling schedules with applications to capacity expansion planning, master production scheduling, and lot sizing", in: Omega, Vol. 26(3), 355-366. Kistner, K.-P. (1992): "Koordinationsmechanismen in der hierarchischen Planung", in: ZfB, Vol. 62(10), 1125-1146. Kistner, K.-P. / Switalski, M. (1989): "Hierarchische Produktionsplanung", in: ZfB, Vol. 59(5), 477-503.
224
References
Kotzab, H. (2000): "Zum Wesen des Supply Chain Management vor dem Hintergrund der betriebswirtschaftlichen Logistikkonzeption - erweiterte Überlegungen", in: Wildemann (2000), 21-48. Kotzab, H. (2001): "Management by ECR - Internationale Bestandsaufnahme und empirischer Vergleich der Umsetzung von ECR”, in: Thexis, Vol. 3, 29-33. Kuhn, A. / Hellingrath, B. (2002): Supply Chain Management - Optimierte Zusammenarbeit in der Wertschöpfungskette, Berlin et al. 2002. Kummer, S. (2001): "Supply chain controlling", in: Kostenrechnungspraxis, Vol. 45(2), 8187. LaLonde, B.J. / Pohlen, T.L. (1996): "Issues in supply chain costing", in: IJLM, Vol. 7(1), 1-12. Lambert, D.M. / Cooper, M.C. (2000): "Issues in Supply Chain Management", in: Industrial Marketing Management, Vol. 29, 65-83. Lambert, D.M. / Cooper, M.C. / Pagh, J.D. (1998): "Supply Chain Management: Implementation issues and research opportunities", in: IJLM, Vol. 9(2), 1-19. Lambert, D.M. / Emmelhainz, M.A. / Gardner, J.T. (1996): "Developing and implementing supply chain partnerships", in: IJLM, Vol. 7(2), 1-17. Lariviere, M.A. / Porteus, E.L. (2001): "Selling to the newsvendor: An analysis of priceonly contracts", in: Manufacturing and Service Operations Management, Vol. 3(4), 293–305. Larriviere, M.A. (1999): "Supply chain contracting and coordination with stochastic demand", in: Tayur et al. (1999), 233-268. Lautenschläger, M. (1999): Mittelfristige Produktionsprogrammplanung mit auslastungsabhängigen Vorlaufzeiten, Frankfurt et al. 1999. Lee, H. / Whang, S. (1999): "Decentralized multi-echelon supply chains: incentives and information", in: MS, Vol. 45(5), 633-640. Lee, H.L. (2000): "Creating value through supply chain integration", in: SCMR, Vol. Sept./Oct. 2000, 30-36. Lee, H.L. / Billington, C. (1995): "The evolution of Supply-Chain-Management models and practice at Hewlett-Packard", in: Interfaces, Vol. 25(5), 42-63. Lee, H.L. / Padmanabhan, V. / Whang, S. (1997): "The bullwhip effect in supply chains", in: Sloan Management Review, Vol. Spring 1997, 93-102. Lee, H.L. / Rosenblatt, M.J. (1986): "A generalized quantity discount pricing model to increase supplier's profit", in: MS, Vol. 32(9), 1177-1185. Lee, H.L. / So, K.C. / Tang, C.S. (2000): "The value of information sharing in a two-level supply chain", in: MS, Vol. 46(5), 626-643. Lohse, M. / Ranch, J. (2001): "Linking CPFR to SCOR - Imation's experience", in: SCMR, Vol. July/Aug 2001, 56-62. Lowe, P.G. / Markham, W.J. (2001): "Perspectives on operations excellence", in: SCMR, Vol. Nov/Dec 2001, 52-60. McClain, J.O. / Thomas, J. (1977): "Horizon effects in aggregate production planning with seasonal demand", in: MS, Vol. 23(7), 728-736. McLaren , T. / Head, M. / Yuan, Y.(2002): “Supply chain collaboration alternatives: understanding the expected costs and benefits”, in: Electronic Networking Applications and Policy, Vol. 12(4), 348-364. Meyr , H. (2004): “Supply chain planning in the German automotive industry”, in: OR Spectrum, Vol. 26(4), 447-470.
References
225
Meyr, H. / Wagner, M. / Rohde, J. (2005): "Structure of advanced planning systems", in: Stadtler / Kilger (2005), 109-115. Miller, T. (2002): Hierarchical Operations and Supply Chain Planning, London et al. 2002. Missbauer, H. (1998): Bestandsregelung als Basis für eine Neugestaltung von PPSSystemen, Heidelberg 1998. Moinzadeh, K. / Nahmias, S. (2000): "Adjustment strategies for a fixed delivery contract", in: OR, Vol. 48(3), 408-423. Monahan, J.P. (1984): "A quantity discount pricing model to increase vendor profits", in: MS, Vol. 30(6), 720-726. Nahmias, S. (1996): Production and Operations Analysis, 3rd ed., Chicago 1996. Neumann, K. / Morlock, M. (1993): Operations Research, Munich / Vienna 1993. Oliver, R.K. / Webber, M.D. (1992): "Supply chain management: logistics catches up with strategy", in: Christopher, M. (Ed.): Logistics - The Strategic Issues, London et al. 1992, 63-75. Otto, A. / Kotzab, H. (2001): "Der Beitrag des Supply Chain Management zum Manangement von Supply Chains - Überlegungen zu einer unpopulären Frage", in: Zeitschrift für betriebswirtschaftliche Forschung, Vol. 53, 157-176. Özdamar, L. / Yazgac, T. (1999): "A hierarchical planning approach for a productiondistribution system", in: IJPR, Vol. 37(16), 3759-3772. Peck, H. / Jüttner, U. (2000): "Strategy and relationships: Defining the interface in supply chain contexts", in: IJLM, Vol. 11(2), 33-44. Pesch, E. / Voß, S. (1995): "Strategies with memories: local search in an application oriented environment", in: OR Spektrum, Vol. 17, 55-66. Pfohl, H-C. (2000): "Supply Chain Management: Konzept, Trends, Strategien", in: Pfohl (Ed.): Supply Chain Management: Logistik plus? Logistikkette - Marketingkette - Finanzkette, Berlin 2000, 3-42. Pochet, Y. / Wolsey, L.A. (1995): "Algorithms and reformulations for lot sizing problems", in: DIMACS Series in Discrete Mathematics and Theoretical Computer Science - Vol. 20, 245-293. Porter, M.E (1985): Wettbewerbsstrategie - Methoden zur Analyse von Branchen und Konkurrenten, 2nd ed., Frankfurt 1985. Raghunathan, S. (2001): "Information sharing in a supply chain: A note on its value when demand is nonstationary", in: MS, Vol. 47(4), 605-610. Rasmusen, E. (1994): Games and Information - An Introduction to Game Theory, 2nd ed., Cambridge / Oxford 1994. Rohde, J. / Meyr, H. / Wagner, M. (2000): "Die Supply Chain Planning Matrix", in: PPS Management, Vol. 5(1), 10-15. Rohde, J. / Wagner, M. (2005): "Master planning", in: Stadtler / Kilger (2005), 159-177. Rota, K. / Thierry, C. / Bel, G. (2002): "Supply Chain Management: a supplier perspective", in: Production Planning & Control, Vol. 13(4), 370-380. Sarmah, S.P. / Acharya, D. / Goyal, S.K. (2006): “Buyer-vendor coordination models in supply chain management”, in: EJOR, Vol. 175, 1-15. Schneeweiss, C. (1999): Hierarchies in Distributed Decision Making, Berlin et al. 1999. Schniederjans, M.J. (1995): Goal Programming - Methodology and Applications, Norwell et al. 1995. Schocke, K.-O. (2000): Maschinenbelegungsplanung mehrstufiger Fließfertigungen - vom Modell zum Leitstand für die chemische Industrie, Wiesbaden 2000.
226
References
Scholl, A. (2001): Robuste Planung und Optimierung - Grundlagen, Konzepte und Methoden, experimentelle Untersuchungen, Heidelberg 2001. Seifert, D. (2002): "Collaborative Planning, Forecasting and Replenishment - EMarktplätze als Katalysatoren für das Wertschöpfungsmanagement von Industrie und Handel", in: Thexis, Vol. 03-2002, 14-21. Shapiro, J.F. (1979): "A survey of lagrangian techniques for discrete optimization", in: Hammer, P.L. / Johnson, E.L. / Korte, B.H. (Eds.): Annals of Discrete Mathematics 5 Discrete Optimization II, Amsterdam et al. 1979, 113-138. Shapiro, J.F. (1999): "Bottom-up vs. top-down approaches to supply chain modeling", in: Tayur et al. (1999), 737-759. Shapiro, J.F. (2001): Modeling the Supply Chain, Pacific Grove et al. 2001. Silver, E.A. / Pyke, D.F. / Peterson, R. (1998): Inventory Management and Production Planning and Scheduling, 3rd ed., New York et al. 1998. Simatupang, T.M. / Sridharan, R. (2002): "The collaborative supply chain", in: IJLM, Vol. 13(1), 15-30. Simchi-Levi, D. / Kaminsky, P. / Simchi-Levi, E. (2004): Managing the Supply Chain: The Definitive Guide for the Business Professional, Boston et al. 2004. Simpson, N.C. (1999): "Multiple level production planning in rolling horizon assembly environments", in: EJOR, Vol. 114, 15-28. Simpson, N.C. / Erengüc, S.S. (2001): "Modeling the order picking function in supply chain systems: formulation, experimentation, and insights", in: IIE Transactions, Vol. 33, 119-130. Skjoett-Larsen, T. / Thernoe, C. / Andresen, C. (2003): “Supply chain collaboration – theoretical perspectives and empirical evidence”, in: International Journal of Physical Distribution and Logistics Management, Vol. 33(6), 531-549. Smeltzer, L.R. (1997): "The meaning and origin of trust in buyer-supplier relationships", in: International Journal of Purchasing and Materials Management, Vol. 33(1), 40-48. Sridharan, V. / Berry, W.L. / Udayabhanu, V. (1987): "Freezing the master production schedule under rolling planning horizons", in: MS, Vol. 33(9), 1137-1149. Stadtler, H. (1988): Hierarchische Produktionsplanung bei losweiser Fertigung, Heidelberg 1988. Stadtler, H. (1996): "Mixed integer programming model formulations for dynamic multiitem multi-level capacitated lot-sizing", in: EJOR, Vol. 94, 561-581. Stadtler, H. (1998): "Hauptproduktionsprogrammplanung in einem kapazitätsorientierten PPS-System", in: Wildemann, H. (Ed.): Innovationen in der Produktionswirtschaft Produkte, Prozesse, Planung und Steuerung, Munich 1998, 169-192. Stadtler, H. (2000a): "Hierachische Systeme der Produktionsplanung und -steuerung", in: Domschke, W. / Kolisch, R. / Petzold, H.-J. / Stadtler, H. (Eds.): Schriften zur quantitativen Betriebswirtschaftslehre, No. 1/2000, Darmstadt 2000, 1-34. Stadtler, H. (2000b): "Improved rolling schedules for the dynamic single-level lot-sizing problem", in: MS, Vol. 46(2), 318-326. Stadtler, H. (2003): "Multi-level lot-sizing with setup times and multiple constrained resources: Internally rolling schedules with lot-sizing windows", in: OR, Vol. 51, 487502. Stadtler, H. (2005): "Supply Chain Management - An overview", in: Stadtler / Kilger (2005), 9-35. Stadtler, H. (2005b) "Linear and mixed integer programming", in: Stadtler / Kilger (2005), 473-483.
References
227
Stadtler (2007): „A framework for collaborative planning and state-of-the-art“, in: OR Spectrum, available online at http://www.springerlink.com/content/g28w7489 p0635818/ (09/28/2008). Stadtler, H. / Kilger, C. (Eds.) (2005): Supply Chain Management and Advanced Planning Concepts, Models, Software and Case Studies, 3rd ed., Berlin et al. 2005. Stadtler, H. / Sürie, C. (2000): "Description of MLCLSP test instances", available online at http://www.bwl.tu-darmstadt.de/lib/allgemein/lehre/forschung.php?FG= bwl1 (05/15/2003). Stank, T.P. / Frankel, R. / Frayer, D.J. / Goldsby, T.J. / Keller, S.B. / Whipple, J.M. (2001): "Supply chain integration: Tales from the trenches", in: SCMR, Vol. May/June 2001, 62-69. Steven, M. (1994): Hierarchische Produktionsplanung, 2nd ed., Heidelberg 1994. Steven, M. (2001): "Die Koordination im Unternehmen", in: WISU, Vol. 7, 965-970. Stevens, G.C. (1989): "Integrating the supply chain", in: International Journal of Physical Distribution and Materials Management, Vol. 19(8), 3-8. Stölzle, W. (2002): "Supply Chain Controlling und Performance Management - Konzeptionelle Herausforderungen für das Supply Chain Management", in: Logistik Management, Vol. 4(3), 10-21. Stump, R.L. / Heide, J.B. (1996): "Controlling supplier opportunism in industrial relationships", in: Journal of Marketing Research, Vol. 33, 431-441. Sydow, J. (2002): "Zum Management von Logistiknetzwerken", in: Logistik Management, Vol. 4(2), 9-15. Tamiz, M. / Jones, D. / Romero, C. (1998): "Goal programming for decision making: An overview of the current state-of-the-art", in: EJOR, Vol. 111, 569-581. Tamiz, M. / Jones, D.F. (1996): "Goal programming and pareto efficiency", in: Journal of Information and Optimization Sciences, Vol. 17, 291-307. Tayur, S. / Ganeshan, R. / Magazine, M. (Eds.) (1999): Quantitative Models for Supply Chain Management, Boston et al. 1999. Tempelmeier, H. (2003): Material-Logistik - Modelle und Algorithmen für die Produktionsplanung und -steuerung und das Supply Chain Management, 5th ed., Berlin et al. 2003. Templemeier, H. / Derstroff, M. (1993): "Mehrstufige Mehrprodukt-Losgrößenplanung bei beschränkten Ressourcen und genereller Erzeugnisstruktur", in: OR Spektrum, Vol. 15, 63-73. Templemeier, H. / Derstroff, M. (1996): "A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times", in: MS, Vol. 42(5), 738-757. Thomas, D.J. / Griffin, P.M. (1996): "Coordinated supply chain management", in: EJOR, Vol. 94, 1-15. Thonemann, U.W. (2002): "Improving supply-chain performance by sharing advance demand information", in: EJOR, Vol. 142, 81-107. Thorn, J. (2002): Taktisches Supply Chain Planning - Planungsunterstützung durch deterministische und stochastische Optimierungsmodelle, Frankfurt 2002. Troßmann, E. (1992): "Prinzipien der rollenden Planung", in: WiSt, Vol. 3-1992, 123-156. Tsay, A. / Nahmias, S. / Agrawal, N. (1999): "Modeling supply chain contracts: A review", in: Tayur et al. (1999), 299-335. Tsay, A.A. (1999): "The quantity flexibility contract and supplier-customer incentives", in: MS, Vol. 45(10), 1339-1358.
228
References
Venkataraman, R. / Nathan, J. (1999): "Effect of forecast errors on rolling horizon master production schedule cost performance for various replanning intervals", in: Production Planning & Control, Vol. 10(7), 682-689. VICS (2002): "CPFR - nine step process model", available online at http://www.cpfr. org/documents/pdf/CPFR_Tab_2.pdf (08/13/2002). VICS (2004): “Collaborative Planning, Forecasting and Replenishment (CPFR®) – an overview”, available online at http://www.vics.orgimagescommitteescpfrCPFR_ Overview_US-A4.pdf (09/15/2008). Vollmann, T.E. / Berry, W.L. / Whybark, D.C. (1984): Manufacturing Planning and Control Systems, Homewood 1984. Voß, S. / Woodruff, D.L. (2000): "Supply chain planning: Is MRP a good starting point?", in: Wildemann (2000), 177-204. Weng, Z.K. (1995): "Channel coordination and quantity discounts", in: MS, Vol. 41(9), 1509-1522. Whang, S. (1995): "Coordination in operations: A taxonomy", in: Journal of Operations Management, Vol. 12, 413-422. Wildemann, H. (1997): "Koordination von Unternehmensnetzwerken", in: ZfB, Vol. 67(4), 417-439. Wildemann, H. (Ed.) (2000): Supply Chain Management, Munich 2000. Williamson, O.E. (1975): Markets and Hierarchies - Analysis and Antitrust Implications A Study in the Economics of Internal Organization, London 1975. Zäpfel, G. (2001): "Bausteine und Architekturen von Supply Chain Management - Systemen", in: PPS Management, Vol. 6(1), 9-18. Zäpfel, G. / Wasner, M. (2000): "Modellierung von Logistikketten und Möglichkeiten der Optimierung, gezeigt an einem Praxisfall der Stahllogistik", in: ZfB, Vol. 70(3), 267288. Zeier, A. (2001): "Zur Funktionalität von Supply-Chain-Management-Standardsoftware dargestellt am Bezugspunkt SAP APO", in: Logistik Management, Vol. 3(2/3), 35-52. Zhang, J. / Kim, N.-H. / Lasdon, L. (1985): "An improved successive linear programming algorithm", in: MS, Vol. 31(10), 1312-1331. Zhao, X. / Xie, J. / Leung, J. (2002): "The impact of forecasting model selection on the value of information sharing in a supply chain", in: EJOR, Vol. 142, 321-344. Zijm, W.H.M. (2000): "Towards intelligent manufacturing planning and control systems", in: OR Spektrum, Vol. 22, 313-345. Zimmer, K. (2001): Koordination im Supply Chain Management - Ein hierarchischer Ansatz zur Steuerung der unternehmensübergreifenden Planung, Wiesbaden 2001.
List of Figures Fig. 1. Supply chains of a manufacturer and one of his suppliers ............................................. 6 Fig. 2. MRP II planning tasks.................................................................................................. 13 Fig. 3. Hierarchical planning system (source: Schneeweiss (1999), p. 19) ............................. 16 Fig. 4. Supply chain planning matrix (source: Rohde et al. (2000), p. 10) .............................. 18 Fig. 5. Collaborative planning visualized (source: Kilger / Reuter (2005), p. 259)................. 21 Fig. 6. Collaborative planning cycle (source: Kilger / Reuter (2005), p. 271)......................... 22 Fig. 7. Logistical network structure (source: with adaptations from Thorn (2002), p. 31) ...... 26 Fig. 8. Planning with rolling horizons (source: Fleischmann et al. (2005), p. 84)................... 30 Fig. 9. Links between planning domains................................................................................. 35 Fig. 10. Upstream Planning scheme ........................................................................................ 47 Fig. 11. Structure of a centralized planning model (source: Holmberg (1995), p. 67) ............ 51 Fig. 12. Integration – hierarchy matrix of coordination schemes ............................................ 55 Fig. 13. Two party collaborative planning .............................................................................. 58 Fig. 14. Iterative planning steps - flow chart .......................................................................... 61 Fig. 15. Original and preferred order pattern........................................................................... 65 Fig. 16. Interdependence between savings and deviation........................................................ 70 Fig. 17. Relationship between goal programming objectives.................................................. 74 Fig. 18. Cumulated original and compromise order quantities................................................ 75 Fig. 19. Compromise generation and evaluation as hierarchical planning .............................. 80 Fig. 20. Weighted GP objective function ................................................................................ 82 Fig. 21. Anticipated and actual partner cost increases............................................................. 83 Fig. 22. Shape of acceptance function..................................................................................... 86 Fig. 23. Compromise generation process flow ........................................................................ 87 Fig. 24. Process steps overview............................................................................................... 95 Fig. 25. Acceptance function for detrimental solutions......................................................... 100 Fig. 26. General two-tier supply chain structures.................................................................. 104 Fig. 27. Process flow with multiple buyers ........................................................................... 105 Fig. 28. Process flow with multiple suppliers........................................................................ 110 Fig. 29. General multi-tier supply chain structure ................................................................. 112 Fig. 30. Interface-by-interface planning process ................................................................... 113 Fig. 31. Bilateral negotiations in multi-tier supply chain ...................................................... 114 Fig. 32. Rolling collaborative planning with negotiation horizon ......................................... 119 Fig. 33. Process flow rolling planning................................................................................... 120 Fig. 34. Process flow with limited exchange of cost effects.................................................. 126 Fig. 35. Flexibility and bonus payment schemes................................................................... 145 Fig. 36. Example curves of announced savings and expected payoffs .................................. 157 Fig. 37. Software components and interactions..................................................................... 167 Fig. 38. Frequency distributions of gaps vs. central planning ............................................... 183 Fig. 39. Frequency distribution of remaining gaps................................................................ 185 Fig. 40. Cumulated frequencies of gaps vs. central planning ................................................ 193 Fig. 41. Multiple partners - cumulated frequencies of gaps vs. central planning .................. 200 Fig. 42. Rolling schedules, deterministic demand – gaps vs. central planning...................... 206 Fig. 43. Rolling schedules, uncertain demand – gaps vs. central planning............................ 211
List of Tables Table 1. Supply chain business processes ............................................................................. 9 Table 2. Dimensions of supply chain integration ................................................................ 10 Table 3. Principles of Supply Chain Management .............................................................. 11 Table 4. Basic decisions of master planning ....................................................................... 27 Table 5. Overview of mathematical programming models ................................................. 31 Table 6. Negotiation process example................................................................................. 60 Table 7. Example of order / supply pattern shift limits ....................................................... 68 Table 8. Item weighting example ........................................................................................ 79 Table 9. Process flow example............................................................................................ 97 Table 10. Example effects of negotiation horizon............................................................. 123 Table 11. Savings sharing arrangements ........................................................................... 137 Table 12. Example of period-dependent bonus payment schemes .................................... 146 Table 13. Example payoffs with cooperative and non-cooperative behavior .................... 153 Table 14. Example game................................................................................................... 154 Table 15. Capacity utilization profiles .............................................................................. 170 Table 16. Overview of input parameters for test problems ............................................... 173 Table 17. Test classes for single buyer and supplier ......................................................... 174 Table 18. Average demand of end products ...................................................................... 176 Table 19. Problem dimensions by test class ...................................................................... 176 Table 20. Limits on the computational time...................................................................... 178 Table 21. Central planning results..................................................................................... 179 Table 22. Upstream Planning results................................................................................. 180 Table 23. Negotiation scheme results................................................................................ 181 Table 24. Remaining gaps of negotiation outcomes.......................................................... 184 Table 25. Division of total costs by TBO profile .............................................................. 186 Table 26. Computational results by cost structure............................................................. 187 Table 27. Computational results by capacity profile ......................................................... 188 Table 28. Average gaps vs. central planning by iteration.................................................. 190 Table 29. Negotiation results with limited exchange of cost information ......................... 191 Table 30. Negotiation results without cost anticipation..................................................... 192 Table 31. Test classes for multiple buyers and one supplier ............................................. 194 Table 32. Average demand of end products with multiple buyers .................................... 195 Table 33. Multiple partners - central planning results ....................................................... 196 Table 34. Multiple partners - Upstream Planning results .................................................. 197 Table 35. Multiple partners - negotiation results (original scheme) .................................. 198 Table 36. Multiple partners – remaining gaps of negotiation outcomes............................ 199 Table 37. Multiple partners - negotiation results (limited exchange) ................................ 199 Table 38. Example of demand forecast and schedule updates........................................... 202 Table 39. Rolling schedules, deterministic demand – Upstream Planning results............. 204 Table 40. Rolling schedules, deterministic demand – negotiation scheme results ............ 205 Table 41. Rolling schedules, uncertain demand – Upstream Planning results................... 207 Table 42. Rolling schedules, uncertain demand – negotiation scheme results .................. 209 Table 43. Rolling schedules, uncertain demand – results by capacity profile ................... 212
List of Symbols Indices j operation / item ∈ J k buyer 1…K ∈R r resource t planning period 1…T Index sets / boundaries J set of operations / items JO set of order items (operations) JS set of supplied items (operations) set of items j supplied to buyer k JSk K number of buyers set of buyers k provided with item j KJj R set of resources set of direct successor operations of j Sj T planning horizon frozen horizon TF TN negotiation horizon Data ar,j unit requirement of resource r by operation j capacity of resource r in period t Cr, t Cmax maximum cost (CP-0 solution) minimum cost (CP-1 solution) Cmin cfj setup cost associated with operation j unit holding cost of operation j chj cor unit cost of overtime at resource r penalty cost rate for extra supply of item j cxsej Ej,t (external) demand for operation j in period t target value for relative distance of item j (component of vT) Dj Djmax maximum absolute distance of item j G optimal GP objective function value (CP-2 solution) maximum lot-size constant for operation j Lj,t initial inventory level of item j Ij 0 I j, t / I j,t upper / lower bound on inventory level of j at the end of period t
ISj0
initial inventory level of supply item j
IS j, t / IS j, t
upper / lower bounds on supply inventory of j at the end of period t
O m,t / O m,t
upper / lower bound on overtime on resource r in period t
rj,k
unit requirement of operation j by successor operation k
X j, t / X j, t
upper / lower bound on output level of j in period t
XOj,t
proposed order quantity of j in period t
min XO cum, j, t
minimum cumulated order quantity of j in periods 1 through t
max XO cum, j, t
maximum cumulated order quantity j of in periods 1 through t
XSj,t
proposed supply quantity of j in period t
234
List of Symbols
min XS cum, j, t
minimum cumulated supply quantity of j in periods 1 through t
max XS cum, j, t
maximum cumulated supply quantity of j in periods 1 through t
C
W WD wj ∆C* ∆Ci ∆CiB/S, ∆PiB/S ε Variables c d dj dpj dnj d+j,t / d-j,t gp ij,t isj,t or,t xj,t xsj,t xoj,t xsej,t yj,t ∆
weight of cost objective weight of modification objective weight of item j in distance measure and deviation from target point total cost effect of best solution total cost effect of previous solution local cost effect of compromise pattern cost increase due to partner’s previous proposal arbitrarily small number (<< 1) total cost percentage modification of supply pattern relative distance of item j positive deviation from target distance of j negative deviation from target distance of j shift of supply quantity of j in t to the next / previous period relative deviation from optimal GP objective function value inventory level of operation j at the end of period t supply inventory of j at the end of period t overtime at resource r in period t output level of operation j in period t supply quantity of j in period t order quantity of j in period t extra supply quantity of item j, period t setup variable of operation j in period t deviation from minimum cost
