Parts Management Models and Applications A Supply Chain System Integration Perspective
Parts Management Models and Applications A Supply Chain System Integration Perspective S ameer Kumar University of St. Thomas Minneapolis, Minnesota
Spriinger
ISBN 0-387-22821-7 ©2005 Springer Science + Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springeronline.com
Dedication
This book is dedicated to the Family, Parents and Friends
Preface
Parts are commonly used in making, repairing or maintaining consumer or industry products. Parts could be purchased or manufactured by a business enterprise. Advance models were applied to parts operations for manufacturers of transport refrigeration equipment and high-pressure positive displacement plunger pumps. Both companies have an established network of dealers for sales and service of equipment and parts. A number of areas in the parts business operation were researched which show the potential for improved operational efficiency and customer service that increase market share when advanced process models were used to integrate the supply chain. This book covers the subject of parts management through: (1) an introduction to areas of parts business operation with potential for substantial improvements and overview of various models proposed in Chapter 1; (2) quantitative effects on customer service level of inventory miscount and lead time variability and methods to reduce these factors in Chapter 2; (3) optimal division of items based on economics within a two-level distribution system; which items should be serviced through dealers and which items directly by the company to end-customers in Chapters; (4) optimal ordering procedures for a multi-item common supplier system with either constant or random demand rates for various items in Chapter 4; Vll
viii
Parts Management Models and Applications (5) attribute based classification scheme to promote standardization of design and manufacturing techniques for expediting product development and control design proliferation in Chapters 5 and 6; (6) knowledge base management to enhance manufacturing operations effectiveness in Chapter 7; (7) showcasing improvement in planning and fulfillment process of a manufacturing operation through integrated supply chain efforts in Chapter 8; and (8) summative understanding of the significance of holistic approach to parts management and presenting various aspects of successful Dell Computers Supply Chain.
The book attempts to present a detailed overview of management of parts operation whether it relates to procurement, engineering design, manufacturing, warehousing or distribution. It also makes emphasis on the combined look at all business functions of a company including working closely with major suppliers and customers.
Acknowledgments
The book is the blending of author's research interests and twenty plus years' experience working in industry on projects relating to Parts Supply Chain Optimization. The holistic view described in "Parts Management Models and Applications" book is adapted from published papers focused on various aspects of parts management covering: procurement, design, manufacture, inventory, distribution, customer service and the entire value chain. The major contribution of the book comes from a number of models developed, viewpoints and industry applications for managing parts business operation in a supply chain context. I have acknowledged the citation of the adapted work published in professional literature as end notes at the end of various chapters in the book. I am indebted to my family, parents and friends for their unconditional support. I also wish to thank the editor and the entire production team at Springer for their assistance and guidance in successful completion of this book. Sameer Kumar Minneapolis, Minnesota
IX
Contents
Chapter 1 - Introduction To Parts Management
1
Chapter 2 - Inventory Miscount & Lead Time Variability - Effects & Control Mechanisms? Chapter 3 - Optimal Division Of Items Within A Two-Level Distribution System
49
Chapter 4 - Optimal Ordering Procedures For A Multi-Item Common Supplier System
69
Chapter 5 - Parts Proliferation And Control
99
Chapter 6 - Economic Viability Of Component Management For A New Product Design! 17 Chapter 7 - Manufacturing Operations Effectiveness Through Knowledge Based Design 133 Chapter 8 - Serve Your Supply Chain, Not Operations
155
Chapter 9 - Holistic View Of Parts Management
189
Appendices
199
References
205
Index
219
xi
Parts Management Models and Applications A Supply Chain System Integration Perspective
Chapter 1 INTRODUCTION TO PARTS MANAGEMENT
This book deals with management of parts business operation covering such issues as, their procurement, design, manufacturing and distribution to ultimate customers. Various models are described and their applications shown using examples of a leading manufacturer of transport refrigeration equipment and a manufacturer of high pressure positive displacement plunger pumps. These companies have established network of dealers for sales and service for both equipment and parts. Majority of the parts are purchased from other manufacturers. The parts market is very competitive. Both price and customer service, are important factors in determining the market share. The focus of this research is to improve customer service; reduce costs through improved inventory and operational management techniques; and address improvements in supply chains and not on individual business operations in a company.
1.
POTENTIAL AREAS OF IMPROVEMENTS
After a preliminary study of the system, the following areas were selected where potential for substantial improvements existed using the examples of above-mentioned companies. Inventory Count and Procurement Lead Time Errors in inventory count affect ordering decisions and consequently customer service level. If reported inventory count for an item is smaller than its actual inventory, extra inventory will be carried all the 1
2
Parts Management Models and Applications
time. If reported inventory count is larger than the actual inventory, the ordering for the item will be delayed and more stockouts will result than planned through the model. Procurement lead time is an important factor in ordering decisions. Usually lead times are assumed to be constant in inventory decision models, as variable lead times models become somewhat more complex. However, ignoring lead times variability, when it is substantially sizeable, can have a devastating effect on customer service. The ordering procedures in the company treats procurement lead times as constants when they are indeed variable. The management has been concerned about both the accuracy of the inventory counts and about the variability of the lead times not being considered in ordering rules. Chapter 2 covers three major themes. The first deals with developing quantitative effects of inventory miscount and non-incorporation of lead times variability in ordering rules on Customer's Service Level individually and jointly. Development of Procedures for Reducing Inventory Miscounts The sources of errors were found to be primarily due to data entry. These errors persisted for long times in the system. There were no formal procedures to identify these errors and correct them. The second theme in Chapter 2 deals with developing parity checking procedures based on material conservation concepts at the micro level, for identifying and correcting data entry errors during receipts and issues of materials. The micro-level implementation of the conservation equation required development of a coding scheme for tracking the flow of materials during their transient stages. The checking for the compliance of the audit procedure is done on an ongoing basis by a simple physical inventory program. Implementation of EDI Communication Network with Suppliers to Reduce Lead Times Variability Electronic Data Interchange (EDI) as a technology has been proven to reduce procurement lead times and ordering costs substantially. The third theme in Chapter 2 deals with presenting an explicit relationship between EDI and JIT. A simple model illustrates how lot sizes can become smaller with EDI network. It emphasizes and quantitatively shows that any reductions sought in lot sizes without a genuine reduction in ordering cost and lead times would impose penalties instead of achieving economies. EDI network lowers inventories and safety stocks.
Introduction to Parts Management
Optimal Division of Items within a Two-level Distribution System Two-level distribution systems are common as was the case in the company studied. Expensive and low demand items were presumed serviced directly by the Company, whereas other items distributed through dealers. The existing division of the items is more or less on a subjective basis. It was commonly felt within the company that dealers should keep shelf inventory for more items. They made their decision regarding whether an item should be on shelf or not, on an individual basis. If an item is not profitable, they would not inventory it. Chapter 3 gives an economic rationale for subsidizing dealers to encourage them to keep shelf inventories for more items. The subsidization is justified on account of the resulting increased market share and profitability. This Chapter develops a rational basis for deciding which items should be serviced through dealers and which items directly b)^ the company. Management has been debating this issue for a long time. Development of More Appropriate Lot-sizing Rules for Common-supplier Cases Existing ordering rules were based on the assumption of separability of the objective function on an item basis and the traditional EOQ models were being used. In reality, several items had a common supplier. The ordering cost, while ordering from a common supplier, had two components - a major common part "A", which was independent of the number of items ordered and a minor component "a" which linearly increased with the number of items. Chapter 4 develops lot-sizing rules for constant and random demands for various items. The first part of Chapter 4 develops optimal ordering procedures for a multi-item system supplied by a common supplier, with constant demand rates for various items. The model presented in this Chapter allows for planned stockout levels, computed on the basis of the total cost minimization. The second part of Chapter 4 deals with heuristic ordering rules for multi-item single supplier case with random demands. The assumption of constant demand rate may not be valid in certain cases where demand variability is sizeable. The ordering rules developed in this chapter include when to order and which items to order. An order is placed when composite stockout cost rate exceeds a multiple of the average ordering cost per order. Appropriate values of the parameters used in operational management rules are determined by minimizing the total variable cost.
4
Parts Management Models and Applications
Parts Proliferation and Control As is typical in any parts inventory system, there were lots of items in the inventory very similar to each other and interchangeable. No formal procedures existed to control the proliferation of parts. The valid point for controlling this proliferation was the Design Department. It was here where decisions to add new parts were taken. One of the procedures for controlling parts proliferation is to provide the design engineer with a list of parts similar to the new part that he is planning to design, for his perusal and evaluation as to whether one of the existing parts can be a substitute. Chapter 5 develops a classification scheme to form and retrieve a subset of items similar to the new proposed design. The classification scheme is attribute based. A finite number of attributes characterize an item. The selected attributes for variety control purposes are the ones that relate to various design characteristics. The Principal Components Analysis technique is used to generate principal components, where a fewer number of components would explain a major portion of total variance in the values of the attributes. The grouping of the items on design similarity criterion is done hierarchically using these principal components. Chapter 6 explores the viability of standardization of design and manufacturing techniques to expedite product development and control design proliferation using an example of a leading transport refrigeration unit manufacturer. An incremental approach to implementing standardization in a product development environment using a conceptual framework for component management decision support system is presented to build a case for its technical feasibility. The primary objective of this chapter is to provide an economic justification for implementing the proposed system. A three level decision making hierarchy is proposed with economic optimization for levels 1 and 2 representing standardization of system modules and capacity decisions for a product line respectively. Thermodynamic optimization for level 3 represents control systems to keep the system dynamically balanced in changing environments. Other potential applications amenable to classification are identified. Enhancing Manufacturing Operations Effectiveness Through Knowledge Based Design Chapter 7 is based on the realization that global competition has pushed firms to continuously improve and upgrade their manufacturing operations. Role of knowledge base and learning to facilitate this phenomenon are explored. Developing a knowledge base requires organizing knowledge and expertise for a field of inquiry and making it
Introduction to Parts Management
5
available in formats suitable for users to support and aid various operational, developmental, and organizational functions. Classification and coding form the basis for organizing knowledge bases. Most classification schemes are attribute based. Classification implies grouping objects into similar classes on the basis of some similarity criteria pertinent to one or more attributes. Learning in the context of classification implies discovering new attributes, bases for grouping and requires frequent updating of the knowledge base. When a system evolves, ideally so should its knowledge base and classification scheme. A formal knowledge base makes a firm's knowledge cumulative and serves an important integrating and coordinating role for the organization. These concepts have been applied to support manufacturing activities at a leading, transport refrigeration unit manufacturer. An example application utilizing classification as a tool for knowledge acquisition in design support activities at this firm is presented. Serve Your Supply Chain, Not Operations Chapter 8 describes a pilot study carried out to improve planning and fulfillment process in a division of a manufacturer of high-pressure positive displacement plunger pumps. The focus was to develop a synchronized system from source to consumption with continuous flow of information and materials for one of this division's main product lines. System-wide changes were accomplished using a cross-functional team with the goal of reducing waste and investment in inventory. Traditional measures of manufacturing efficiency and utilization were compared to proposed measurements of throughput (T), investment in inventory (I), and operating expense (OE). Although traditional measures showed actual decline; proposed measures showed improvement and increased profitability of 200% for this product line. These new performance measures reflected a change from local to global thinking. Improved capacity management in the system was achieved by sharing information between suppliers and customers. Holistic View of Parts Management Chapter 9 summarizes understanding of total parts management. It also describes a highly successful Dell Computers supply chain. In this supply chain, the company closely matches product demands with manufacturing of products and procurements of parts from suppliers.
6
Parts Management Models and Applications
The approaches outlined in this book were used to adapt simple models to accurately address complex operational dynamics. The holistic approach to synchronizing systems from source to consumption has resulted in increased profitability, improved customer service and well coordinated business operations. These new advanced models described in the book are not limited to industries studied but have general applicability.
Chapter 2 INVENTORY MISCOUNT AND LEAD TIME VARIABILITY - EFFECTS AND CONTROL MECHANISMS
This chapter consists of three major sections; each has a focus on different aspect of inventory performance management system. The first studies the quantitative effects of inventory miscount and non-incorporation of lead time variabihty on customer sen^ice level and on the inventory holding cost in a parts management system. An inventoiy miscount for an item implies a discrepancy between its actual physical inventory count and its quantity as per computer records. Tlie second section focuses on schemes to reduce inventoiy miscounts from the operational management point of view. The third section illustrates how EDI networks lower both ordering costs and lead times and consequently result in smaller lot sizes and smaller safety stocks.
1.
INVENTORY MISCOUNT AND LEAD TIME VARIABILITY
This section establishes the need tbr developing procedures for reducing inventory miscounts and for incorporating the level of miscounts along with the lead times variability in tlie computation of reorder points.
8
1.1
Parts Management Models and Applications
Introduction
The importance of short delivery times for spare parts has been widely stressed in the professional literature (Duchessi, Kumar and Levy 1988; Ronen 1983). The impact of lead time variability on the total system cost has also been extensively studied (Buchanan and Love 1985; Gupta 1979; Lau and Zaki 1982; Magson 1979). The study originatedfromthe management commitment to raise customers' service level without further increasing investments in inventories. The company manufactures and also services transport refrigeration units. The chapter focuses on the parts distribution portion of the business. The Service Parts System has approximately 45,000 parts. About 80% of the parts are purchased and the remaining 20% manufactured by the company. Approximately 10%) of the manufactured parts are contracted out to specialized vendors and they are provided witfi a major portion of the needed components and raw materials. About 95%) of the yearly sales of service parts are from one-third of the parts. Exponential smoothing techniques with trend are currently being used to forecast future demands. A fixed lead time, subjectively determined, is assigned for every part. The reorder points are based on the average lead time demands and the management prescribed service level. However, the actual service level realized falls far below the prescribed service level on which the reorder points are presumably based. The consistently lower realized service level has been a puzzling problem for the management for some time. The diagnostic steps carried out suggested that the two main causes for the lower realized values of the service level were: (i) Miscount in the inventories of the parts, and (ii) Non-inclusion of lead time variability in computing reorder points. The magnitudes of their effects are assessed through the following model.
1.2
The Model Quantifying Effects on Service Level^
We begin with describing the notations used in the proposed model.. Notations The following notations for each item j have been considered. (The index j is subdued in the development of the model.) t = When t is used as a suffix of a variable, it denotes the value of the variable at time t, I^ = Inventory on hand as per computer records, I^ = Actual physical inventory on hand.
Introduction to Parts Management Wt At /' Q R P
= = = = = =
P D^ D L cr^ a^ (7^ K K h_ L I
= = = = = = = = = = = =
On-order quantity, Inventory already allocated but still in stock, Inventory position as per computer records, Order quantity, Re-order point, Fraction of the demand desired to be met, from the shelf inventory, also called service level, Actual service level realized, Demand rate, Average demand rate, Procurement lead time, Standard deviation ofdemand over lead time, Standard deviation of demand rate, Standard deviation of lead time, Safety stock factor used in computing reorder point. Effective safety stock factor, Holding cost per unit item per unit period, Average lead time, Relative error in on-hand inventory given by
(i{t)-i{t))/m, fit)
= Probability density function of I,
i (T; HL = Probability density function of
G,{K)=l{U-K)cl>[u)dU, where ^(f/)denotes the density function of a unit normal distribution.
EFFECT OF INVENTORY MISCOUNT The ordering decision for an item is based on the Inventory Position It', where
i;=i,+w,-A,.
(1)
10
Parts Management Models and Applications As shown in Figure 2-1, a quantity Q is ordered when It' (Inventory Position based on computer records) hits the reorder level R. The actual service level realized is affected by the deviation of I^ (the actual physical inventory)fromIt (on-hand quantity as per computer records). It is assumed that demand follows a normal process. The demand during lead time L will follow a normal distribution with mean DL and variance cr^ . Its densityfiinctionis denoted by^(x). If the lead time variability is duly considered, the reorder point R is given by
(2) where
(3) and K is the safety stock factor. Assume that the management prescribes a service level P, where P denotes the fraction of the demand desired to be met from the shelf inventory (say, P is 0.95. as an example). As per management's prescribed service level, the total average demand over an ordering cycle duration that may not be metfromthe shelf inventory will equal
Q{l-P)
(4)
Introduction to Parts Management
11
\y/
Figure 2-1. Illustrating reorder point and ordering procedure
Tlie truncated mean of a normal distribution ^(x) with mean DL and 2
variance GJ>, is given by
[{x-R)l>{x)dx. This measures the average demand per ordering cycle not met from shelf inventory. Substituting \x - DLj/ GJ^ = U, the above integral becomes
12
Parts Management Models and Applications [{x-R)cl){x)dx
= cr^G^{K).
(5)
Equating (4) and (5) gives the following equation: G,{K) = Q{\-P)lc7,^
(6)
Once the value of K is known, the value of R can be easily computed on solving K^[R-
~DL)I CJ^^ .
(equation (2))
Since at the time of placing an order It'= R, we have K = [R-WLIa^)=Q{\-P)lcr^^
(7)
Substituting the value of It given by (1), equation (7) becomes G,ii:-^~L)lcj,^]=Q{\-P)la^^.
(8)
If /^ ^ /^, then the actual performance will deviate from the planned performance level.
Consider two cases, case 1 when I^ (/^ and case 2 when I^ > /^.
Casel. / / / r In this case, the actually realized service level P will fall below the planned service level P. The value of P is given by G^ ((/, + PF, - 4 - D Z ) / c r ^ J = 2(1 - P) / cTo,. Recall that the relative error in inventory miscount is denoted by
(9)
Introduction to Parts Management
13
The values of P for various values of P and t are given in Table 2-1. These values are plotted in Figure 2-2. The calculation of P in the previous section assumes a constant lead time ( a L = 0). The calculations for variable lead times are given in the following section. These tables are based on a typical item with the following parameter values:/) = 451.6, cr^ = 377.2, L = 2.04, o-^ =0.77, Q=1420.
Table 2-7. Values of P for Various Values of P and £
^\^^
£
P ^ " ^ ^ .85 .90 .95 .96 .97 .98 .99
.1
.2
.3
.4
.5
.6
.82 .87 .93 .94 .95 .96 .98
.78 .83 .89 .90 .92 .94 .96
.73 .78 .85 .86 .88 .90 .93
.68 .73 .79 .81 .83 .85 .89
.63 .67 .73 .75 .77 .79 .83
.57 .61 .66 .67 .69 .71 .75
Parts Management Models and Applications
14
0J5 0.9
wv<'"
0.15 OJ 0.65
m"
M'^'-
-«
\
1 : '
;
m
0.85 0.8
4^.-
,f - . 1
1
/ "- '"' m^
;
""'
•"•
»
m
* ''"^
0,55 0,5
'
0,8
?
0.85
(
0.9
J
0J5
Figure 2-2. Graphs showing the relationship between prescribed and actually realized service levels for various values of i
Case 2. / > / . fo this case, the realized service level p will be better than the management prescribed service level P. The values of P for various values of P and i are given in Table 2-2. These values are plotted in Figure 2-3.
2.1
Estimation for the Level of Inventory Miscount for the System
The population of items is classified into six categories labeled / = 1,2, 3, 4, 5 and N. The category N denotes new^ items introduced during the preceding six months. The other five categories denoted by / are on the basis of the annual demand of the items in units, / == 1 being the category for the items w^ith the low^est annual demand.
Introduction to Parts Management
15
Table 2-2. Values of P for Various Values of P and ^
p
-.1
-.2
-.3
-.4
-.5
.85
,88
.91
.94
.96
.965
.90
.92
.94
36
.97
.975
.95
.%
.97
.98
.98
.982
.96
31
.978
.984
.985
.988
.97
3T1
.98
.988
39
.992
.98
.985
.989
.992
.994
396
^ ^ • ^ ^ - ^
^
Figure 2-3. Graphs showing the relationship between prescribed and actually realized service levels for various levels of I
Let n^ denote the number of items in category /, and let d^ be the average demand rate per item within category /. Let m^ = n^d^ where m^, denotes the total activity level for items in category /.
16
Parts Management Models and Applications
A stratified random sample of 100 items, proportional to m^was taken from each category / and their I values were computed by comparing the values of /^, and I^. The results are summarized in Table 2-3. A normal distribution for I was hypothesized and validated by the x'^ goodness offittest.
Table 2-3. System-Wide Estimation of Inventory Miscount Level( O^ = Observed Frequencies)
t
0,
-co
-2.1
-1.5
-1.2
-.9
-.6
-.3
0
.3
.6
.9
1.5
2.1
to
to
to
to
to
to
to
to
to
to
to
to
to
-2.1
-1.5
-1.2
-.9
-.6
-.3
0
.3
.6
.9
1.5
2.1
+00
9
3
5
2
4
7
12
17
19
11
11
0
0
The density function f(^) is N (-0.2, (1.3)^), a normal distribution. If the distribution oft continues at the current level, the composite performance curve will be given by P(P) = ljiP,l)f{l)M+
[ PiP,£)fii)di
(10)
Integration of (10) is achieved using discrete approximation of f (^). The value of integral given in (10) is computed for two scenarios. Scenario 1. The improvement in P for items with negative £ is not allowed to cancel the degradation in P for items with positive £. This is achieved by taking P (P, ^) = 0 in equation (10) for ^ < 0. The values of p for various values of P are given in Table 2-4. These values are plotted in Figure 2-4.
Table 2-4. Composite realized Service Level P for the System for Various Values of?
p p
.85 .72
.90 .76
.95 .82
.96 .83
.97 .84
.98 .88
.99 .90
Introduction to Parts Management
0.95
17
---
: ~
0. 9 -U
A
,_.——-^
0. 85 t- -
^
^^^^^^^^ —
0. 8 1 0. 75 1 " 1 0.7 1
0
,
f"^ 1
-. 2
U..-^-.^.--.-
-
3
\
^ 4
5
7'
6
8 P
Figure 2-4. Composite realized service level curve for the system plotted against P
Scenario 2. The improvements in P for items with i < 0 are allowed to cancel out the degradation in p for items with £ > 0. The values of p for various values of P are given in Table 2-5. These values are plotted in Figure 2-5. Table 2-5. Composite Realized Service Level P for System for Various Values of P
p p
.85 .82
.90 .84
95 .88
.96 .89
97 .90
.98 .91
Parts Management Models and Applications
18
084
086
QB8
09
Figure 2-5. Composite realized service level curve for the system plotted against P
2.2
Effect of Inventory Miscount Error on Holding Cost of the Safety Stock
The effect on the holding cost of the safety stock may be computed from the following expression: Planned average safety stock = KCTJ^ - a^ G^ (K),
(11)
Actual average safety stock = Kaj^ - a^ G^ (K),
(12)
where K =
(I,+W,-A,-DL)/a^^
(13)
and (14) Actual minus Planned average safety stock = (12)-(11) = iK-
K)a^^ - cT^, (G^ {k) - G, (K))
Introduction to Parts Management
19
= {i,-I,)-a^^iG^{k)-G^iK))
--n,-a^^(G^iK)-G,{K))
(15)
= - i I^,ignoring aj^ (Gy (K) - G^ (K)) being relatively quite small for inventory holding cost purposes. When £> 0, there are some savings in inventory holding costs. The system-wide savings in holding cost
=
Y.^^1,
(16)
Items with £>0
However, when £<0, there is extra inventory holding cost. The system-wide extra holding cost Items with ^<0
The system-wide net holding cost
=
"Z-MI,Items with ^<0
Y.^11,
(18)
Items with ^>0
EFFECT OF IGNORING LEAD TIME VARIABILITY In the current procedures, reorder points are computed assuming lead time being constant at value L and ignoring its variance Gj^. In reality, lead time has significant variance. Let R^^ be the reorder point as per current procedure, i?^, corresponding to the prescribed service level P when (JJ = 0, is given by:
G^iRc -DL)/a-J
= Qi\-P)/a,y^
(19)
20
Parts Management Models and Applications where a i^ = ^JLa^ .
The realized service level P is given by the actual system where the lead time vanability is impacting. We have G, i(R, - DL) I a^^) = 0(1 - P) / a^^
where a^ is given by equation (3). Values of P for various values of P and c^ I ^ L are given m Table 2-6. These values are plotted in Figure 2-6.
(20)
Introduction to Parts Management
21
Table 2-6. Values of ^ for Various Values of P and ^ ^
.85 .90 .95 .96 .97 .98 .99
0.5
1
2
3
4
.85 .87 .92 .94 .95 .96 .98
.79 .81 .87 .88 .90 .91 .94
.64 .65 .71 .73 .75 .77 .80
.47 .48 .55 .56 .59 .61 .65
.30 .32 .38 .39 .42 .44 .48
Figure 2-6. Graphs showing the relationship between prescribed and actually realized service
22
Parts Management Models and Applications
3.1
Estimation of Lead Time Variability for the System A gamma distribution is hypothesized for the ratio (a^ /
and the
hypothesis is confirmed by % ^^^^ ^xov^v the historical lead time data of vendors. The estimates for the parameters a and ^ of the gamma distribution (Kokoska and Nevison 1989) are obtained using the method of moments. We have c^ = 1.95,y5 = 1.04.
The estimates have been rounded to a computational simplicity.
= 2.0 and /? = 1.0 for
The composite estimated system service level is given by
P(P) = f P(P,(cT, lfL))g{a, lfL)d{a, 141)
(21)
Integration of (21) is achieved using discrete approximation of gicJi^HL) . Values of P for various values of P are given in Table 2-7. These values are plotted in Figure 2-7.
Table 2-7. Composite realized Service Level for Various of P and F >
P
P
.85
.90
.95
.96
.97
.98
.99
.58
.59
.65
.67
.69
.71
.74
Introduction to Parts Management
p
23
r
0.75 ^
0.7 0.65 0.6
^-""^
•
0.55 1
0.5 0.8
1
0.85
0.9
0.95
P
'
Figure 2-7. Composite realized service level curve for the system plotted against P (the degradation of P is due to ignoring lead time variability only).
J O I N T E F F E C T O F IGNORING LEAD T I M E VARIABILITY AND HAVING INVENTORY MISCOUNT In computing the composite effect on the realized service level based on current practice of ignoring lead time variability and inventory miscounts, the reorder point R is given by
G^{{R-DLI<j^) where La J
= Q{\-P)lcr^^
(22)
Parts Management Models and Applications
24
The realized service level p is affected by inventory miscount value i and the lead time variability Cj. The value of p is given by
G^((I^^W,-A-DL)/cT^^)
=
Q(l-P)/a^^,
(23)
It is assumed that both errors are independent. Values of P for various values of P, i and a^ I y L are given in Table 2-8. These values are plotted in Figure 2-8. Table 2-8. Values of P for various values of P, £ and CJ^ / ^ L
G^lil
1.0
.1
.2
.3
2.0
.4 .5
.1
.2
.3
3.0
.4
.5
.1
.2
.3
4.0
,4
.5
.1
.2
.3
.4
.5
0.85
.76 .72 .68 .63 .58 .60 .56 .53 .48 .44 .43 .40 .36 .32 .28 .26 .23 .19 .16 .12
0.90
.77 .73 .(^3 .65 .59 .62 .58 .54 .50 .45 .45 .41 .37 .33 .29 .28 .24 .21 .17 .13
0.95
.83 .79 .75 .70 .64 .67 .63 .59 .54 .49 .51 .47 ,43 .38 .33 .34 .30 .25 .21 .17
0.96
,85 .81 .76 .71 .66 .69 .65 .61 .56 .50 .53 .48 .44 .39 .34 .36 .32 .27 .22 .18
0.97
.86 .84 .78 .73 .67 .71 .67 .62 .57 .52 .54 .50 .45 .41 .35 .37 .33 .29 .24 .19
0.98
.88 .84 .80 .75 .69 .73 .69 .64 .59 .54 .57 .53 .47 .43 .37 .40 .36 .31 .25 .21
0.99
.91 .87 .83 .78 .72 .77 .72 .67 .62 .57 .61 .56 .51 ,45 .40 .44 .39 .34 .29 .23
Introduction to Parts Management
25
-^
crj4L^2,t=2
^^ aJ 41=4,1^.3 -^^ a^/4L^A,i = A
O^OOE^QO
0.85
0.9
m
p 1
F/gwre 2-5. Graphs showing the relationship between prescribed and actually realized service levels
4.1
Estimation of System-Wide Composite Realized Service Level P
The estimated composite service level is given by ^(^^ = f
£ ^ ( ^ ' ^ ^ /^,e)f(e)gia,
/^)d(i)d(a,
141).
(24)
26
Parts Management Models and Applications Integration of (24) is achieved using discrete approximations of / ( ^ ) NL)
and g{(jj
The values of P for various values of P are computed for scenario 1 and are given in Table 2-9. These values are plotted in Figure 2-9. Table 2-9. Composite realized Service Level P for the System for Various Values of P (The Degradation of P is Due to Inventory Miscount and Lead Time Variability [for Scenario 1])
p
p
.85
.90
.95
.96
.97
.47
.49
.54
.55
.57
.98
.59
.99
.62
Introduction to Parts Management
0-84
0-86
0.88
0-9
27
0-92
0-94
0-96
0.98
1 P
Figure 2-9. Composite realized Service Level ^
for the System for Various Values of P
(The Degradation of ^ is Due to Inventory Miscount and Lead Time Variability [for Scenario 1])
5.
CONCLUSION - INVENTORY MISCOUNT AND LEAD TIME VARIABILITY The realized service levels in a parts distribution system were consistently lower than the management prescribed service levels and this had puzzled the management for a long time. The system diagnostic revealed that the two main causes were inventory miscount and non-inclusion of lead times variability in re-order points formulae. The inventory miscount errors generally creep in the computer records at data entry points. Items with high levels of transactional activity are more susceptible to inventory miscounts. Inadequate audit procedures can lead to the perpetuation of these errors and their prolonged consequent effects. This points out the need for developing improved parity checking procedures and periodic audit schemes (Saipe 1979; Stohr 1979). The non-inclusion of lead times variability takes place on account of the common tendency to simplify operating rules. However, the impact of ignoring this variability is serious on the realized customer service level.
28
Parts Management Models and Applications
The degradation in the prescribed service level due to inventory miscounts and non-inclusion of lead times variability was quantified, when these factors are operating individually and collectively. The management was convinced that more systematic audit procedures should be developed to correct inventory records, and lead times variability should be incorporated in computing reorder points. Any attempts to improve service level without correcting the above deficiencies would require un-needed additional investments in inventories.
6.
INVENTORY ACCOUNTING PROCEDURES^
This section illustrates an internal audit procedure devised for identifying most of the data-entry errors, which are one of the main causes of inventory miscounts during the flow of material through in-transit stations. Inventory miscount errors, which escape the internal audit procedure, are further reduced through cycle counting. Cycle counting schedule is optimally determined by minimizing the sum of the cycle counting cost and the penalty cost owing to additional stockouts and overstocking due to inventory miscounts.
6.1
Introduction
Accuracy in inventory figures from an accountant's point of view is needed just before financial statements are prepared. Furthermore, the accountant's objective is to estimate the dollar value of the total inventories within some specified limits of statistical confidence. However, for operational management, the need for accuracy in inventory counts is ongoing, and it is in the physical count at the individual item level. A cyclecounting program on a scheduled basis will tend to stabilize the level of miscount errors compared with the monotonically increasing errors which result in annual counting schemes up to the time of the yearly count. In the next section, current procedures for inventory transaction handling and the levels of inventory miscount errors for a company dealing with spare-parts distribution are studied. The effects of inventory miscount on the customer service level are reviewed. Internal audit and cycle-counting procedures for reducing inventory miscounts are developed.
Introduction to Parts Management
6.2
29
Inventory Miscounts and Control Procedures
Inventory miscounts can lead to a substantial degradation in customer service level, which becomes all the more serious when lead times are random. Alexander (1985) states that confidence in a system is lost if it is often in error, and in such cases the replenishment rules are often overridden, making the system more volatile. Most real-life systems are non-stationary. Alexander stresses the need for carefully adjusting the estimates of the parameters in the replenishment rules for non-stationary systems. Kohn (1978) stresses the need for timely highlighting of inventory miscount errors and eliminating their causes. Covin (1981) suggests having a control group of items which are counted weekly for learning about the sources of inventory miscount errors and for monitoring the effectiveness of stockroom procedures. Morey (1985) stresses the need for a compromise solution through the elimination of the causes of errors, adjustment of cycle count frequencies, and adjustment of reorder points for attaining the desired customer service level. Cycle-counting schemes can be time-based and/or special-eventbased. Besides having time-based cycle counting, Backes (1980) suggests cycle-counting on special events, such as when the inventory- record for an item reaches zero and when the on-hand quantity is found to be insufficient to fill an order. Neeley (1983) considers inventory records for an item as a two-state Markovian Process, the states being: (1) records in error and (2) records not in error. The time-based cycle-counting frequencies are determined to achieve the specified desired levels for the system's stationary probabilities being in an error-free state. Kumar and Arora (1992) give quantitative expressions for the degradation in customer service as a function of the composite inventorymiscount level. They attribute the main cause of inventory miscounts to data-entry errors incurred during various transaction-accounting activities. French (1980): stresses the need to maintain accuracy in the work-in-process inventories; this depends on the accuracy of the data-entry system and also, critically, on the availability of monitoring schemes at appropriate points within the production network. Tayi (1985) suggests sampling-based cycle-counting procedures for estimating the total dollar value of inventory for financial control purposes.
30
7.
Parts Management Models and Applications
CASE STUDY The management of the company studied had been concerned for some time about the realized customer service level being consistently and significantly below that planned. The diagnostic procedures had indicated that one of the main causes for the lower realized customer service level was inventory miscounts (Kumar and Arora 1992). These exist when there is a discrepancy between the actual physical count of an item and its reported quantity as per computer records. The company had about 45,000 SKUs (stock-keeping units), one fourth of which covered about 90 per cent of the total transaction activity. A customer service level of 95 per cent had been the company's objective, implying that on average 95 per cent of the SKUs should be in stock at the time of servicing an order. The company's annual sale for the spare parts was about $65 million and it was maintaining an average inventory of about $18 million. The company was generating monthly demand forecasts covering a 14 months' time horizon, using exponential smoothing techniques. The estimates of the parameters in the forecast model were updated quarterly, based on a running past-three-years' demand history. Current Inventory Procedures for the Case Study The material inflow and outflow activities for the company were grouped in the following three main categories, which are displayed in Figure 2-10: • Regular receipts • Customer returns • Issues for customer orders. Activities in each of the three categories involved the following ten types of transaction subcategories: (1) Regular receipts - no inspection (2) Customer returns (3) Regular receipts - inspection (4) Packaging-kit components issues (5) Assembly-kit components issues (6) Packaging-kit receipts (7) Assembly-kit receipts (8) Customer-order picks (9) Restock orders (10) Drop ship orders.
Introduction to Parts Management
31
Most of the data-entry activities occurred at the time of the receipt of lots from the venders and the issue of lots to the customers. In the current procedures, the system had internal debiting and crediting schemes to account for the flow of material between different stations. The material account for an item at a station was debited when it was received and credited when it was issued from the station. There were no control procedures for tracing and correcting data-entry errors associated with the material-flow activities. These errors continued to accumulate and resulted in growing discrepancies between the computer records and the actual physical inventory counts. Replenishment orders were based on computer records and, these being in error, resulted in either more frequent and excessive stockouts or excessive over-stocking. There was a need for simple internal control procedures that would identify errors for timely correction.
Parts Management Models and Applications
32 RegularreceqJts
Customer
Vfendor
Order entry
Reject
Dock
Order actrvatjon in \fty^rehouse
Dock
Figure 2-10. Different Transaction-flow Patterns during Material Inflow and Outflow in the Parts Warehouse
7.1
Proposed Internal Control Procedures
Materials usually flow in lots which can be split into sublots; sublots can take different routes in the network. The stations within a network are classified into the following two types: external stations (vendors, customers, salvage) and internal stations.
Introduction to Parts Management
33
Internal stations are further divided into the following two subcategories: in-transit stations and stock stations. Material is not intended to be stocked at in-transit stations. Lots or portions of lots may stay at in-transit stations for short intervals but all incoming lots should ultimately leave them. When a credit entry is made at the issuing station, an associated debit entry is automatically made at the receiving station by the computer. Consequently the entries at the two stations are always identical. If one of them is in error, the other is in error by the same amount. A code is needed for tracing the flow of various lots through intransit stations. A four-field code was developed, of which three fields were used for identifying a lot or sub-lot and the fourth for identifying the station. The description of the proposed code denoted by (x, y, z, t) is as follows: X denotes the control number, which is preceded by an appropriate letter (P, C,R or S) identifying the transaction categories of purchase receipts, customer issues, customer returns, and material salvaged respectively. y denotes the sub-lot number of an incoming lot. When the incoming lot is not split, y is assigned a value of zero. z denotes the transaction subcategory type. The ten subcategories of transactions for the case study were listed above. t designates the station number.
7.2
Rules for Internal Inventory Control
Definition: Open Control Number A control number, the lots and sub-lots of which have not yet cleared the in-transit stations, as per inventory records, is called an open control number. Rule 1 A data-entry error is implied when for an open control number total credits exceed total debits at any of the in-transit stations. These errors are presumably pursued and corrected. A data-entry error is not implied when for an open control number total debits exceed total credits at any of the in-transit stations. This is because a portion of the lot pertaining to a control number can temporarily reside at an in-transit station. However, since an in-transit station is not a stock station.
34
Parts Management Models and Applications
ultimately inventory pertaining to each control number should clear such stations within a reasonable upper time-bound (To). Two sets of open control numbers are identified: Si is the set of open control numbers for which L < To, and S2 is the set of open control numbers for which L > To, where L is the age of a control number, given by the difference between the current date and the date of initiation of the control number. Some control numbers may exit set Si with the miscount errors identified and corrected by Rule 1, and some control numbers in set Si will be transferred to set S2, as these get older than TQ. Rule 2 Each open control number in set S2 is checked periodically for each in-transit station individually for compliance with the equality condition of the total debits and the total credits. If the equality condition holds for each in-transit station, this control number is deleted from set S2. Rule 3 This rule is designed for identifying and correcting inventory miscounts at stock stations. If the depletion rate at any time exceeds a prescribed upper-bound value, a special count for that item is triggered. This upper bound for each SKU will be established from the variance of the historical demand rates. The above procedure is illustrated through an example. Example Figure 2-11 shows a simple material-flow network, where S is an external source station; A, B and C are internal in-transit stations; and D, E and F are internal stock stations. Table 2-10 shows actual material flow pertaining to a control number, whereas Table 2-11 shows the associated computer records for the flow. Some errors have been purposely introduced in the records to illustrate the working of the three rules.
Introduction to Parts Management
35
Table 2-10. Actual Flow
s Dr
A
Cr
Dr
10
10
B
Cr
Dr
4
4
C Cr
6
D
Dr
Cr
Dr
6
4
4
Cr
E Dr
Cr
F Dr
Cr
4
Figure 2-11. A Simple Material-flow Network with Different Types of Stations
Table 2-11. Data Entries for the Flow
s Dr
B
A
Cr
Dr
8
8
Cr
Dr
4
4
6
D
C Cr
Dr
Cr
Dr
6
4
4
Cr
E Dr
Cr
F Dr
Cr
4
A comparison of the entries in Tables 2-10 and 2-11 is given in Table 2-12. The control number referred to is an open control number, as all
36
Parts Management Models and Applications
debits and all credits are not equal for each of the in-transit stations A, B, and C. A check is then made for compliance with Rule 1. Table 2-12. A Comparison of the Entries in Tables 2-10 and 2-11
Actual flow pertaining to a control number (Table 2-10) |T A lot of 10 units originates from the external source station S and flows to the in-transit station A. 2. This lot is split into two sublots of 4 and 6. The sublet of 4 units flows from A to B and sublot of 6 units flows from A to C. 3. The sublot of 4 units flows from BtoD. 4. From the sublot of 6 units, 4 units flow from C to E.
Computer records with some induced errors (Table 2-11) 1. Erroneously S is credited for 8 units and A is debited for 8 units (instead of the actuallO units). 2. Station A is correctly credited for 4 unitsand B debited for 4 units to account for the flow of the sublot of 4 units from A to B. 3. Station A is correctly credited for 6 units and C debited for 6 units to account for theflow of sublot of 6 units from A to C. 4. Station B is correctly credited for 4 units and D debited for 4 units. 5. Station C is correctly credited for 4 units and station E debited for 4 units.
Rule 1 identifies an error condition at in-transit station A, as the total credits for the control number exceed total debits. This error is traced immediately and it is presumed that it is corrected. This control number still remains in set Si. At the end of time To, it is transferred to set S2. A check is made for compliance with Rule 2.This rule will not be complied with as long as the 2 units remaining at station C do not clear. Rule 2 is designed for internal control. It will keep a watch that all intransit inventory is ultimately accounted for and does not disappear. Rule 3 will identify and reduce inventory miscounts at stock stations.
7.3
Model for Cycle-counting Frequencies
Errors escaping the internal control system and resulting in inventory miscounts will be corrected at cycle counting. Inventory records for an SKU are reset to an error-free state immediately following its cycle counting. In this section a model is developed for determining optimal values for cycle-counting frequencies.
Introduction to Parts Management
37
Notations T denotes inter-cycle-count time. Ti denotes the average time during a cycle over which an item's inventory records are in error. During Ti one or more errors can occur. Ci denotes the average inventory-counting cost per count per item. C2 denotes the average penalty cost per time incurred during the error phase. This penalty cost may depend on the magnitude of the error. In this article, for simplicity, the penalty cost is assumed to be independent of the magnitude of the error. D denotes demand rate per unit time. Q denotes the economic lot size. a denotes the mean error-occurrence rate for the item, a is assumed to be proportional to D/Q, which measures the activity level for the SKU. 7.3.1
Model
It seems realistic to assume that inter-arrival time between two consecutive data-entry errors for an SKU follows an exponential distribution. The value of Ti is given by T
T^ = ^{T-t)e-''ae-''dt,
(1)
On simplification of (1), we obtain r^ = r / 2 +1 /(4a^'"') - 1 l{Aa)
(2)
The total unit-time cost C(T) is given as C(r) = Q / r + C 2 ( i ) / 0 ( l / r ) ( r / 2 + l/(4ae'"O-l/(4a)). The optimal value of T, denoted by T*, is obtained by setting dC(T)/dT = 0, and, solving for T*, we obtain
(3)
38
Parts Management Models and Applications
[2a(C,/C,)
+
i2a(C,/C,)(Q/D)-(2a(C,/C,)(Q/D)yy"]
x[(a-4a\C,/C,)iD/Q)]-\ (4) If data-entry error rate a is assumed to be proportional to D/Q, then a is given as a = Ka,(D/Q)
(5)
where K is a proportionality constant and a^ is a system error parameter. Substituting this expression for a in (4), we obtain T*=
[2Ka,(C,/C,)
+
(2Ka,(C,/C,)-(2Ka,(C,/C,)yy^']
x[(Ka,-4K'a,\C,/C,))(D/Q)r (6) In order to simplify the management of the cycle-counting function, similar items are grouped on the basis of the parameter values of C2/C1 and D/Q. Table 2-13 shows a company-wide item classification. The two entries in each cell of the table represent: (1) the number of SKUs in each category; (2) the optimal inter-cycle-count duration T* for the category, as obtained on solving equation (6).
Introduction to Parts Management
39
Table 2-13. A Company-wide Classification of Items on the Basis of the Values of the Parameters C2/C1 and D/Q - The Estimated Values of ^ Q =0.1 and C, = $2 are Used in Computing the Values of T*
r\.^^^ D/Q
0.05
Ca/cT"^^^^-^^ [5
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.50
0.60
300
275
250
225
190
175
160
140
100
50
28
23
20
18
17
16
15
14
210
200
160
140
110
85
75
45
53
34
10
250
220
27
17
14
12
10
9
9
8
8
7
15
225
200
160
180
140
120
90
65
60
40
18
12
10
8
7
6
6
6
5
5
20
175
180
150
160
120
100
80
60
50
35
14
9
7
6
5
5
5
4
4
4
25
150
150
145
140
100
90
70
50
45
30
11
7
6
5
45
4
4
3
3
3
115
120
140
130
90
70
60
45
40
25
9
6
5
4
4
3
3
3
3
3
100
100
120
110
70
60
50
40
30
20
8
5
4
4
3
3
3
2
2
2
90
80
70
65
55
50
45
35
20
15
7
5
4
3
3
3
3
2
2
2
75
70
60
55
50
45
35
25
15
10
6
4
3
3
2
2
2
2
2
2
65
60
50
45
40
30
20
12
10
5
5
3
3
2
2
2
2
2
2
30 35 40 45 50
_2
Estimated expected total system-wide cycle-counting and penalty cost per unit time, W, is given by (7) 7=1
Where j denotes a category in the item classification matrix given in Table 2-13 and J is the total number of classes. An important system parameter is the value of K in equation (5). Achieving a reduction in the value of K through improved internal control procedures and improved
Parts Management Models and Applications
40
cycle-counting frequencies is an important objective of operational management. Table 2-14 shows the estimated values of W for various values of K. These values are plotted in Figure 2-12. It was estimated that at the end of one year after the internal control and cycle-counting procedures were implemented, the value of K moved down from five to one. This resulted in an estimated annual saving of $1.02 million. Table 2-14. Total System Cost W per Unit Time for Various Values of K K
1
2
3
4
5
6
7
8
9
10
W($)
3,519
4,653
5,382
5,899
6,279
6,562
6,771
6,922
7,024
7,087
6
7
9
10
8.00 7.00 6.00 - 5.00 Z 4.00
^ 3.00 2.00 I
1.00 h 0.00 ^ 1 2
3
4
5 K
Figure 2-12. Plot of Total System Cost W per Unit Time against K
Introduction to Parts Management
8.
41
CONCLUSION - INVENTORY ACCOUNTING PROCEDURES
Inventory management systems are becoming more and more computer-based. Internal audit procedures which are capable of identifying data-input errors on a timely basis are becoming increasingly important. The proposed audit procedures would likely eliminate most of the data-entry errors related to inventory transactions during receipt and issue of the parts. The implementation of the internal audit procedure required a slight enhancement of the company's prevailing inventory transaction code. A computer-based program would check for the compliance of the proposed internal audit rules on an ongoing basis. It will generate a list of open control numbers. These control numbers will be checked for non-compliance with Rule 1. A timely tracing of these non-compliances would eliminate most of the errors. If open accounts do not clear out of set Si in a reasonable time period To , these will be transferred to set S2. A periodic list of accounts in set S2 will force more accountability as a result of Rule 2 for the material flow within in-transit stations. The scope for pilferage will decrease significantly. Any data-entry errors for stock-station transactions will be identified and corrected as a result of Rule 3. Cycle-countingfrequenciesbased on the minimization of the sum of cycle-counting cost and penalty cost would give better stratified cycle-counting procedures. Cycle counting would periodically reset miscount errors to zero and adjust inventory records to tally with the actual physical counts. Once the proposed internal audit procedures and revised cycle-countingfrequenciesare implemented, the value of error rate K will go down over time. A lower value of K would further lower cycle-counting frequencies.
9.
IMPLEMENTATION OF EDI COMMUNICATION NETWORK WITH SUPPLIERS^
This section describes how EDI networks lower both ordering costs and lead times and consequently result in smaller lot sizes and smaller safety stocks.
42
9.1
Parts Management Models and Applications
EDI and JIT
Electronic Data Interchange (EDI) has been the new technological mode through which buyers and suppliers exchange relevant business information. Replenishing inventory through EDI networks help companies achieve substantial reductions in both ordering costs and lead times. It is a significant valid step in achieving Just-m-Time (JIT) inventory control. "JIT" is often perceived as switching to smaller lot sizes. Any change in lot sizes from their original optimal values that are not achieved through genuine parameter changes would impose penalties instead of achieving any economies The reduction in lot sizes should be achieved by changing necessary parameters. Lowering ordering cost and or lead time will reduce optimal lot sizes and safety stocks respectively. Reducing lot sizes without genuine parameter changes will do more damage than good. The simple model given below compares the effects of reducing lot sizes with and without parameter changes. We initially consider a singleitem inventory system with random demand and random lead time. The following notations are used in the model: i = Inventory holding rate/dollar/ year V = Unit cost of the item Q^= Fixed order quantity or replenishment lot size D^a = Average annual demand rate of the item D^Average daily demand rate of the item A= Fixed ordering cost per order Var(D)=Variance of daily demand rate Lj=Procurement lead time of the item L = Average lead time of the item Var(L)=Variance of the lead time of the item K= Safety stock factor
The total expected annual cost, T, is divided into two components, Ti and T2. The component Ti, represents the average annual cycle inventory holding and ordering cost. The component T2 represents the sum of the average annual safety stock holding cost (T2') and the annual stockout cost
Introduction to Parts Management
43
The average annual cycle holding and ordering cost, Ti (Q), is given by Ti(Q) = iv(Q/2) + ( 5 . / Q ) A Minimization of this cost yields optimal lot size as
Q*= ^llADahvi The optimal value of Ti(Q) is given by Ti(Q*) = (iv/2) -jlADaliv
+ (Da/^2ADa/iv)
A
I.e.,
T,{Q^)=^2ADaliv
(1)
Suppose that we change the lot size from Q* to Q=KQ*, where K< 1. Then Ti/(Q) is given by Ti (KQ*) = (ivK/2) ^llADaliv
-^(Da /{K^jlADa
I iv)) A
I.e.
Ti (KQ*)= ((K^+1)/2K) ^2ADa/iv since ( ( K V I ) / 2 K ) > 1 for all K.
> ^lADaiv
,
(2)
44
Parts Management Models and Applications Hence, any reduction in Q* imposes a penalty.
T,(KQn
^t(cr
Ti'(Q*')
KQ*
Q*
Q*
Figure 2-13. Graph of T, (KQ*) for Values of K <1
The graph of Ti (KQ*) plotted for values of K< 1 is shown in Figure 2-13. Curve I displays the cost penalty imposed when lot size is reduced from its optimal value Q* without parameter changes. On the other hand, if ordering cost is reduced from A to mA, where m< 1 (denote mA=A'), the new cost curve Ti'(Q), displayed as curve II, will be lower than curve I. Its optimal value is given by Ti'(Q*')=
^l2A'Daiv
(3)
and
Q*'=
^|2ADaliv
Comparing annual costs given by (1) and (3), we have ^jlADaiv
<^J2ADaiv , since A'
(4)
Introduction to Parts Management
45
We have achieved a genuine reduction in optimal lot size, accompanied with a cost saving instead of a penalty. A significant savings in the cost component, T2, will also occur through lead time reductions. A major portion of this savings is in T2', the holding cost of safety stock. Savings in the stockout cost component, T", is less significant with higher values of safety stock factor K. The average value of T2' is given by T2'= ivK ^j{Df var(Z) + L ydir(D) Ordering through an EDI network will lower the values of L and var (L).
9.2
Case Study
Thermo King Corporation, a transport refrigeration equipment manufacturer which is currently proceeding with EDI implementation in its spare parts distribution business, expects to reduce the order preparation time (component of Z ) from five days to one day and the average mailing time from three days to one day. EDI implementation is also expected to improve operation at the supplier end, leading to more expeditious processing and shipment of orders. This will lead to further reductions in L and in var(L). Let j denote index for item. Ordering cost is assumed to be the same for all items. Now, Ti (prior to EDI implementation) =
Ti (after EDI implementation) = J
We have A'= mA, where m is the reduction factor in ordering cost.
Parts Management Models and Applications
46
9.2.1 Expected Annual Savings The expected annual savings in Ti component =
Y^^lADajVji
(1-V^)
The company has 20,000 active spare parts items and an annual sales of $65 million. The value of the relevant parameters needed in computing Ti and r2 are indicated in Table 2-15.
Table 2-15. Value of Relevant Parameters Needed to Compute TI and T2'
Value of Parameters: Prior to EDI A= $50/order L = 20days Var(L)=16days K=3 i = .3
Value of Parameters: Post-EDI Implementation A'= mA = $10/order (Hence m = .2) L = 12 days Var (L) = 4days K=3 i = .3
Using the historical data for Daj, Vj for the previous year, values of expected annual savings in Tiand T2' components are approximately $3.4 million and $380,000, respectively. Furthermore, it should be noted that cash amounting to $4.9 million is expected to be released from inventories over time ($3.6 million due to reduction in cycle inventory and $1.3 million due to reduction in safety stocks inventory).
Introduction to Parts Management
10.
47
CONCLUSION
For many manufacturers, the cost savings in one year in cycle and safety stock inventories alone will justify the implementation of EDI as it not only facilitates reduction of lead-time but also lead-time variability.
Adapted from the paper by authors: Kumar, Sameer and Arora, Sant, (1992), "Effects of Inventory Miscount and Non-inclusion of Lead Time Variability on Inventory System Performance", HE Transactions, Vol. 24, No. 2, pp. 96-103. Adapted from the paper by authors: Kumar, Sameer and Arora, Sant, (1992), "Development of Internal Audit and Cycle-counting Procedures for Reducing Inventory Miscounts", International Journal of Operations & Production Management, Vol. 12, No. 3, pp. 61-70. Adapted from the paper by authors: Kumar, Sameer and Arora, Sant, (1990), "EDI at Thermo King: A Significant Step Towards Achieving JIT Savings", EDI Forum, Vol. 3, pp. 62-63.
This page intentionally blank
Chapter 3 OPTIMAL DIVISION OF ITEMS WITHIN A TWO-LEVEL DISTRIBUTION SYSTEM^
1.
INTRODUCTION
One of the important problems associated with the design of a parts distribution system is the number of levels and the distribution of parts within these levels. This article develops mathematical models for a twolevel distribution system with three approaches for the division of the total item set S into subset Si, items served directly to the end-user by the company and subset S2 served through dealerships. A system approach incorporates the effect of service parameters on the captured market demand, improves total profitability and provides a larger coverage of items through dealers as compared to the other two dealer and company itembased approaches.
2.
DISTRIBUTION SYSTEMS - BACKGROUND
The importance of improved customer service in gaining increased market share (Kyj 1987) and increased profitability (Christofides and Watson-Gandy 1973) is well recognized. However, customer service is rarely included explicitly in decision models. There are several attributes of 49
50
Parts Management Models and Applications
customer service and these differ in their importance from one system to another (Wagner 1977). An important attribute in spare parts business is promptness in delivery. In most of the competitive spare parts marketing models, the elasticity effect of promptness in delivery on the captured market share has not been explicitly included. Over time a customer develops an image, positive or negative, about his suppliers based upon their general price levels and their promptness in deliveries. With a prolonged negative image any supplier would lose even captive customers. This is particularly true for industrial customers. Demand for the spare parts arises basically in two modes: • Parts demand arising from preventive maintenance tasks; and • Parts needed in unscheduled repairs. Demand of parts for preventive maintenance is more predictable and users can plan for a timely acquisition for this portion of the demand. Demand for parts in unscheduled repairs is more unpredictable and action for their acquisition usually follows after failures have occurred. Prompt availability of these parts is essential. Any delay in their delivery would prolong the equipment's non-operational phase. An important characteristic of the two types of spare parts demand is that they are essentially independent of each other. Usually, prompt deliveries can be achieved if distribution is done through a dealer network. However, it may not be possible to justify the distribution of expensive and low demand items through a dealer network. This article considers how delivery time is affected by the division of parts into two categories: (1) items distributed to the end-users directly by the company, and (2) items distributed through a dealer network. Most real life distribution systems for spare parts are multi-level instead of single level. In a single level system, distribution to end-users is done directly from the manufacturer's facilities. In a two-level system, distribution occurs in two stages - from the company to dealers and then from dealers to end-users. Two-level parts distribution systems are more common than single level systems. A company using a two-level system may distribute directly more expensive and low demand items to end-users. Businesses with worldwide distribution may need more than two levels for some fraction of their demand. Rules for the replenishment of inventories at various levels have been extensively studied in the literature. Muckstadt and Roundy (1987) studied the co-ordination of purchase and shipment rules for multiple-item, multi-retailer systems for a single warehouse supply source. They considered a two-level push system with constant demand rates for each item and with no back orders allowed.
Optimal Division of Items
51
Shipments were dispatched to retailers at regular intervals and these intervals were decision variables determined by minimizing the expected sum of the unit time replenishment cost and inventory holding cost (for both company and retailers). The company's procurements from suppliers were synchronized with deliveries to retailers, which was defined by them as "nesting". Each item's inventory was replenished up to a predetermined level, which was based on the item's demand characteristics and other relevant costs. For computational simplicity, the authors have considered a relaxed problem whose optimal solution cost was within 6 per cent of optimal cost of the actual problem. Jackson (1988) also considered a similar two-level push system, however, allowing back order at the retailers' level. The demand at each retailer location was assumed to be independent and stationary. Each item's inventory was replenished up to a predetermined level, which was obtained by minimizing the expected total holding and shortage costs over an ordering cycle. A sizeable reduction in back orders was achieved by following push system-based replenishment policy. Lee (1987) considered a multi-echelon pull system with Poisson demand which is more relevant for repairable items. He allowed lateral transshipments between bases (retailers) to provide improved service support. A continuous review of inventories was carried out and a (S -1,S) replenishment policy was followed for every item at each base, where S-1 represented re-order point, and S represented order-up-to-level. Lee's model is more applicable for expensive low demand items, with high delay cost. The optimization was carried out by minimizing the sum of unit time expected inventory holding cost, back order cost and emergency lateral transshipment cost subject to specified service levels. Fincke and Vaessen (1988) developed a simulation model of a two-level distribution system with stationary and random demand and an ordering policy based on periodic review. In this model they developed and analyzed strategies for reducing overall distribution costs and the capital tied up in the distribution chain. The model showed that it was more economical to use a "push" system as opposed to a "pull" system when distributing finished goods to subsidiary companies in different countries. They emphasized that substantial economies could be achieved through having improved production planning, shorter planning periods, more accurate production delivery dates, and smaller batch sizes.
52
3.
Parts Management Models and Applications
A MIXED TWO-LEVEL PARTS DISTRIBUTION SYSTEM
This chapter considers a mixed two-level distribution system as shown in Figure 3-1, where expensive and low demand items are distributed directly from the company to the end-users and others are distributed through a dealer network. The notations used here are given below: Notations a Average ordering cost per order for the company for procurements from their suppliers a' Average ordering cost per order for a dealer for procurements from the company a" Average special delivery cost per order incurred by a dealer for a special delivery' from the company A Average delivery cost per order from the company to an end-user A' Average delivery cost per order from the company to a dealer A" Average delivery cost per order from a dealer to an end-user r Average carrying cost per dollar inventory per unit time (ij) A class of items is characterized by two parameters, demand and cost. The set of all items is divided in a number of discrete classes. Class (i,j) denotes the set of items with demand Dj and cost Cj Cj Unit cost for any item in classes (i,j) with the same j bj Delay cost per item per unit time for any item in the classes (i,j) with the same j . Zj Selling price of any item in classes (i,j) with the same j K Safety stock factor M Total number of end-users m Total number of company's dealers qtj Average order size per order from an end-user to the company placed for an item in class (i,j) qijd Average order size per order placed from an end-user to dealer d for an item in class (i,j) D^ Total potential market demand rate for any item in classes (i,j) with the same i D^ Captured demand rate for any item in classes (i,j) with the same i Did Potential market demand rate for any item in classes (i,j) with same i in the domain of dealer d D^^ Captured demand rate for any item in classes (i,j) with same i in the domain of dealer d
Optimal Division of Items L
53
Average lead time for replenishment of order for an item from supplier to the company L' Average lead time for replenishment of orders for an item from company to dealer (T,^ Standard deviation of potential market demand over average procurement lead time from supplier to the company for an item in classes (ij) with the same i CJ,^.^ Standard deviation of potential market demand over average procurement lead time from company to dealer for any item in classes (iJ) with the same i Qij Order quantity of any item in class (iJ) for the company from their supplier Q'ijd Order quantity of any item in class (iJ) for dealer d to the company Jj Average delay per order for an end user when served directly by the company (assumed same for all items and for all end-users) dj Average delay per order for an end user when served by a dealer (assumed same for all items and all dealers and end-users) /li Sum of total potential market demand rate for items served to the end-users directly by the company ^2 Sum of total potential market demand rate for items served to the end-users through the dealers F Parameter signifying market share in the captured demand sensitivity model E Parameter signifying the elasticity factor in the captured demand sensitivity model a Represents composite service level index in the captured demand sensitivity model Pi(iJ) Profit from an item in the class (iJ) based on the total, potential market demand, when it is directly supplied from the company to end-users P2(iJ) Profit from an item in the class (iJ) based on the total, potential market demand, when it is supplied to the end-users through the dealers P Total expected profit for the company from the service parts operation £,£^,£2The three parameters defining the two straight lines used in the cut for the set S into Si and S2 in the systembased approach Uij Number of different items in class (i,j)
Parts Management Models and Applications
54
Pi'(iJ) Profit from an item in class (i.j) based on the captured demand rate D^, when the item is directly supplied from the company to the end-users P2'(ij) Profit from an item in class (i,j) based on the captured demand rate D^, when the item is served to the end-users through the dealers. The focus of this chapter is to determine the appropriate division of the set S (of all parts) into two subsets Si and S2, where items in Si, are distributed directly from the company to end-users, and items in S2 are distributed through a network of dealers. The performance measure used is the expected total profit to the company. The primary design variable in the proposed model is the division of set S into Si and S2.
1
Suppliers
..^--—-^-.
^ f
'
--^^--^^--^-.^^^
"""~^—-"*'
Company
;~'^-^—^_ i
1[
End-users ^
„
.._,._._._._._.._...
^.---^X^
^
i
__^^—-
I
Dealers
.^^^_
'
.
1
Figure 3-1. A Mixed Two-level Distribution System with Direct Sales for Some Parts
The spare parts business is very competitive. The demand captured by the company is quite sensitive to pricing and overall service level. For this article, the two parameters of service level considered are: order fill rate and delivery times. Distribution through a dealer network will ensure prompt delivery. However, all items may not justify distribution through local dealers. The term "coverage" is commonly used to denote the fraction of the items distributed through local dealers.
Optimal Division of Items
55
Table 3-1 shows the four important cost components incurred by the company, dealers and end-users for a one-level, and pure and mixed two-level systems. Table 3-1. Various Cost Components Included in One-level, and Pure and Mixed Two-level Parts Distribution Systems
Cost incurred by Cost Components One-level distribution Inventory-holding cost Delivery cost Ordering cost Service delay cost Two-level distribution (for both pure and mixed systems Inventory-holding cost Delivery (special) cost Ordering cost Service delay cost
4.
Company
Dealers
End-users
X X X X
X
X
X
X
X
X
X
X
X
X
AN ITEM ~ BASED VERSUS A SYSTEM-BASED APPROACH FOR THE DIVISION OF SET S INTO S1ANDS2
In the decision relating to the division of set S, there are essentially two approaches. (1) An item-based approach: from the dealer's point of view or from the company point of view; (2) A system-based approach. A number of simplifying assumptions have been made in order to avoid undue complexity. The article emphasizes that using a system's approach is more desirable than any of the item-based approaches in the decision relating to the division of set S. The following observations are made prior to the development of the model: 1. The two important parameters influencing the division of set S are the levels of demands and costs for various items. The N items within the system are classified into (pxq) similar classes, on the basis of their
j
56
2.
3.
4. 5. 6.
7.
Parts Management Models and Applications demand level and cost. All items within a single similar class will be treated alike, that is, these will be all together in set Si or S2. A two-level distribution system is considered. Systems with more than two levels will require an extension of the model, as certain similar classes may be distributed only up to an intermediate level in the multilevel distribution network. These intermediate levels for various items and for various locations will be decision variables to be determined by the extended model. The replenishments from the company to dealers follow a pull system giving the dealers the control on replenishments. It is assumed that the company has an electronic data interchange (EDI) network with the dealers and the company is aware of the stock depletions at the dealer's level. The EDI network prevents the demand variability at the company level from getting inflated owing to communication delays even when dealers follow a pull system. The number of dealerships (m) and their respective territories are assumed to be given. Both the dealers and the company use (s,S) policy for all items, where s represents re-order point, and S represents order-up-to-level. It is assumed that ordering costs per order, procurement lead times, delivery costs per delivery are the same for all classes. This assumption of equality of these parameters holds reasonably well in most real-life systems. However, the assumption can be easily relaxed and these values can be different without adding any undue complexity to the model. The company keeps a minimum safety stock of one for each item. For items in set S2, the dealers maintain a minimum stock level of one for every item. For an item with a stock level of one, an order is triggered when its stock level hits zero.
4.1
Item-based Approach
In the item-based approach, the decision about each item is made independently of other items. A rule commonly used by dealers is not to stock an item if its average annual inventory holding cost exceeds its annual special delivery cost. In an item-based approach from the company's point of view, several alternative criteria are possible. This article compares profits Pi and P2 based on the total market demand for each item in class (ij) when the item is distributed directly and through the dealer network respectively. An item is included in set Si if Pi > P2 , otherwise it is included in set S2
Optimal Division of Items
57
When Pi = P2 set S2 has been favored in this article in view of the emphasis on achieving improved availability through local dealers. Expressions for the profits Pi(ij) and P2(ij)are: Pi(ij) "^ (Sale price per item - cost per item) x total market demand (Holding cost of cycle inventory and safety stock at the company) (Delivery cost to end-user) P2(ij) ^ (Sale price per item -cost per item) x total market demand (Holding cost of cycle inventory and safety stock at the company) (Delivery cost to dealers) -(Holding cost of cycle inventory and safety stock at dealers) - (Delivery cost for delivery from dealers to endusers). That is,
Pmr{(Z^-C^)D,}-{rC^m^/2) P2(i,)= {(Z^ -q)D,}-{rq[(Q,/2) m
m
+ Kcr^,]}-{ADJq^j} +
(D
Kc7j}-{Y,A'Djg,j,}m
{X^'Z)„/g,,}-{J[rC/(g,,/2) + /:o-„,,)]-[£^"D„/^,J} (2) d=\
d=\
d=\
Each term in the braces corresponds to the terms listed in the above expressions for profits. The terms Qy and Q'yd are order quantities for dealers to company and for end-user to dealers respectively. These are based on the classical EOQ formula and their values are given by: Qy = paD^
/ ( C / ) and Q\,,= ^(2aD'^, ) / ( C / )
Attention may be drawn to the two extreme cases, when one of the set Si or S2 is empty. When S2 is empty, the two-level system reduces to a single-level system. When Si is empty, all parts are distributed through dealers' network and it becomes a pure two-level system. The next section develops a mathematical model for the division of S on a system-based approach. The model considers the effect of the availability parameter on the captured demand. A system-wide profitability for this approach is compared with profitability for the other two item-based approaches. Gardner (1987) advocates an aggregate approach to modeling for systems requiring a concern for total performance.
58
4.2
Parts Management Models and Applications
System-based Approach
A mathematical model is discussed in the next section for the system-based approach. It has the following two basic parts: 1. A market share model, which expresses captured demand as a function of the composite availability parameter. 2. A system-based model for the division of set S which optimizes a company's total profit.
5.
MODELS FOR CAPTURED DEMAND AND PROFITABILITY This section develops mathematical models for (1) Captured demand elasticity as a function of promptness in delivery (2) Distribution planning within a two-level system.
5.1
Captured Demand Elasticity Model
There are several studies available in the literature on the captured market share. Notable among these is a study by Kotler (1971). Kotler described several models for estimating and optimizing market share. The role of service parameters such as prompt deliveries, avoidance of lost sales were considered in the models for determining the most profitable ways to reach the markets. Kotler's emphasis on the inclusion of service parameters in distribution planning models was an important point. Kotler also considered different pricing alternatives, one of which was a competition oriented pricing. Such pricing policy implied that a company should keep its prices at the industry-wide average level. Roller's suggestion of considering prices being competition based presented a rationale for not explicitly including prices in the distribution planning models, and thus avoiding these models from becoming unduly complex. In this model an important service parameter considered is promptness in delivery of parts to end-users and this is attainable through a higher level of coverage of items by dealers. The inclusion of coverage and its effects on the captured demand requires the development of "Captured Demand Elasticity Model".
Optimal Division of Items
59
It may be recalled that here N items are divided into (pxq) similar classes on the basis of the demand and the cost of the items. These classes are arranged in a matrix format as shown in Table 2. In this matrix scheme, across a row the demand level Di stays fixed for varying values of CJ;. Similarly across a column price level Cj stays fixed for varying values of Dj. Equation (3) links the captured demand rate D'i and the total market demand rate Di for items in class (i,j): D] = FE^'D. (3) where F represents market share parameter, (assumed same for all items in class (i,j)); E represents market elasticity factor for the captured demand (assumed same for all items); and a is a composite service level index defined as
a = (Z,d, ^A,d,)/( X(^,AK)
(4)
where
^2 = E^(/A.
S = S^ ^82,5^
'^ 5*2 = Empty set.
The two parameters E and F, assumed as given, are in turn functions of several factors such as price, number of other competitors, advertising, etc. The values of Aj and /ij and consequently of a depend upon the cut of S into Si and S2. The cut in the proposed model is defined by two parallel straight lines AE and CD as shown in Figure 3-2 involving three parameters £ ,£^,£2^^ opposed to the cut by line AB in the company item-based approach. Lines AE and CD are intended to expand the set S2 when systembased approach is followed. The rationale for choosing straight lines for expanding the set through two parallel straight lines is equivalent to the company providing a subsidy to dealers, comprising constant components,
60
Parts Management Models and Applications
^ J, or 12 depending upon P2 > 0 or P2 < 0, and another component linearly varying with P2 at a marginal rate I
/ /
^
/
^ ^
B
E
/•' c
1 f
^
/
PAfl A Figure 3-2. Explanation of the Division of Various Cells in the Matrix of Table 3 on Company-based Item Approach and Systems Approach
5.2
Distribution Planning Model Using System-based Approach
The two item-based approaches from the dealer and the company points of view were discussed earlier. This section develops a model for the system-based approach. In the company-item-based approach, the values of the profits Pi and P2 for the points on the line AB making an angle of 45° with the x-axis are equal (Figure 3-2). If for an item in class (ij), Pi < P2, then this class is served through the dealers, otherwise it is served directly by the company. Recall that profits Pi(i,j) and PiCiJ) for an item in class (i,j) are based on the total potential market demand. In order to improve the
Optimal Division of Items
61
coverage of items at dealerships, the set S2 is expanded to include some additional items for which Pi > P2, This expansion of set S2 will be justified if the losses incurred (equal to the sum of the difference of (P1-P2) over these items) can be recovered through a change in the value of a and result in a consequent increase in the captured market share and an increase in profitability.
62
Parts Management Models and Applications
Table 3-2. Classification of Items into Similar Classes on the Basis of their Annual Demand and Unit Cost
c ID 10
40
80
120
180
2041 1415
m 61
9 104 400 5 11 280 128 157 310 520 557 170 557
50 150 355 119 28 185 378 248 170
110 195 260 242 45 175 632 537 160
1032 1002
1544 1354
2055 1704
3345 2955
160
190
140
50
1002
1354
1704
2955
412 125
1060
1619
2372
2986
4516
130
120
125
120
40
-66
1093 1728
2257 2772
3422 3724
4587 4678
7511 7431
450 126 51 350 122 18 400 12 214 150 -213
90
120
110
120
100
30
1975 3595
4183 5585
6397 7677
8612 9631
14155 14881
110
100
70
60
25
2862 5570
6120 8562
12646 14844
20814 22368
20
20
21281
34374
-230 1662
100 500
-390 2592
75 367
80 5586
9385 11657 60 90 10813 16045
4391
9288
14296
30
25
25
1890 8105
11049 20211 16856 25682
20
15
14145 24647
40408 66691 50348 76275
4000
1523 1049
40 ~450
1 340
1400
100 ~8 476 37 9 995 160 7
30 ~400
742 120
800
75 ~25 319 353 60 679 110 70
20 ~600
52
20
50 "T50 173 237 170 368 64 150 885 682 150
10
10
24202
36778
500
"1
1088 2958
104 3
326 1
2244 6037 1340 3433
2
1
4588 12274 2890 9792
0 0 0 0 10 3964 0 0 6056 0 5 10434 0 0 9950 0 40 19704 0 19903 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0
10
4630 3964
0 0 10 15 20 29398 38577 61540 0 34703 43685 66Q55 0 0 4 0 8 119281 185041 0 92981 102223 128144 192552 0 19315
200 ~5
0 0
Optimal Division of Items
63
The expansion of the set S2 in the system-based approach is achieved by two parallel straight lines shown in Figure 3-2. The total profit for the company in the system-based approach is a function of the three parameters i ,^1,^2 ^"^ '^ ^^ given by:
P{U,J,)=
X '^(/•^iO,y)+ E^^.A(u)
(5)
The expressions for P'i(ij) and P'2(ij) are similar to the expressions for Pi(ij) and P2(ij) developed earlier for the item-based approach, excepting that here captured demand is substituted for the total potential market demand. The optimization problem is concerned with finding the values for £ i^ and 12 which maximize P(^,^j,^2)- The total profit P for the case study has been optimized using Hookes and Jeeves method (1961). The results are given in Table 3-3.
6.
CASE STUDY COMPARING ITEMS APPROACHES VERSUS SYSTEMS APPROACH
The company has approximately 10.000 active parts with an annual sales of $70 million. Currently a mixed two-level system is used. Total number of dealers are 50. About 25 per cent of the total sales are direct sales to the end-users, and the remaining 75 per cent are through the dealer network. There are about 3.000 end-users.
6.1
The items which dealers stock have to be individually profitable to them
The total set of items is divided into 99(11 x 9) discrete classes on (Demand x Cost) basis as displayed in Table 3-2. In this case study, demand for each item has been assumed to follow Poisson process. The assumption of Poisson distribution has been tested to hold for a sample of 50 items. The probability of a unit in the field requiring a spare part (both for preventive maintenance and unscheduled repairs) follows a Bernoulli distribution with a small probability (p) and the total number of units (n) in the field being large, the total demand for a part follows a Binomial distribution. The theoretical basis for the demand following a Poisson distribution is that Binomial approximates to Poisson as n becomes large and p becomes small.
64
Parts Management Models and Applications
In Table 3-2, the three numbers in each cell are the number of items nij in each class (ij) and the values of profits Pi(ij) and P2(ij)-
6.2
Relationship between Cuts as Shown in Table 3-3 and Figure 3-2
It may be recalled that in the dealers' item-based approach an item is a stock item for a dealer if its average annual holding cost does not exceed the annual special delivery cost. In the company item-based approach, for an item to qualify as a stock item, profit P2 should at least equal Pi. In the system-based approach, set S2, as obtained in the company item-based approach, is allowed to expand, provided this expansion increases profitability for the company resulting from increased market share through improved coverage. Table 3-3 gives the three cuts, two corresponding to the two item-based approaches, and the third on the system's point of view. It may be observed that the dealer's domain has expanded in the system-based approach as compared to the two item-based approaches. Table 3-3 shows various classes explicitly. However, Figure 3-2 does not show the classes explicitly but to every point there is an associated class. Denote
The solution of equation (j) (i,j) = 0 would give the cut for the companyitem-based approach. The relationship between Figure 3-2 and Table 3-3 for the company-item-based approach is as follows. With reference to Table 3-3, the partial derivative
^(Uj)
measures the change in ^(i,j)
as Dj changes, while Q stays fixed. If the value of this partial derivative is shown to be negative, this would imply that going down the column in Table3, the classes will become more favorable for distribution through dealer network. We have,
d
-^(hj) =
5D/^
d dD,, ^r—^(i,j)x-
aA,
5Z),
Optimal Division of Items 5 ^'^W^^^^j^
A' ^
65
"" d (since5]Z),^ = D, therefore —-Z^<,=1) d = \...m
(A-A") ^ijd
ijd
d (l){i,j) < 0 if and only if dD,
A' ^ ijd
^{A
-4")^^^^
^^
^^^
^ijd
For the values of the parameters in the case study, condition (6) holds for all classes. This implies that classes with the same Q are becoming more favorable for distribution through dealers as their demand rates increase. If a class is on or below line AB in Figure 3-2, the same class will be below the cut A'E' in Table 3-3, where cuts AB, A'B' in Figure 3-2 and Table 3-3 are for company's item-based approach.
Parts Management Models and Applications
66 Table 3-3. The Three Cuts
u
10
20
30
40
50
100
75
200
500
10
500
600
400
450
150
25
8
5
2
20
450
i 400
355
260
170
60
9
3
1
m''\ 280
185
175
150
70
7
2
1
; 310
] 170
160
150
90
10
0
0
ni9o
140
40 80
400
120
150
170
^ 160
laO
125
130
""120 i '
340
120
120
110 '"
i'20
500
100
110
100
70
SOO
75
[ 80
1400
30
[Is
^5
20
i 4000
20
15
10
10
50
10
0
0
40
5
0
0
"100 \ 1 30
J^
0
0
•""25 :;
0
0
0
20 ii
0
0
0
0
0
0
0
0
0
125 1 _ 1 2 0 _
m ^
_60_ 8
System's approach
4 ;i 1
1 Dealer item-based ap|)rDa<:h Company item-based appt oacli
Similarly, the partial derivative
^(/, 7) measures the change in
(j) (ij) as Cj changes while Dj stays fixed. If the values of this partial derivative are shown to be positive, this would imply that going across a row in Table 3-3, the classes will become more favorable for distribution to the end-users directly by the company. We have.
dC
-(t>{iJ) = d=\
Y.r[Q\.J2-^Kcj,,.,]>0
(7)
Optimal Division of Items
67
For the values of the parameters in the study, condition (7) holds for all classes. Since the values of partial derivatives of (f) (ij) with respect to Dj and Cj change sign once only, the regions Si and S2 are contiguous. In Table 3-3 items above the cut form set Si, and those below the cut form set S2
7.
CONCLUSION
The current division of the set S in the company follows an itembased approach from the dealers' point of view. The items which dealers decide to stock have to be individually profitable to them. They usually compare holding cost against special delivery cost in making these decisions. The customer's delay cost is usually ignored in their consideration. Table 2-4. Divisions of Set S into Si and S2 along with Captured Market Share and Profitability for the Three Cases.
Company Item-based Approach
Dealers Item-based Approach
Systems Approach
6,482 3,017 79,770,401 72,582,397
6,262 3,237 79,770,401 70,959,780
5,872 3,627 79,770,401 72,926,904
Pi= Profit from company's direct sales
118,542
255,759
117,694
P2= Profit from dealer items
886,078
712,018
891,946
P= Total profit
1,004,620
967,777
1,009,640
Performance Parameters Number of items in sets Si S2
Potential sales Captured sales
Table 3-4 shows results for the case study. The systems approach as compared to the company item-based approach results in a switch of 610 items from set Si to S2, with an additional sale of $344,507, and when compared to dealer item-based approach, a switch of 390 items with an
68
Parts Management Models and Applications
additional sale of $1,967,124 occurs. These comparisons are shown in Table 3-4. The optimal value of the parameters for the two lines used in the system's approach are: i=\, i^ =90, i2= 40. The impact of price has been ignored because various companies operate under the policy of match the competitors' prices. If a company were not operating under this policy then certainly price levels would influence captured demand. A dealer item-based approach is the one that is most commonly prevalent in the service parts distribution sector. Most car dealerships' service centers will fall in this category. For most of the unscheduled nonmaintenance repairs a customer has to make more than one visit for repairs. In a competitive environment, a system-based approach is definitely more desirable. Dealers' item-based approach is myopic. It ignores customers' delay cost. A company item-based approach does include the customers' delay cost. It may be acceptable in a non-competitive market environment. However, in a competitive environment, a system-based approach is definitely a more desirable one to follow.
1
Adapted from the paper by authors: Kumar, Sameer and Arora, Sant, (1990),"Customer Service Effect in Parts Distribution System Design", International Journal of Physical Distribution and Logistics Management, Vol. 20, No. 2, pp. 31-39.
Chapter 4 OPTIMAL ORDERING PROCEDURES FOR A MULTI-ITEM COMMON SUPPLIER SYSTEM
This chapter presents two models for a multi-item common supplier system with constant and random demand rates respectively for various items. In the first model, optimal inventory-management rules are developed allowing for planned stockouts, whose optimal values are determined on the basis of the total cost minimization. The second model is structured on new heuristics ordering rules for managing multi-items. In this model, the inventory position for each item is continuously reviewed and an order is placed when the projected stockout cost for all items exceeds a certain multiple of the average ordering cost. Rules are offered for determining which items to include in the order, and also for determining order-up-to-level for each item. These rules involve two parameters, whose optimal values are estimated by simulation.
1.
CONSTANT DEMAND FOR VARIOUS ITEMS^
In this section, we review theoretical basis for the first model and illustrate the application of the model (including cost evaluation and comments on its performance) using an existing example in the literature and finally provide some concluding remarks on the model.
70
Parts Management Models and Applications
1.1
The Model - Constant Demand Model
Inventory problem for multi-item system with a common vendor is considered. The ordering cost is assumed to have two components: a major common ordering cost S is incurred whenever an order is placed, and a minor ordering cost Sj is incurred if item j is included in the order. The demand for item j is assumed to be at a constant rate Dj. This problem has been considered in the literature with stockout costs being infinity (Goyal 1974). In our formulation, the stockout costs are finite, with the result that there are planned stockouts at the end of the ordering cycle for each item. The values of stockout cost may be difficult to assign directly. An inventory or production manager can make a choice more easily among different alternatives with varying stockout levels when their associated holding-cost components are made available to him. The value for stockout cost bj for item j is assigned once his choice is known (assuming that the manager's choice is the optimal one). In our formulation, the stockout levels are determined as a result of the optimization process instead of being prescribed externally. The following notations are used in the proposed model: Notations * is used as a superscript to denote the optimal value for a variable. n = number of items N = number of purchase orders in a planning period Nj = number of replenishments for the jth item in the planning period kj = relative ordering frequency for the jth item (equal to N/Nj) Uj = fraction of the supply available immediately after replenishment and meeting the back-orders for item j S = common ordering cost per order, which is independent of the number of items included in the order and the size of orders for these items Sj = minor part of the ordering cost incurred whenever item; is included in the order Dj = deterministic demand rate for item j T = common inter-order time hj = holding cost per unit per unit period for item j bj = stockout cost per unit per unit period for item j C = total variable system cost for the planning period; this includes ordering cost, holding cost and stockout cost
Optimal Ordering Procedures
71
The following additional assumptions are made here: (i) The procurement lead time is constant for all items. (ii) Minimization of total cost per unit period is taken as the criterion of optimality. (iii) The parameters of the system have constant values over time. The total variable cost for all items in the planning period will be
Substituting Nj = N/ kj = l/( kj T) in (1), we get C(N,{Nj},{Uj}=C(T,{kj},{Uj})
= ( S + ^ SA)/T+(^ Yj^^hU]^\
E Djbjkj(l-Uj)^))T.
(2)
T, {Uj} are continuous variables, whilst {kj}are non-negative integers. Figure 4-1 shows the relationship between these three sets of variables.
Parts Management Models and Applications
72
\, o
'fN v.
^ ^ \
T~r
1 Time
•la
N * Figure 4-1. Illustration of inventory on-hand graph over time for two items, one with kj = 1, and the other with kj = 3.(
On-hand inventory for item 1)(
On-hand
inventory for item 2)
Substituting A= S + ^
S/kj and
7=1
^
7=1
^
7=1
we have C(T, {kj}, {Uj})=A/T+BT. Optimizing with respect to T, we have
I*=4ATB and C{T*) = A^A/B
(3) (4)
+ BylA/B =
lyfls.
(5)
Optimal Ordering Procedures
73
We now optimize total cost function C with respect to {Uj}. Minimizing Q}, which is equivalent to minimizing C, we get f/;=Zj^/(6^+/j^)forj = l , 2 ,
n.
(6)
Substituting the optimal values for T* and {U^} in the total cost equation (2), we get
C(T*, {Uj}, {kj})=
l\\S^•YS^ /A:,]J[lX^,^^y(^ H^ +^))' +^Z^y^^;(^ '^^ +^))'] "•^ ^ - i J
7=1
J
J
J ^ J
^ J
J '^
^
V ^v=i
L ^
^y=i
Optimal values for {kj} are obtained w hen the following conditions are satisfied: C(T*,{^;}, k\,{k]^+m))
<
c(T^{U]},kl+UK,j^m})
C(T\{u;},KAk],}:^m})
(8)
This is the classical discrete optimization technique, which has also been used by Goyal (1974). The following double inequality condition is obtained on solving the inequalities given by (8): kl (kl - 1 ) < B^^ / ( ( ^ , + S)R'„ ) < A:: (A:: +1) for m = 1, 2, 3 , . . . , n, (9)
74
Parts Management Models and Applications where m-\
n
Kr =i:hjDjkjbj
lib, +/.,)+ Y.KPjkib.> Hbj + h.),
7=1
J=m + \
m-]
n
^•nr -ILS.K. j-\
2.
+ Y^Sj Ik^ and R^= (h^D^ /SJ(b„ l{b^ + hj). j=m+]
EXAMPLE
We consider Goyal's example with 15 items supplied by a common vendor. The demand and cost parameters other than the stockout cost in our example are the same as in his example. Here we allow planned stockouts, as stockout costs are finite. We determine optimal policies with no stockouts as considered by Goyal, and also with finite levels of stockouts. Optimal values for T and {Uj} are chosen using equations (4) and (6). Compliance of condition (8) for selecting {kj} is iteratively achieved. A second subscript r is used to denote the iteration number r for kj, Aj and Bj. Initially we pick kjo = 1 for every j . Based on {kjr_i} values, values for Bjr/((Ajr + S)Rj') are computed for every j , and corresponding new values of {kjr} satisfying constraint (8) are obtained. The iterative process continues until the new set {kjr+i} is the same as {kjr} for all j . Table 4-1 gives lower bounds and upper bounds for Bm/ ((S + AnORm') for different values of km. Table 4-1. Bounds for Bn,/((S+A J R^Q km-4 K=2 k^—3 kn.-l Lower 0 2 12 6 bound Upper bound
2
6
12
20
kn.=5
km=6
k„.=7
k^-8
20
30
42
56
30
42
56
72
The total cost per year using Goyal's method, with no stockouts allowed, is 11,450. In order to use the algorithm given in this chapter, Table 4-2 has been constructed, in which the 15 items are arranged in ascending
Optimal Ordering Procedures
75
order of Rj' value for the items. The procedure for determining {k^ } is the same. These computations are shown in Table 4-3.
2.1
Comments On the Example
When stockout costs are finite, the system allows for planned stockouts. When stockout costs are infinite, the system will not allow stockouts. The total system cost with planned stockouts will be cheaper ($9698.71), as shown in the example.
Table 4-2. Computations for Rj- for S = $43.50
J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Dj 1500 2000 2500 4000 10000 4250 10000 12500 20000 15000 6000 50000 8000 35000 10000
hj 2 3 3 1.25
1 2 1.45
1.6 2 2 5 1 8 2 10
bj 3 4 4 2 2 3 2 2 2 3 6 2 10 3 12
Sj 9 6 7 5 10 5 8 4.5 7 5 6 8 8 8 10
Rj.=(hjDj/Sj)(bj/bj+hj))
200 571.43 612.24 615.38 666.67 1020 1050.72 2469.14 2857.14 3600 4090.91 4166.67 4444.44 5250 5454.55
76
Parts Management Models and Applications Table 4-3. Computations for determining the combination {k j )
First set of computations : when kjo-1, forj = 1,2,3, ..., 15
and
S + Aj,=S + f^Sj/kj,+
J
f^Sj/kj,
r~
Bj,/((S+AjORj')) 270,054.59/(132 x 200)= 10.23
kji
kj2
kj3
3
4
4
2
272,026.02/(129 x 571.43) = 3.69
2
2
2
3
274,597.45/(125 x 612.24) = 3.59
2
2
2
4
280,091.95/(123.5 x 615.38) = 3.69
2
2
2
5
279,579.12/(116 x 666.67) = 3.62
2
2
2
6
287, 812.46/(116 x 1020) = 2.43
2
2
2
7
289,606.66/(110.5 x 1050.720 = 2.49
2
2
2
8
295,307.15/(110x2469.14)= 1.09
1
1
1
9
No need to compute Bji/((S+Aji)Rj')) for these items
-15 Total Total Total Total
cost per year based cost per year based cost per year based cost per year based
on on on on
{kjo} = {kji} = {kj2} = {kj3}}=
8755.74 8699.73 8698.71 8698.71
Optimal Ordering Procedures
3.
77
CONCLUSIONS - CONSTANT DEMANDS
Such problems with a common vendor are very commonly encountered by small food stores, where a number of items are coming from the same source. The assumption for constant demand rates may not be very realistic. Introducing randomness of demand increases the complexity of the system. In real life, random demands are more frequently encountered. As an approximate solution for the random demand case, the values of the optimal inter-order time and order frequencies determined from the constant demand-rate model can be used, where the mean demand rates are substituted for the constant demand rates. The effects of randomness of demand are absorbed by adjusting safety-stock levels, which are reflected in the values of the re-order points.
4.
RANDOM DEMAND FOR VARIOUS ITEMS^
In this section, we review theoretical basis for the second model. Such systems are encountered in many real life situations such as, independent convenience stores, mom and pop grocery stores, ethnic grocery stores, neighborhood hardware stores, small independent retailers and family pharmacies. Many of these systems are grossly mismanaged from an inventory point of view. Ordering rules developed can become the backbone of inventory and order management software required to support such small business operations.
4.1
Background
For many small businesses such as, corner convenience stores, independent grocery stores, neighborhood hardware stores, or family pharmacies; inventory is simply goods they keep on shelves to generate sales. Despite the investment required to maintain appropriate levels of inventory, they invest little effort into monitoring it. Perhaps, the high cost of implementing technology solutions has delayed a more rapid overhaul of inventory management systems in such operations (Broome 1999; Nevill, Rush and Sadd 1998). Increased competition from super-centers and larger grocery chains is leading smaller business operations to continue efforts in coordinating
78
Parts Management Models and Applications
fulfillment of customer demands and resultant replenishment schedules. This emphasis on coordination builds upon quick response mandates, currently underway in the consumer marketplace for achieving inventory effectiveness, which is critical to the success of an organization in any business sector (Anonymous - Quick Response .. 1997). The following sections propose development of the theoretical basis for an inventory and order management software to support small independently run neighborhood businesses such as, independent convenience stores, mom and pop grocery stores, ethnic grocery stores, neighborhood hardware stores, small independent retailers, family pharmacies, etc. This software would consist of three modules. Module 1 is used to create and update inventory database real-time and also facilitate cycle counting of inventory, as and when necessary. Module 2 is used to estimate two parameters used in rules for - when to order, determining which items to include in the order, and determining order-up-to-level for each item. Module 3 is used to generate orders based on ordering rules. The chapter describes detailed theory and logic to develop these modules, particularly modules 2 and 3, illustrated in the example and details of the model outlined below.
4.2
Comparative Analysis of Multi-Item Common Vendor Inventory Models
The scope of this chapter, as stated earlier, is to develop new heuristic ordering rules to manage multi-item inventories for small businesses in the ftilfiUment of random customer demands and resultant replenishment schedules from a single vendor. In such multi-item single vendor inventory systems, the cost of placing a purchase order for a number of items consists of two components; a major common ordering cost S, incurred whenever an order is placed, and a minor ordering cost Sj when item j is included in that order. Goyal (1974; 1989), Ibrahim and Thomas (1986), Klein and Ventura (1995) and Kumar and Arora (1990), considered the common vendor problem with constant demand rates, and determined a common ordering period T , and a set of integer multipliers {kj} of the common ordering period. Item j is included in every kj*^ order. They considered cases with no stockouts, and with planned levels of stockouts at the end of each ordering cycle. The common vendor problem with random demands is more complex. It is not easy to write a total cost expression for this case, accounting for all cost components. Following decisions are involved in the management of inventory: - Rules for when to order;
Optimal Ordering Procedures
79
- Rules for which items to include in an order; and - Rules for quantity of an item to order. The approach for solving this problem has to be based on a number of good heuristic rules. One of the approaches followed in the literature, as described in a paper by Axsater (1996), has been to establish a portion of parameters needed for operating the system on optimizing a static model with constant demand rates set equal to average demand rates. Thereafter, these parameters were used to determine remaining parameters employing a set of heuristic rules. Love (1979) compared his heuristic rules with various approaches, available in the literature at that time and showed that his heuristic approach was superior to others. Love's model, though old, still stands out as a significant contribution. In Love's model, a common ordering period T , and a set of integer multipliers {kj} are determined based on the optimization of a static model with constant demand rates for the items. In this model, expressions were established for order-upto quantities Wj's for the case when no planned stockouts are allowed. The value of Wj is set equal to the sum of the average demand for item j over kj ordering cycles and an appropriately determined safety stock. Love (1979) establishes the reordering level Sj for each item j , based on a planned service level a, (probability of running out of stock prior to a replenishment, common for all j's). An order is placed when the inventory position of the first item hits its reorder level Sj. Another level, Cj, was established for each item. Item j is included in the order, if at the time of placing the order, its inventory position is below Cj. Inventory position is defined as the sum of inventory on-hand, and quantity on-order. These ordering rules are referred to as (Wj, Sj, Cj) rules. Love's rule of placing an order, when the first item hits its reorder level is not a good one. This policy can be improved if the decision, 'when to order' considers the total stockout cost for all items instead. In our formulation, stockout costs are finite, with the result that there are planned stockouts at the end of the ordering cycle for each item. Values of stockout cost may be difficult to assign directly. An inventory or production manager can make a choice more easily among different alternatives with varying stockout levels when their associated holding-cost components are made available to him or her. The value for stockout cost bj per unit per unit period for item j is assigned once his or her choice is known (assuming that the manager's choice is the optimal one). Papers of Silver (1974, 1981), Thompstone et.al. (1975), Federgruen et.al. (1984), Browne and Zipkin (1991), and Atkins and lyogun (1988) fall in this category of models. Silver (1974) found optimal values for the parameters Wj, Sj, and Cj for all j's, under the assumption of independent Poisson demand for each j . These values were determined to achieve a set of
80
Parts Management Models and Applications
pre-prescribed service levels Pi and P2; Pi denoting the probability that a cycle ends with no backorders, and P2 denoting the fraction of the demand that is satisfied with no backorders. Thompstone and Silver (1975) extended the above models for compound Poisson demands and non-zero lead times. Federgruen et.al (1984) determined optimal values of parameters with compound Poisson demands minimizing total cost with the additional constraint that the minimum prescribed level for the fraction of demand to be satisfied directly from stock was met. Atkins and lyogun (1988) determined lower bounds on system cost following Federgruen et al.(1984) ordering rules. They offered heuristic rules for picking parameter values. Carlson and Miltenburg (1988), instead of seeking tradeoffs between various cost components, chose values for controllable variables on the basis of prescribed service levels. In their model, inventories are reviewed periodically. An order is placed at review time, if the estimated shortage over the review time plus the lead time (without order) exceeds the allowed shortage during the lead time for a family of items. An item is included in the order, if the estimated shortage for the item over the review time plus the lead time exceeds the allowed shortage for the item during the lead time. The order quantity for an item is selected to achieve an optimum balance of ordering cost, inventory carrying cost, and invoice (material and freight) cost. The above papers deal with Poisson and Compound Poisson demand distributions. In this chapter, it is assumed that demand for items follows a normal distribution as a multi-item, single supplier inventory system considered typically deals with fast moving items including "C" manufacturing parts such as nuts, bolts, screws, fasteners, etc.
4.3
Inventory Management Policy
The inventory management policy followed is as follows: The common ordering period T*, and the set of integer multipliers {kj} are determined in a similar way to Love (1979), by minimizing the total annual cost with constant demand rates set equal to average demand rates, but allowing planned stockouts at the end of ordering cycles. Order-upto levels {Wj}, are essentially similar to those in Love, being the sum of average demand over kjT*, and safety stocks. Safety stocks are, however, determined by a different formula. The safety stock for item j is set equal to a pj multiple V L Gj, the standard deviation of demand over the lead time. The parameter Pj is set equal to P(bj/hj), where bj is the stockout cost per unit item per unit period, and hj is the holding cost per unit item per unit period for item j . This
Optimal Ordering Procedures
81
rule would lead to maintaining higher safety stocks for items, which are cheaper but have higher stockout costs. Following heuristic rules are followed for the decision of when to place an order and which items to include in an order. The decision 'when to place an order' is reviewed on a continuous basis. Hence, in the heuristic rule, the total stockout cost for all items over the lead time is compared with the average ordering cost. The rule states: An order is placed when the total projected stockout cost for all items over the lead time exceeds a certain multiple ai of the average order cost per order. The n
average ordering cost per order is given by § + V s Vk • The optimal JL^
J=I
J
J
value for the parameter ai is to be determined. The inclusion of item j in an order is a discrete decision. If item j is not included in the order being placed, it would be included at the earliest in the next order after an average time of T . Hence the projected stockout cost for item j is estimated over (T +L) and is compared with its ordering cost component Sj (minor component of the ordering cost incurred when item j is included in the order). The heuristic rule states: Include item j in the order, if its projected stockout cost over the lead time and the average ordering cycle time T exceeds a multiple dj of Sj. The order size for items ordered are given such that, their inventory positions are brought upto level Wj. The derivation of Wj is discussed in section 4.4.3. Optimal values for parameters ai, a2and (3 are determined subsequently by simulation. For simplicity, ai = ai = a is assumed. There are two major differences between Love's model and the model developed in this chapter. The static optimization model presented in this chapter provides for planned stockouts, whereas Love's static model does not. Furthermore, the decision of when to place an order considers total stockout cost for all items, as against placing an order according to Love's rules, when the first item's inventory position hits its re-order level Sj. These two differences make the model presented here as more realistic.
4.4
Random Demand Model
The model based on heuristic ordering rules for random demand case is developed here. Notations
82
Parts Management Models and Applications
n N Nj kj Uj S Sj Dj Gj LDj
The notation used in the model, and the example are listed below: Number of items, Number of purchase orders in a planning period, Number of replenishments for the j ^ item in the planning period, Relative ordering frequency for the j ^ item and it equals N/Nj, Fraction of the supply available immediately after replenishment and meeting backorders for item j , Common ordering cost per order, which is independent of number of items included in the order and size of orders for these items, Minor part of the ordering cost incurred whenever item j is included in the order, Mean demand rate for item j in units in the planning period, Standard deviation of d e m a n d per unit period (Wiener Process), M e a n lead time d e m a n d for item j ,
ylLcTj
Standard deviation o f lead time d e m a n d for item j ,
hj bj T T* L Ij(t) Xj qj M C
Holding cost per unit per unit period for item j , Stockout cost per unit per unit period for item j , C o m m o n m e a n inter-order time, Optimized c o m m o n m e a n inter-order-time C o m m o n procurement lead time, Inventory o n hand for item j at time t, D e m a n d for item j during lead time L , Order quantity for item j , Total n u m b e r of orders placed in the simulation period, Total variable cost for the planning period (that is, unit period),
CI C2 C3
Order cost per unit period, Holding cost per unit period, Stockout cost per unit period.
4.4.1
Expressions for Common Average Inter-Order Time T and ordering interval multipliers {kj}
In this section, we develop expressions for common ordering period T and ordering interval multipliers {kj}, assuming demand for item j is occurring at a constant rate Dj. The total variable cost for the planning period is given by
Optimal Ordering Procedures
83
C = SN+XS^N^ +l/2|;(D^/Nj)h^U/ +1/2^^^^)10,(1-^^)' j=i
j=i
(1)
j=i
Substituting ^ = N/kj = l/(kjT) in (1), we get C = (SN+Js^/k^)/T+(l/2^D^hjkjU/ +l/2XDjbjk/l-Up^)T j=i
j=i
(2)
j=i
Substituting A = SN + J S j / k j , a n d
B=
(l/2jDjhjkjU/+l/2jDjbjkj(l-Uj)'),wehave j=i
j=i
C = A/T + BT Optimizing with respect to T, we have
(3)
dC/dT = -A/T*'+B = 0 (4)
T* = V A ^ and C(T*) = A V B / A + B V A ^ - 2 V A B
(5) (6)
We now optimize total costftinctionC with respect to {Uj}. Minimizing C^ is equivalent to minimizing C. C'(T*) = 4AB
4(S + XS^/kj)(l/2XDjhjkjU/ + l/2XD^bjkj(l-U^)^) j=i
j=i
j=i
(7)
84
Parts Management Models and Applications Equating
== U , we get
U ; = b / ( b j + h j ) f o r j = l , 2 , ...,n
(8)
Substituting the optimal values for T , and {Uj} in equation (5), we get
T* =
2(S + X S A ) / l ; ( D ^ h ^ k ^ b / ( h ^ + bp)
(9)
Substituting the optima! values for T*, and {Uj}, in the total cost equation (2), we get
c{r,{\]])^{k^)^
hi^-^Y^^
(10)
Optimal values for {kj} are obtained when following conditions are satisfied:
c(T*,{u;},k;,{k;,j ^ i}) < c(T*,{u;},k;+i,{k:,j ^ (.}) and also C(t{l|}Jc;{^,j^^})
Substituting values of cost functions in the inequalities (11), we have k]{k\ -1)
+1)
(12)
Optimal Ordering Procedures
85
and B,, = Xhp,k^b/(b^ + h^)+
Y.^p,k,h/(h,+h.)
If for the f^ item, k*^;^k^, then the new {kj} combination will be {ki, k2,."5kj,...,k ^,.--?kn} and this should be improved. 4.4.2
Heuristic Ordering Rules for the Random Demand Case
We assume that demands for various items follow the Wiener Process (normal distributions with means and variations of demand directly proportional to time). The density function for the lead time demand, Xj, for itemj is given by f^(Xj) = (1/V2^aj)e'^''^"'^''^^''''^'^'
(13)
As a consequence of random demands, safety stocks are introduced while determining order-up-to-levels.
4.4.3
Safety Stock in order-up-to-level Wj
The level of safety stock for itemj is set equal to the Pj multiple of the standard deviation of demand over the common replenishment lead time. We have Safety stock for item j = pj(VLaj)
(14)
= (P bj/hj)(VLaj), where P is a common parameter for all items. We take Pj as a product of a common parameter p and the ratio b/hj. Order-upto-level Wj is given by W^=DjkjT*+P(b/hj)VLa^
(15)
86
Parts Management Models and Applications In sections '4.4.5 to 4.4.7, rules for the decisions involved in the management of inventories are developed which use stockout quantities for various items.
4.4.4
Expected Stockout Quantity for item j
Expected stockout quantity computed at time t for item j during lead time L
= J(Xj-I^(t))f,(X^)dXj,
VUa^
}((z-(I^ -LD^))/VLaj)f,(z)dz, (Ii-LDi)/VLOi
where z = (Xj - LDj)/VLOJ
= V L O J j(z - k)f,(z)dz, where k = (I^ - L D ^ V V L G J
= VLGjG.Ck), where G^(k) = J(z - k)f,(z)dz
4.4.5
(16)
When to Order
According to our heuristic ordering rules, an order is placed when the total expected stockout cost at any time over the lead time exceeds a constant multiple ai of the average ordering cost per order. We assume that the average stockout duration for the average stockout quantity given by (16) is over half the lead time L, that is, place an order if.
Optimal Ordering Procedures
87
2](L/2)b^VLa^G,((I^(t)-LD^)/VLa^) > a/CS + ^S/k^) j=i
(17).
j=i
j=i
j=i
where aj = aj'(2/L) In computing the total stockout cost it has been assumed that at the time of placing an order at most one order is pending. With this assumption, just prior to placing an order, inventory position would equal inventory on hand. 4.4.6
Which items to include in the order
An item is included in an order if its expected stockout cost over the sum of the lead time and the average order cycle time exceeds or equals a constant multiple a2 of the item's ordering cost. That is, include item j in the order, if, bj(L/2)VL + T*ajG,((Ij(t) - (L + T * ) D J ) / V L +1*0^) > a^'S^
b j V L 7 r ' a j G , ( ( I j ( t ) - (L + T*)Dp/A/L + T*aj) > a^S^,
(19)
(20)
where Q.^ = ^^Q.I\J) 4.4.7 How much to order for items being ordered The rule for the order quantity for item j is given by qj = Wj - I j ( t ) = D^kjT* +p(b^/h.)VLa^ -I^(t) (21) Implicit within our inventory operational management rules are parameters ai, a2 and (3. A proper choice of ai, a2 and p values will lead to an efficient
88
Parts Management Models and Applications
distribution of the incremental cost due to demand randomness among ordering, inventory holding and stock-out cost components. Approximate optimal values of ai, a2 and P are obtained employing simulation. In the next section, a small example is described to illustrate how these heuristic rules are more realistic as compared to existing approaches available in the literature.
5.
EXAMPLE
In this section, we illustrate and compare our ordering rules (where an order is placed when the total expected stock-out cost over the lead time exceed a multiple of the total ordering cost) with Love's ordering rules (where an order is placed when inventory position of the first item hits its re-order level Sj) using his four items example through Monte-Carlo simulation. The problem data are identical for the two ordering rules, excepting we have assumed certain values of bj's, whereas we do not know the values for bj's assumed by Love in his example. The simulation covered a period of 190 days. In order to minimize the impact of differences due to initial conditions, the first 10 days were not included in the performance statistics. The data are given in Table 4-4. The starting inventory for item j , for both models was selected equal to sum of the average demand over kjT* plus the safety stock. The simulation was carried out following ordering rules of two methods. The search for the optimal values of parameters a and p was made using the sequential grid technique. Table 4-5 gives performance statistics such as, total number of orders placed in the simulation period, order cost per unit period, holding cost per unit period, stockout cost per unit period and total variable cost per unit period for various values of a and p around the optimal value.
Optimal Ordering Procedures
89
Table 4-4. Data for a four items common vendor example
n=4, S=400, L=l
J
Dj
1
4
2
hj
b.
Sj
2
2
3
2
9
3
4
2
1
3
4
2
6
1.5
3
4
16
4
5
2.5
5
J
V
J
Table 4-5. Grid showing sequential search of minimum total cost per unit period = $241.70 by our heuristic model
2
1
0.5
M= 19 Cl= 43.38 C2= 75.00 C3= 249.61 C = 367.99 M= 27 Cl= 61.65 C2= 98.00 C3= 90.29 C= 249.94 M= 36 Cl= 82.20 C2= 136.00 C3= 35.12 C= 253.32
M= 20 01=45.67 02= 68.00 03=239.15 0= 352.82 M= 27 01= 61.65 02= 93.00 03= 87.05 0=241.70 M= 35 01=82.20 02= 125.00 03= 37.87 0= 245.07
M= 20 01=45.67 02=68.00 03=241.64 0=355.31 M= 28 01= 63.93 02= 89.00 03= 91.15 0= 244.08 M= 37 01= 84.48 02=118.00 03= 42.40 0= 249.88
a
1.0
0.5
0.2
90
Parts Management Models and Applications
Our matching solution with Love's solution (in terms of equal stockout cost) when a==0.02 and p=l is given in Table 4-6. The details of performance statistics for our non-optimal solution are given in Table 4-11. Table 4-6. Value of a and p, sequentially searched by grid method and refining the grid until stockout cost per unit period in our heuristic model matched with Love's model
p
2
1
0.5
M = 38 Cl= 86.73 C2= 284.00 C3= 12.55 C= 383.28 M = 39 Cl= 89.03 C2= 296.00 C3= 11.57 C= 396.60 M = 39 Cl= 91.23 C2= 295.00 C3= 9.06 C= 395.38
M = 38 €1= 86.76 C2= 260.00 C3= 13.95 C= 360.71 M= 40 Cl= 91.33 €2= 265.00 C3= 11.46 C= 367.79 M= 42 Cl= 95.90 C2= 287.00 C3= 8.88 C= 391.78
M= 39 Cl= 89.05 C2= 245.00 C3= 12.65 C= 346.70 M= 42 Cl= 95.90 €2= 265.00 €3= 10.27 C=361.17 M= 43 Cl= 98.18 C2= 271.00 C3= 9.93 C= 379.11
a
0.03
0.02
0.01
Figures 4-2 through 4-5, display response surfaces plots for ordering cost, holding cost, stockout cost and total cost per unit period respectively for various values of a and (3 parameters. These graphs use results reported in Table 4-5, which are based on the heuristic model proposed in this chapter.
Optimal Ordering Procedures
91
100 Ordering Cost per unit period
80 gQ 40 20 0
Alpha
0 22
Beta
Figure 4-2. Graph illustrating Ordering Cost per unit period for various values of parameters - Alpha(a) and Beta(P).
Holding Cost per unit period
Alpha
Figure 4-3. Graph illustrating Ordering Cost per unit period for various values of parameters - Alpha(a) and Beta(P).
92
Parts Management Models and Applications 250 o* .. * 200 Stockout Cost per 150 unit period
100 50 0
Beta
Figure 4-4. Graph illustrating Stockout Cost per unit period for various values of parameters - Alpha(a) and Beta(P).
400 -r . . ^ -^ 300 Total Cost per unit 200 period ^ 100
Alpha
0-5 ^ ^ 0 2;
Beta
Figure 4-5. Graph illustrating Total Cost per unit period for various values of parameter Alpha(a) and Beta(P). Table 4-7 gives values of parameters for Love's static model. Table 4-8 gives performance statistics for the random case following his ordering rules.
Optimal Ordering Procedures
93
Table 4-7. Operational Management Parameters for Love's Static Model a=3,95 Item
Starting
Safety
inventory at t=0
included in Wj
stock
Cj
Wj
Sj
1
15
9
17
12
20
2
25
5
31
21
45
3
14
2
18
12
28
4
79
6
51
32
112
Table 4-8. Simulation Performance Statistics following Love's Heuristic model
Number of orders placed = 94 Item
Average inventory
Stockout
Unit days short
Orders for items
frequencies 7
55
55
68
14
58
58
69
3
11
20
20
55
4
42
28
28
41
1 2
Total simulation days used
=180
Order cost per unit period
=216.54
Holding cost per unit period
=349.00
Stockout cost per unit period
= 11.24
Total variable cost per unit period
=576.78
Table 4-9 gives values of parameters for our static model. Tables 4-10 and 4-11 give performance statistics following our ordering rules.
94
Parts Management Models and Applications Table 4-9. Static Model based operational management parameters for the heuristic model in this chapter {Ry = (hjDj/Sj).(bj/(bj +hj))}
a=0.001, p=8.5,r=4.271 Starting Item
inventory at t=0
1
26
2 3 4
-
Safety stock
Wj
included in Wj
bj/(bj+l^)
kjo
Rj'
kji
9
27
3/5
8/5
1
1
43
5
43
1/3
12/5
1
1
19
2
19
1/5
16/3
1
1
74
6
75
1/3
12
1
1
Table 4-10 gives performance statistics when the total cost per unit period is minimum. Our total cost is 58% lower than Love's total cost. With the given data, according to the optimal solution calculated by our method, the stockout level is higher than the stockout level in Love's solution. If a better service level is desired in terms of reduced stockout then the right method to achieve it will be found by assigning higher values to parameter's bj's. However, since we do not know Love's bj's, we assume his stockout level as being prescribed by management.
optimal Ordering Procedures
95
Table 4-10. Simulation Performance Statistics for the optimal solution using heuristic model proposed in this chapter KufiTib*! of orckrs placed = ll Item
Avctragf
Stock-<3ut
U M days shoft
Order fcT-iteniJ
1
B
<^
S6
Zfj
27
2
14
14
119
119
27
3
6
I
no
131
n
4
22
>7
131
131
27 1 ^ . _ _ _ _ ^
Tatai strnulatLisn ^^ji
*• usti
Qrdcf con pcT tjgnif pensd Ht^l^tig c 0 it ptr v£ii*i period Stock out Cf^t fm urat
f^noi
Ti^tal vanabk c ost pet uriit "^tmz i
—
^
6l6f.
^
241 70
~- ^ — — J
Table 4-11 gives the corresponding solution where our stock-out cost matches Love's stock-out cost. The cost of other two components, that is, inventory holding cost and ordering cost (excluding stock-out cost) rises to $356.33.
Parts Management Models and Applications
96
Table 4-11. Simulation Performance Statistics for our non-optimal solution matching with Love's stockout cost Number of orders placed =40 Item
Average
Average
Stockout
inventory
stockout
frequencies
Unit days short
Order for items
1
26
3
1
1
40
2
17
4
52
52
40
3
6
3
82
82
40
4
23
8
77
77
40 = 180
Total simulation days used Order cost per unit penod
= 91.33
Holding cost per unit period
=265.00
Total vanable cost per unit penod not including stock-out costs
=356.33
5.1
Necessary Conditions for optimal values of a and p
Since, Total variable cost per unit period = (Order cost + Holding cost + Stock-out cost) per unit period that is, C = C1+C2 + C3 For optimal values of a and P, we should have a c _ 5C1 _ aC2 _ 5C3
(0
0
(ii)
dc 5C1 ac2 ac3 = 0
(iii)
da
ap
da
5p
da
5p
da
ap
Since our grid search covers the set of discrete values of a and P, values of derivatives around the optimal should change sign; and compliance of conditions (ii) and (iii) may be confirmed in Table 4-5 around a=0.5, p=1.0. However, in our matching solution (with Love's solution in terms of equal stock-out cost), it may be noticed in Table 4-6 that conditions (ii) and (iii) are not satisfied as the solution is not optimal on the basis of total cost. It may be pointed out that as a decreases, we tend to become more responsive to the dynamics of the system through more flexible ordering. As p decreases, Wj decreases. In the optimal solution, we have smaller safety stocks for various items as compared to Love's solution. We respond to the dynamics
Optimal Ordering Procedures
97
of the system with more frequent ordering as opposed to additional inventories. Consequently, ordering rules developed in this chapter, compared to Love's solution for the example considered by Love, show a reduction in the total variable cost of over 50%.
6.
IMPLEMENTATION OF PROPOSED ORDERING RULES
The proposed ordering rules are the backbone of inventory and order management software to support the type of small business operations mentioned earlier in the chapter. The architecture of various software modules required is outlined below: Module 1 provides capabilities to create and update inventory database real time and also facilitate cycle counting of inventory as and when necessary. It has features to review on-line order and inventory status information. A number of computer programs provide the required capabilities. One program updates inventory real-time as it is used to meet customer demand and also when order is received from the vendor. Another program facilitates cycle counting of inventory to ensure physical count and computer record tallies. The third program allows user queries for order status and inventory information. Module 2 is used to initiate simulation, using data pertaining to demand and various associated costs for items stocked by the business operation. Such simulation assists in determining optimal values of parameters a and p used in the proposed heuristic ordering rules. This module may be run every 3 to 6 months when it is perceived that magnitude of demand and various associated costs for items stocked have significantly changed. Module 3 is used to initiate proposed heuristic ordering rules to generate order, with a list and quantities of items, to be placed on a common vendor. This module is to be run daily to generate orders for the vendor. Prior to using this module, it should be ensured that current values of parameters a and p, and associated costs for items are recorded in the inventory database.
7.
CONCLUSIONS - RANDOM DEMANDS
Multi-item inventory problems with a common vendor and with random demands are commonly encountered in many real-life situations. The
98
Parts Management Models and Applications
problem is of great interest specially in inventory management situations, where ordering cost is common for a number of items with random demands. Initially, optimal values for common ordering cycle time T*, and integer values for order frequencies {kj} are established based on minimizing the total yearly cost with deterministic demand rates set equal to their respective average demand rates for various items. Using these parameter values and variance of lead time demands, values for order-up-to quantities {Wj} are established. Heuristic ordering rules developed in this chapter for the random demand case consider projections of total stock-out cost for all items at the time of placing an order. These rules involve two parameters a and p whose optimal values are determined by simulation. The model developed in this chapter responds to system's randomness through more flexible ordering rule, as opposed to responding through increasing safety stocks. It can be developed as an inventory and order management software as described in the chapter, which will facilitate management of the above multi-item, single vendor inventory system by many small businesses on a much wider scale.
Adapted from the paper by authors: Kumar, Sameer and Arora, Sant, (1990), "Optimal Ordering Policy for a Multi-item, Singlesupplier System withConstant Demand Rates", Journal of Operational Research Society, Vol. 41,No. 4, pp. 345-349. Adapted from the paper by authors: Kumar, Sameer and Chandra, Charu, (2002), "Managing multi-item common vendor inventory system with random demands", International Journal of Physical Distribution and Logistics Management, Vol. 32, No. 3, pp. 188202.
Chapter 5 PARTS PROLIFERATION AND CONTROL^
1.
INTRODUCTION
In a parts inventory system, many parts in the inventory are similar to each other and, therefore, can be substitutes. No formal procedures currently exist to control proliferation of parts. The valid point for controlling this proliferation is the Design department where decisions to add new parts are made. As new products are designed, it becomes important to control unnecessary design proliferation of parts. The system should have the capability of providing to the Design Engineer, a list of existing parts similar to the new part that is being planned to design. A new part should be designed only if the Design Engineer certifies that none of the existing parts in the similar class can be a good substitute for the new proposed design. When a decision to add a new part is taken and this part obsoletes one or more of the existing parts, this fact should be recorded in the database and gradually the dominated parts should be taken out of usage (Mosier and Janaro 1990, Floyd 1998, Anonymous 1999). The Product Data Management (PDM) systems, currently operating in many companies are not geared to retrieving a small set of existing parts with similar or closer design and/or manufacturing attributes for the Design engineer to review. The PDM systems being used have broad classification capabilities (Dickerson 2000). 99
100
Parts Management Models and Applications
Group Technology (GT), which exploits similarities within parts seem to hold a promise in bringing improvements in several other areas such as - grouping for cellular manufacturing, grouping of maintenance operations for better scheduling and worker training, and promoting more standardization in general (Oh and Gravel 1986, Park 1986, and Park and Lee 1998). Due to the increased popularity of cellular manufacturing, cell formation techniques have recently seen increased attention, while application of coding and classification (C&C) systems appear to have been slow due to considerable effort required to derive the GT code for each part in a company's database. The coding process had been largely manual, which would introduce inconsistencies and errors. The advent of automated GT coding, supported by more comprehensive and standardized product models has eliminated these barriers and enhanced GT applicability. A GT code assigned to a part is a string of alphanumeric characters that represent important design and manufacturing related attributes. A number of GT coding schemes have been developed for mechanical applications but at present, only a few electrical applications have been developed (Reodecha and Bao 1985, Ham et al. 1986, Harhalakis et al. 1992). This is largely due to the fact that GT related research for electrical parts has been carried out in defence related areas and existing codes are customized and proprietary (Kinsey 1992). GT coding schemes used for mechanical parts include MICLASS (OIR Multi-M 1986), Opitz (1970), DCLASS (Allen and Smith 1982), and KK3 (Japan Society 1980). Although the format and classification of the various coding schemes is different, they all encapsulate information on six basic part characteristics: main shape, form features on the main shape, feature position, dimensions, tolerances, and material. As mentioned earlier, application of group technology has been slow due to enormous effort required in coding a company's part database. However, recent advances in this field have addressed this problem. Shah and Bhatnagar (1989) have developed an automated GT coding system based on Opitz scheme for machined parts. Henderson and Musti (1988) have also developed an automated coding system for rotational parts using DCLASS. Bond and Jain (1988) have developed a system to automatically generate Lockheed sheet metal GT codes from a 3-D CAD model. Candadai et al. (1994) have extended the work by Harhalakis et al. (1992) which illustrates how the PDES/STEP (Product Data Exchange using Standard for the Exchange of Product model data) information of an electricalmechanical part is used as an input to an automated code generating system, yielding a mechanical and electrical GT code and critical design information. The importance of this work is that the output of this system is
Parts Proliferation and Control
707
considered as input to the search methodology that has been developed. The objective of the problem at hand is to identify existing designs among the company's part database, which are similar to a candidate part at the design stage. The similarity here is on one or more part characteristics as specified by the design engineer. Formal procedures for controlling unnecessary parts proliferation are urgently needed, particularly nowadays when product shelf life is relatively short. A program should also be initiated to reduce existing number of current parts, eliminating the duplication of similar parts. The success in the proposed design support function for variety control will depend upon the ability to group parts and retrieve these groups easily on the basis of their design similarities. A model is needed as a basis for classifying objects (McCarthy 1995) where the term, object, is used in a generic sense. As an option, objects may be classified directly by experts on the basis of their similarity judgments. Alternatively, less dependent upon experts, is classifying objects based on their attributes. In this chapter, the latter approach has been chosen. There are two further possibilities within this approach: • Developing capabilities to make probabilistic statement for an object belonging to a certain class, conditional to the presence of certain attributes. This approach requires a lot of data and seems non-practical in a manufacturing environment. • Developing classification capabilities based on weighting of relevant attributes. The second possibility is chosen for the purpose of the model described in this chapter. Basic steps involved in planning for classification are: Step 1: Identification of types of object in the system that need to be classified. Step 2: Identification of purposes, and defining similar classes for each purpose. Step 3: Identification of attributes for various objects and defining their measurements. Step 4: Development of procedures for generation of similar classes for various The objective of the problem at hand is to identify existing designs among the company's part database, which are similar to a candidate part at
102
Parts Management Models and Applications
the design stage. The similarity here is in one or more part characteristics specified by the design engineer. The first three steps listed above result in the generation of mechanical and electrical GT codes, and critical design information as described earlier (Candadai et al. 1994). This output generated by the coding system is used as input to the proposed search and retrieval procedure that acquires search intent information from the design engineer and identifies a set of potentially useful similar parts. Planning for the development of classification schemes should be done for the total company's needs rather than using a piecemeal approach, taking one function at a time (Marion et. al.l986, Dangerfield and Morris 1991,Kosankeet. al. 1999).
2.
PRINCIPAL COMPONENTS ANALYSIS-BASED CLASSIFICATION MODEL (SPATH 1980, ARABIE ET. AL. 1996, GORDON 1999).
This technique defines new coordinates, where a fewer number of them can explain a sizeable fraction of the variance of given data. The model for the Principal Components Analysis is given by Zj-ajiFi + aj2F2+ .... + ajnFn (j = l,2,3,...,n), where each of the n observed attributes is described linearly in terms of the "n" new uncorrected components Fi, F2, ...., Fn. Coefficients of components are frequently referred to as "loadings". Each object is represented geometrically by a point in an n-dimensional space. The Principal Components Analysis technique involves rotation of the coordinate axes to a new set of orthogonal coordinate axes, wherein each of the "n" original attributes is described in terms of the "n" new principal components. An important feature of new components is that they explain in a given sequential order, a maximum portion of the total variance of attributes. More specifically, the first principal component is that linear combination of original variables which explains a maximum portion to total variance of attributes; the second principal component, uncorrected with the first, further explains a maximum portion to the residual variance; and so on. The total variance is completely explained by the "n" principal components. It is desirable that all attributes be measured in standardized units so that intra-distances between objects are not affected by a change of scale.
Parts Proliferation and Control
103
The starting point of the technique is to compute correlation matrix among various attributes in their standardized measures. The Eigen values Xj's and Eigen vectors Uj's of the correlation matrix are computed. Eigen vectors Uj's are multiplied by their corresponding Jx~ 's to get a new scaled vector Wj's:
The elements of Wj's may be interpreted as correlations of attributes with the jth component. The variance of the jth component is given by (>.j/number of attributes). The column vectors Wj's represent different columns of a matrix, called Component matrix. The varimax matrix rotation technique is also used in this model. It results in rotation of components in such a way that new loadings tend to be either relatively large or small in absolute magnitude as compared to original loadings in the Component matrix. This technique retains orthogonality between components during rotation. A fewer components will become the basis for classification of objects, instead of the original "n" attributes, if they account for a large percentage of the total variance. In the example considered, the first few components account for a large percentage of the total variance and corresponding component loadings of each are highly correlated to a single distinctive attribute. The grouping of objects in the original data set is done using these components hierarchically. Mahalanobis distance is used to measure intra-distance between a new object from the mean of various groups. Mahalanobis distance avoids double counting of distances on account of interdependencies among attributes. Mahalanobis distance is given by ?=(P.m d*1J
Pj/ W-^(P,-Pj)
between object i and object j , where (Pi - Pj Y is the transpose (Pj - Pj), W'^ K
is the inverse matrix of W = ZWi ? ^^^ Wi is obtained for each of the i=l
i=l,2,3,...,K groups by
104
Parts Management Models and Applications Wi= I ( P m i - Q ) ( P m i - C i ) ^ m=l
where nj is the number of objects in the ith group. Pi and Pj are column vectors each with n rows listing the n measurements on the ith and jth objects respectively. (Pmi - Ci) is the difference of the coordinate of the m^^ object and the i^^ group mean. The sum of all the Wj scatter matrices result in the matrix W = K
X Wi which represents, within scatter, a measure of homogeneity among i=l
groupings.
3.
TEST CASE
A test sample of all fans of various types (126 types) in a leading transport refrigeration unit manufacturer was picked for grouping. When designing a fan for evaporator and condenser sections used in a transport refrigeration unit, the design engineer determines the amount of airflow needed and how much space is available to house the fan. The rotational speed of fan is determined from the amount of airflow required. For the evaporator section, the company has been using 3600 revolutions per minute (rpm) speed fans and for the condenser section, 1200-rpm speed fans. The amount of space available helps in estimating the size of the fan. Also, amount of airflow needed and pressure drop in the evaporator or condenser section dictates the motor power rating for the fan. The "bearing type" has no impact on fan design, and it is picked depending upon operating environment considerations. The "bearing type" is dictated by the supplier of the motor and if the need be bearings (size, seals, and grease) are modified to fit the operating environment. Typically, "drive type" has no direct influence on fan design, other than if the fan is engine driven, material strength considerations, such as, type of material and its thickness come into play to deal with vibration concerns due to engine. For a given rotational speed and power rating for the new fan, design engineer would like to ascertain values of other important key design attributes, such as, number of
Parts Proliferation and Control
105
blades, diameter of fan, blade tip angle, rotation direction, hub type, and material. Hub is a device, which makes the transition between the fan blades and the shaft. The design based attributes for fans used in the classification are - number of blades, diameter of fan to the nearest inch, blade tip angle in degrees, direction of rotation, hub type and material. The table showing values of attributes is given in Appendix A. Table 5-1 gives description of various attribute values for a fan.
Table 5-1. Description of attribute values associated with fan
Attributes Blade tip angle
Rotation direction Hub type
Material
Actual Categorical Values Values 1 11 to 15° 16 to 20" 2 21 to 25° 3 4 26 to 30° 5 31 to 35° 36 to 40° 6 41 to 45° 7 46 to 60° 8 1 Clockwise 2 Counter clockwise Split block 1 Keyed 2 Set screw 3 Pinned 4 Belt drive 5 Steel 1 2 Aluminum Plastic 3
The mean and standard deviation for attribute values are given in table 5-2.
106
Parts Management Models and Applications Table 5-2. Mean and Standard Deviation for categorical values of attributes
Mean Attributes Number of Blades Diameter of fan Blade tip angle Rotation direction Hub-type Material
4.4286
Standard Deviation 0.7422
15.1190 26.4127 1.5873 1.7619 1.0873
4,0291 7.26 0.4943 0.8526 0.3103
The correlation coefficient matrix among various attributes is given in table 5-3. Table 5-3. Correlation coefficient matrix for various attributes Number of
Diameter
Blade tip
Rotation
Blades
of Fan
angle
direction
Hub type
Material
1.0000
0.3814
0.2594
-0.0810
-0.2420
0.4614
0.3814
1.0000
-0.0372
0.0851
-0.4062
0.0876
0.2594
-0.0372
1.0000
-0.0101
0.0793
0.3212
-0.0810
0.0851
-0.0101
1.0000
-0.0832
-0.2326
Hub type
-0.2420
-0.4062
0.0793
-0.0832
1.0000
0.2001
Material
0.4614
0.0876
0.3212
-0.2326
0.2001
1.0000
Number of Blades Diameter of Fan Blade tip angle Rotation Direction
The Eigen values A,j's for the correlation matrix are Xi= 1.85227
?i2= 1-56782
^3= 0.98458
^4= 0.71468
^5 = 0.50571
^6= 0.37489
Parts Proliferation and Control
107
The corresponding normalized Eigen vectors, (Uj) 's, are shown in the respective columns of the following matrix U. 0.63176 0.40425 0.34691 U= -0.14109 -0.20766 0.50406
-0.06295 -0.48902 0.32582 -0.32728 0.61401 0.40818
0.00201 -0.07809 0.54707 0.82479 0.11320 -0.03890
-0.10188 -0.28811 0.60386 -0.37484 -0.51230 -0.37282
-0.45582 0.71280 0.33037 -0.20340 0.33479 -0.14673
-0.61543 -0.01550 -0.02008 0.10404 -0.43877 0.64596
Scaling elements of each eigen vector Uj's in matrix U gives the Component matrix given in table 5-4. Table 5-4. Original Component Matrix ^"^'^-^^^gomp 0 nents
I
II
III
IV
V
VI
Number of blades
0.85982
-0.07883
0.00199
-0.08613
-0.32415
-0.37682
Diameter of Fan
0.55017
-0.61232
-0.07749
-0.24357
0.50690
-0.00949
Blade tip angle
0.47214
0.40797
0.54284
0.51050
0.23493
-0.01229
Rotation direction
-0.19203
-0.40980
0.81841
-0.31688
-0.14465
0.06370
Hub type
-0.28262
0.76881
0.11233
-0.43310
0.23808
-0.26865
Material
0.68602
0.51110
-0.03860
-0.31518
-0.10435
0.39551
Elements in each column vector of the matrix given in table 5-4 represent correlations between components and attributes. In this matrix, loadings of various attributes on different components range over all values.
Parts Management Models and Applications
108
The rotated component matrix given in table 5-5, achieve high loading values for various components with distinctive attributes. Table 5-5. Rotated Component matrix I
II
III
IV
V
VI
Number of blades
0.24058
-0.13176
-0.03829
0.13157
0.19367
-0.93191
Diameter of Fan
0.04289
-0,20201
0.04778
-0.02998
0.96079
-0.17616
Blade tip angle
0.14290
0.03554
0.00567
0.98209
-0.02820
-0.11391
Rotation direction
-0.010675
-0.03264
0.99223
0.00576
0.04339
0.03303
Hub type
0.11384
0.96451
-0.03521
0.03742
-0.20058
0.11776
Material
0.94221
0.12295
-0.12411
0.16049
0.04351
-0.23247
For the given example, following observations are made with respect to loadings in the rotated components matrix. Attribute 6 (Material) loading on Component I accounts for 30.9% of the total variance of attributes (?LI/6 = 1.85227/6 = 0.3090). Attribute 5 (Hub type) loading on Component II accounts for additional 26.1% of the total variance. Attribute 4 (Rotation) loading on Component III accounts for additional 16.4% of the total variance. Attribute 3 (Blade pitch angle) loading on Component IV accounts for additional 11.9% of the total variance. These four Components loadings account for 85.3% of the total variance of variates. Clustering based on these four Component loadings resulted in 28 clusters/groups as shown in table 5-6.
Parts Proliferation and Control
109
Table 5-6. Clusters/groups obtained based on four component loadings
Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Objects 20, 24, 46, 69, 95 28,48,50,51,95, 117 72, 87, 125 56, 105 22, 23, 57, 58, 59, 70, 74, 75, 83, 96 47, 76, 77, 78, 97, 98, 100, 115, 116, 118, 119, 126 52, 53, 79, 80, 81, 84, 85, 86, 93, 123, 124 15,40,88,89,90,91,92,94, 101 43, 45 5, 6, 33, 66, 67 10,11,12,13 1,18,54,103 4, 19 25,26,32,64,65,71 2, 9, 35, 37, 39 41,55,68, 102 21,44 49, 62, 63 34, 82, 120, 121 3,27,29,30,31,60,61, 104 7,8,38 16, 17,73,122 36 42 14 106 108, 109, 110, 111, 112, 113, 114 107
110
4.
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OPERATIONAL OUTLINE FOR THE DESIGN SUPPORT SYSTEM
Consider that a Design Engineer is contemplating to design a new fan. Suppose, the feature vector for this fan is given by [4 20 15 1 2 1], where values represent number of blades, diameter of fans in inches, blade pitch angle, rotation direction, hub-type, and material type respectively. The Design Engineer should review a set of similar fans within the existing set which might be a suitable substitute for the contemplated fan. In order to find out which set is closest to the feature vector of the proposed design, intra-distances between the feature vector and vectors of the group means for various groups are determined. The distance measure used here is the Mahalanobis distance. The group means for various attributes of fan are shown in Table 5-7.
Parts Proliferation and Control
HI
Table 5-7. Group means for various attributes
Group Group means for various attributes (Number of blades, Diameter of fan in inches, Blade tip angle in degrees, Rotation direction, Hub type, Material) i
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
4.2, 14.8, 17.6, 1.2, 1, 1 4.5, 15.17,23.83, 1.17, 1, 1 4.67, 15.33,27.67, 1, 1, 1 5, 15,34.5, 1.5, 1, 1 4.1, 17.4, 18.8, 1.6, 1, 1 5.08,20.25,22.08,2, 1, 1 4.45, 16.45,27.27,2, 1, 1 4.78, 14.89,35.22,2, 1, 1 4,14,17,1,2,1 4, 12.8,23.2, 1, 1.8, 1 4, 10,27.25, 1,2, 1 4,14.5,42,1,2,1 4,11,14,2,2,1 4, 14.33,22,2, 1.83, 1 3.8, 13.6,28.2,2,2, 1 4.25, 16.75,36.25,2,2, 1 4,13,18,1,3,1 4, 15.33,21, 1,3, 1 4,13.5,27,1,3,1 4.25, 12.38,22.25,2,3, 1 4, 10.67,28,2,3, 1 4,12,36.5,2,3,1 4,12,28,1,4,1 4,14,16,2,4,1 4, 10,32,2,4,3 6, 16,35, 1, 1,2 6, 18,36, 1,2,2 6, 18,30, 1,3,2
i
I
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The within scatter matrix for the given data set is
W=
12.464 21.995 66 259 0.5 12.464 1076 .384 117.978 7.834 pi .995 117.978 762.544 8.266 5.334 0.5 7.834 8.266
0 0
0 0
0 0
0 0
The inverse of this matrix is
w-i =
0.153 -0.0001 -0.0004 -0.0006
-0.0001 0.0010 -0.0001 -0.0012
-0.0004 -0.0006 0 -0.0001 -0.0012 0 0.0014 -0.0019 0 -0.0019 0.1922 0
0 0 0 0
Mahalanobis distances are computed for the feature vector of the proposed design from group means of various groups. These distances are given in Table 5-8.
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Table 5-8. Distances between the given feature vector and various group means
Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Group distance from the vector 0.047772 0.1435102 0.259086 0.59395 0.093287 0.2449603 0.3846428 0.7433451 0.044 0.157784 0.3345875 1.08055 0.2982 0.2878949
Group 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Group distance from the vector 0.4619 0.7723813 0.0658 0.0778129 0.25945 0.3248452 0.5130989 0.87525 0.3214 0.2414 0.6902 0.6228 0.6582 0.3630
Smallest Mahalanobis distances for the given vector were 0.044 and 0.047772 relative to groups 9 and 1 respectively. A certain upper bound, B, for the intra-distance between the feature vector and group means will be decided upon. The Design Engineer will be furnished with all groups where intra distance of these groups from the feature vector is below the selected upper bound. As an example, in this case, if the upper bound B = 0.05, then the Design Engineer will be asked to review items within groups 9 and 1. Objects in groups 1 and 9 have attributes as shown in Table 5-9.
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Table 5-9. Attributes of objects in Groups 9 and 1 Number of
Diameter
Blade tip
Rotation
Group
Blades
in inches
angle in
direction
Hub-type
Material
9
4
14
16
1
2
1
4
14
18
1
2
1
degrees
1
4
12
16
1
4
12
20
2
4
14
19
1
4
18
16
2
5
18
17
1
Design engineers reviewed groups of objects retrieved for some typical features for rating the appropriateness of sets presented to them. All of them approved the retrieval scheme for design similarity. However, they shared a concern for sizes of the set as being too large. The size of the sets retrieved will have following influences. Giving larger sets for review will require more work for design engineers. Retrieving smaller sets, through lowering upper bound B, will lead to a relaxed variety control. Tables in Appendix B give another measure of intra and within subset heterogeneity and homogeneity. These tables show mean distances of various objects within a subset from their subset means and between various subset means on the new coordinate system based on principal components. The distance measure used is city block distance (Spath 1980, Gordon 1999).
5.
CONCLUSION
A genuine reduction in sizes of retrieved sets will be achieved by discovering new, more discriminating type attributes. Controlling design proliferation holds a great potential for improving manufacturing productivity and reducing costs. The foundation of the methodology developed rests on concepts of group technology. GT has proven to be ideal in search and retrieval of similar designs. The resulting GT codes are strings of digits that contain important design and manufacturing information of a part. This information is used as input to Principal Components Analysis for
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115
grouping items in similar classes based on their design similarities. Procedures are suggested for using these classes for controlling design proliferation. Further work needs to be done before practical approaches in variety control are developed. The proposed classification and retrieval module should be a part of the Product Data Management software.
Adapted from the paper by authors: Kumar, Sameer and Chandra, Charu, (2001), "Providing Support to Product Design Group for Achieving Variety Control", Journal of Engineering Design, Vol. 12,No. 4, pp. 373-387.
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Chapter 6 ECONOMIC VIABILITY OF COMPONENT MANAGEMENT FOR A NEW PRODUCT DESIGN^
1.
INTRODUCTION
A number of companies today, typically have multiple autonomous divisions or subsidiaries engaged in designing, manufacturing and selling products to customers. Some of them have undergone significant mergers and acquisitions, further compounding organizational complexity. Invariably, a proliferation of suppliers, parts, components and materials occurs that is impossible to control without enterprise-wide decision support processes and standardized content on parts, components, materials and suppliers. Product designers are under pressure to get it right the first time and do it fast (Anonymous - Knowledge base 1999; Floyd 1998; Smith 1995). Decisions they make are critical to product success and the company's bottom line. During the first 10% of the product development cycle, decisions made affect up to 80% of the final product cost, and also have repercussions downstream in manufacturing and service for years (Kosanke, Vernadat and Zelm 1999). Companies would significantly benefit from the implementation of decision support systems to streamline inbound supply and support collaboration among even the most independent divisions and subsidiaries. Such systems would facilitate enterprise-wide collaboration in design, 117
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procurement and operations decisions, and sharing of standardized component and supplier content. These would also enable a firm to: reduce the cost of production parts and supplies by leveraging purchases on fewer parts from a smaller supplier base, accelerate product innovation and timeto-market by increasing component and design re-use across the enterprise, and increase product quality by increasing usage of "preferred" components and suppliers. The study reported in this chapter explores the economic viability of implementing a component management system to support the proposed formalized standardization of three level decision making hierarchy for expediting strategic product development and control design proliferation using an example of a well known transport unit manufacturer.
2.
CURRENT BUSINESS SCENARIO
A leading transport refrigeration company is expanding in new competitive international markets. It is realized by the management of the company that its success critically depends upon - improving the design process; reducing design turnaround time; improving product quality and field services; and reducing overall cost of manufacturing and service. All of these objectives are achievable through standardization of design and manufacturing techniques. It is important that new products are designed and integrated coherently. Manufacturing is optimally distributed on a global basis. Main sub-systems of the company's product, a transport refrigeration unit, include: Refrigerant, Compressor, Evaporator, Condenser, Throttling Device, Motive Power, Lube-oil system, Piping, Seals, Joints, Couplings, Control Systems, Insulation, and Structure. To have an idea of lack of standardization in the company, the degree of proliferation of parts in recent years is a reasonable indicator. During the recent three-year period, number of part master records grew from 191,000 to 236,000, number of product structure records grew from 865,000 to 1,068,000, and active manufacturing part numbers at the end of this threeyear period were 79,000.
Economic Viability of Component Management
3.
119
PROPOSED DECISION HIERARCHY LEVELS
Analysis of this company's operations suggests that product development decisions based on following three level hierarchy would be effective in responding to needs of the marketplace: 1. Standardization of modules for various sub-systems. Such decisions should be taken on a global market basis. 2. Capacity decisions for a particular product line for a specific market. 3. Control systems for keeping a transport refrigeration system dynamically balanced in changing environments. The basis for decisions at levels 1 and 2 should be economic optimization. Thermodynamic optimization consideration should dominate at level 3. Systems are usually designed for worst environmental conditions. Regulated controls are aimed at making units function in equilibrium in changing environments. These controls will usually imply a reduction of capacity, which is achieved either through sub-systems function on "on-off basis," or through "step down modulation." Techniques for reducing capacity and their energy implications play an important role in product design. From our knowledge about the company, it appears that a formalized level 1 does not exist. Introducing level 1 can be an important step towards higher productivity and efficiency on a global basis. We need to have best practice functionality for three groups of users Design engineers. Operations users, and Management within the enterprise: •
Design engineers to be able to quickly locate and select the optimal component for a new design from a central repository of existing parts, assemblies, and designs, enriched with technical and business attributes. • Operations users in procurement, component engineering, and manufacturing facilitate and dynamically manage information to guide design engineers to make the right choices up front in the product development process. • Management can easily set periodic goals and measure success on enterprise-wide strategic product development initiatives.
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ECONOMIC VERSUS THERMODYNAMIC OPTIMUM
A system is thermodynamically optimum if there are no exergy losses. According to the second law of thermodynamics, energy in one form is not completely convertible into other forms. Energy may be looked up as consisting of two parts: Exergy, is the energy in convertible forms; and Anergy, is the energy in non-convertible forms. The first law of thermodynamics states sum of exergy and anergy is constant, while the second law of thermodynamics states sum of exergy is not constant. An economically optimum design of thermodynamic systems in real life will have exergy losses because such a system will not necessarily be thermodynamically optimum. Criteria of optimization should be economic, and not thermodynamic. Economic optimization considers product and components' life cycles, so that company's capital investments and user's operational and maintenance costs are considered in design decisions. This leads to minimization of an objective function, which is the sum of amortized capital cost and annual operating and maintenance costs per unit.
5.
GENERAL MATHEMATICAL STATEMENT OF THE DESIGN PROBLEM
Variables affecting the design problem may be classified into response variables and independent variables, the latter being divided into two subcategories - exogenous and design variables. Response variables define the usual multi-dimensional objective function such as, quality variables, performance variables, etc. Exogenous variables are those, which can not be controlled, for instance operating condition, market or noise variables, whereas design variables are controllable. Design implies deciding on their nominal values and tolerances. A robust design implies picking design variables such that the system (in this case study, a transport refrigeration unit) is stable with respect to exogenous variables.
5.1
A-priori Planned Standardized Modules
Exogenous variables representing operating and market conditions vary over time and over space from one market to another. It will be meaningless to design a customized transport refrigeration unit for each point within the exogenous market (EM) variables space. Let us divide the system into
Economic Viability of Component Management
121
proper subsystems. Consider subsystem], Sj. For each subsystem j , the EM variables space should be partitioned into sub-regions. As an example, for subsystem j within EMj,^ a standardized module i denoted by Sj,^ would be the optimal standardized module. A total system should be synthesized out of these standardized modules. Some of the standardized modules already exist within our reservoir of designs. A few others would be added over time, as new markets are acquired. Some existing designs would be nonoptimal, which should be deleted.
5.2
Main Dimensions of the EM Variables Space
The principal dimensions of the EM variables space include the following: • Goods to be transported giving desired temperatures required (To). • Environmental variables Year-round ambient temperatures and humidity conditions etc., influencing selection of condensation temperature (Tc). • Transport conditions Road conditions, trailer sizes, loading and unloading times and facilities, operating hours per year giving size of the unit and needed structural strengths and insulation needs. • Motive Power Source - during transport and non-transport modes. • Information on costs, amortization factors, general labor rates, etc.
6.
A CONCEPTUAL FRAMEWORK FOR DRAWINGS RETRIEVAL SYSTEM
Entities responsible for developing the Drawings Retrieval System are: Product Design Engineers, as users of the retrieval system. Information Technology Engineers, as basic designers of the retrieval system in collaboration with Product Design Engineers. • Drawings Librarian, to meet design engineers' requests, once the system is operational.
• •
The proposed engineering drawings retrieval system is primarily aimed at promoting standardization on an a-priori planned basis. The first question to ask is, "How will the proposed system work?" The Product Design Engineer will send a request to the Drawings Librarian. The Drawings Librarian will try to satisfy the design engineer's request by providing a set
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Parts Management Models and Applications
of engineering drawings, similar to the subsystem the Product Design Engineer is planning to design. The next question is, "How does our environment differ from a general librarian meeting a general request?" Our domain is much smaller and very well defined. An efficient retrieval system can be designed, provided we can develop a common language for more precisely stating the Product Design Engineer's request, and the coding of drawings for retrieval by the Librarian (Marion, Rubinovich and Ham 1986; Mosier and Janaro 1990; Park and Lee 1998; Tandler 1993). The last question is, "Where is this common language going to come from?" We need to understand the design process. It is sequential involving conceiving, planning, designing, prototyping, testing, evaluating, and implementing. Three important steps in the design process are: 1. Defining relevant operating conditions and market variables for new products. 2. Calculating macro-engineering variables. 3. Transitioning from a macro design to a detailed product design. An optimization model (or a set of models) ideally should guide in executing steps 2 and 3 above. Information Technology engineers should obtain defining attributes for the coding of drawings for easy retrieval from the optimization model. It is important to control unnecessary design proliferation of components as new products are designed. This requires that design engineer is provided with a list of existing parts similar to the new part that is planned for design. New part should be designed, only if the Design Engineer certifies that none of the existing parts in the similar part class is a good substitute for the new proposed design. If the decision is taken to add a new part which obsoletes one or more of existing parts, then it should be recorded in the database. Gradually, dominated part(s) should be taken out of usage. A program or procedure will be required to reduce existing number of current parts and eliminating duplication of similar parts. The success of proposed design support function for variety control will depend upon our ability to group parts and retrieve these groups easily on the basis of their design similarities (Dangerfield and Morris 1991; Oh and Gravel 1986). Component management decision support software, such as "eDesign" (from Aspect Development, Inc., California) enables manufacturers in strategic product development through the use of preferred parts, designs and suppliers.
Economic Viability of Component Management 6.1
123
Model for Classifying Objects
There are two approaches for classification of objects: 1. Classification of objects directly by Experts on the basis of their similarity judgments. 2. Development of classification capabilities based on weighting of relevant attributes. Following steps are involved in planning for classification: • Identify types of objects in the system that needs to be classified. • Identify purposes, and define similar class for each purpose. • Identify attributes for objects and define their measurements. • Develop procedures for generation of similar classes for various purposes. It is important that planning for the development of classification schemes should be for the entire company's needs rather than using a piecemeal approach, taking one business function at a time (Arabic, Hubert and Soete 1996; Gordon 1981; McCarthy 1995; Park 1986). Approach 2 is subdivided into two types of classification models: (i) Principal component analysis based classification. Salient features of this technique include: • Defining new coordinates, whereby a fewer number of these can explain a sizeable fraction of variance in a given data. • Representing each object geometrically by a point in an n-dimensional space. The principal component analysis technique involves the rotation of coordinate axes to a new set of orthogonal coordinate axes, wherein each of the "n" original attributes is described in terms of the "n" new principal components. These components are uncorrelated. • Basis for classification of objects will be fewer components, instead of original "n" attributes, if these account for a large percentage of the total variance. (ii) Clustering algorithms based classification. There are two types of clustering algorithms - partitioning and hierarchical.
Parts Management Models and Applications
124
6.2
Test Case
A test sample of all fans of various types in the company was selected for grouping. Design based attributes for fans used in the classification are: number of blades, diameter of fan to the nearest inch, blade tip angle in degrees, direction of rotation, hub type and material. Principal component analysis revealed that attributes: material, hub-type, rotation, and pitch angle in that order will account for 85% of total variance of all attributes. Grouping based on these four attributes resulted in 20 groups. Next, KMEANS clustering algorithm was applied to the output of principal component analysis (which was hierarchical grouping of objects) (Gordon 1981; Spath 1980). KMEANS clustering algorithm minimizes intra distance within groups and inter distance between groups. The Design Engineer is contemplating to design a new fan. Feature vector for this fan is given as: Number of Blades 4
Diameter in inches 12"
Pitch angle
20^
Rotation Direction 1
HubType
2
Material
1
A set of similar fans within the existing set, which might be a suitable substitute for the contemplated fan is shown in Table 6-1. The Design Engineer uses expert judgment in making choice of a suitable substitute fan from the set of similar fans shown in Table 6-1.
Economic Viability of Component Management
125
Table 6-1. Set of fans similar to the contemplated fan 1 Number of Blades Given Fan A Similar Fans 4 4 4 4 4 4 4 4
1
4 4
Diameter in inches
Pitch Angle
Rotation Direction
Hub Type
12"
20°
1
2
12" 14" 14" 14" 14" IBIB" IB" 16" 22"
19° 16° 17° 18° 21° 21° 21° 22° 22° 27°
Material
3 2 3 2 3 3 3 2 2 3 Legend: 1 Clockwise 2 Counter clockwise
1 2 3 4 5
Split block Keyed Set Screw Pinned Belt Drive
1 Steel 2 Aluminum 3 Plastic
There are issues with appropriateness of the sets presented to the Design Engineer. Concern can be raised, if sizes of the set are too large. This is because giving larger sets for review will require more work for design engineers, whereas retrieving smaller sets will lead to a relaxed variety control. This prototype drawings retrieval system was developed using SAS statistical software to demonstrate the usefulness of component management information retrieval system for new product design.
7.
BENEFIT COST ANALYSIS OF DRAWINGS RETRIEVAL SYSTEM
The following section provides benefit cost analysis using data for the company's manufacturing operation to acquire and implement the proposed "cDesign" component management software.
126
7.1
Parts Management Models and Applications
Design Cost Savings
New designs per year = 2,000 (@ $3,000 per new design. This includes cost of design engineer and draftsman's time, computer time, and computer storage time) Design savings per year for following three, "reduction in part proliferation due to standardization" scenarios: @ 10% = (0.10)(2,000)($3,000) = $600,000 @ 20% = (0.20)(2,000)($3,000) = $1,200,000 @ 30% = (0.30)(2,000)($3,000) = $1,800,000
7.2
Warranty Cost Savings
It is assumed that there is a learning factor in product design. A design matures over 3 years. During first three years, there is a 20%) higher warranty cost. Average life of a design is 10 years. These assumptions were validated by the design engineering group. Warranty cost savings per year = (L- L') x Warranty cost per design per year average over 10 years where L is total number of new designs per year, L' is reduced number of new designs per year as a result of standardization project, m is number of years at a higher warranty rate, M is total hfe of a design. Current average warranty cost per year = $12,000,000 m = 3 years, and M = 10 years. Current number of total designs, N, in the system = 50,000. Number of stable designs =30,000. We assume that external failure rate is due to 20,000 designs. Number of designs at higher failure rate = (m/M)(Total Designs) = (3/10)(20,000) =6,000 Number of designs at mature failure rate = (Number of designs at external failure rate) - (Number of design at higher failure rate) =20,000-6,000=14,000
Economic Viability of" Component Management
127
Thus, 6,000 designs are less than 3 years old incurring external failures at 1.2 times the maturity failure rate; and 14,000 designs are older than 3 years. Let X be the warranty cost per design per year at maturity failure rate. 6,000 (1.2) X + 14,000 X = $ 12,000,000 X = $566 Average warranty cost per design per year (averaged over 10 years) = 1.2 X (m / M) + X [1- (m / M)] = $600 Annual savings per year due to fewer new designs introduced: @10% = (0.10)(2,000) ($600) = $120,000 @20% = (0.20)(2,000) ($600) = $240,000 @30% = (0.30)(2,000) ($600) = $360,000 Annual savings per year due to clearing of the backlog for an anticipated additional standardization of 15% of the 20,000 designs = (3,000) ($566) = $1.7 million
7.3
Ordering Cost Savings
In this study, the standard EOQ N-part inventory model is used for estimating average ordering cost and average cycle inventory cost per year which make up the total average inventory cost per year (Silver 1985). Let Vi, denotes the unit variable cost of part i; D„ the demand per year for part i; ^*, the projected demand per year for part i after standardization; Qj, the replenishment order quantity of part i, in units; r, the inventory carrying rate per year; and A, the ordering cost incurred with each replenishment, in dollars. Therefore, if we use the standard EOQ model for each part, we have
* l2ADi Qi = J V Vjr
(1)
128
Parts Management Models and Applications Now, average ordering cost per year
N Hi N w-r N rA / = Z ^ A = Z D A j T ^ = IJf^/5^ i=lQj i=l V^^Di i=lV 2
(2)
and average cycle inventory cost per year
- E(--)vir- Z J — — —--ZJ—VDiVi i=l ^ j=iv VjT 2 i^iV 2
(3)
After a careful review of existing design engineering practices in the company, a conservative estimate of standardization at 20% was used in the case study. It is assumed that standardization at 20% results in 20%) reduction from existing 30,000 total stable designs, that is, N' = 24,000. It is assumed that the total set of 20,000 parts covers 80% of demand. Reduction in ordering cost per year
r^y
N I
- ( / % ) ( Z V D [ ^
^ '^ ^
i=l
N [~r-ZVDiVi) i=l
(4)
where, annual carrying rate, r = 0.12; ordering cost per order, A= $100; N - 50,000; N' - 24,000; N
Annual demand in dollars before standardization = ZDj Vj = $8 million; i=l N'
and annual projected demand in dollars after standardization = ZDj'vj^ $20 i=l
million. 80% of annual demand in dollars before standardization = $6.4 million
Economic Viability of Component Management
129
80% of annual projected demand in dollars after standardization = $16 million Average annual demand in dollars per part before standardization = $6.4 million / 20,000 = $320 Average annual demand in dollars per part after standardization - $16 million / 20,000 - $800 that is, D,\, = $320, and D'lVi = $800 for each part i. N
Z Vom = (V320 )(50,000) = 894,427.15
(5)
i=l
N
SVD[VJ
S
Jy^
= (V800)(24,000)-678,822.51
= 2.4494897
(6)
(7)
Substituting values given in (5), (6), and (7) into (4) yields Ordering cost savings per year = $528,121.35 = $528,000
7.4
Cycle Inventory Cost Savings
Equation (4) also represents cycle inventory costs savings per year. Therefore, cycle inventory cost savings per year = $528,000 Total benefits or cost savings per year (@20% standardization^ = Design cost savings + Warranty cost savings + Ordering cost savings + Cycle inventory cost savings = $1,200,000 + ($240,000 + $1,700,000) + $528,000 + $528,000 = $4.2 million For economic justification of undertaking engineering projects, 10% minimum attractive rate of return was the cutoff point used by the company.
130
7.5
Parts Management Models and Applications
Benefits of 5 years discounted at 10% per year Present Worth = (3.7907) ($4.2 million) = $15.92 million
Cost of ''eDesign " Component Management System Estimated implementation cost = $5 million Benefit to Cost ratio = 15.92 / 5.0 = 3.18
8.
OTHER POTENTIAL APPLICATIONS AMENABLE TO CLASSIFICATION
A number of areas of opportunities identified in this company, where classification approach could be applied, include the following: 1. Simplifying operational management and promoting standardization. One of the objectives of grouping is seeking reduction in system's complexity, promoting standardization and procedures. Developing knowledge bases, whereby categorical decisions can be prescribed extensively, would eliminate the need to resolve recurring problems over and over again and reinvent already known knowledge. This would relieve operating managers of routine tasks. In probabilistic environments with sizeable uncertainty, categorical decisions may not be justified. Decision support systems can be provided to aid decisionmaking in probabilistic environments. 2. Supporting product design department in scheduling variety control. A variety control system similar to the one described in the case study for parts proliferation will eliminate acquisition of unnecessary tooling. 3. Supporting manufacturing department in a) Promoting group technology. Classification in this case will consider equivalence classes based on manufacturing process similarities. b) Promoting higher facility utilization. This will require categorize and reporting idle times on various equipment, namely, induced idle times due to bottlenecks, non-availability of parts, breakdowns. Diagnosis of various types of idle times can lead to timely corrective steps. c) Enhancing maintenance capabilities. A good classification of maintenance tasks can improve maintenance operations. Following broad categories of maintenance tasks were identified: • Scheduled preventive maintenance tasks, which have to be performed periodically.
Economic Viability of Component Management •
131
Unscheduled maintenance tasks resulting from scheduled inspections. • Unscheduled maintenance functions resulting from failures. Many of the maintenance tasks can be classified and better managed with respect to their scheduling and availability of supplies and parts. d) Seeking improvements in purchasing and inventory costs. A good coding scheme should avoid parts from having multiple codes as it results in split purchase orders and in stock-outs, even when inventories are present. The complexity of multi-part systems can be reduced by aggregating objects over different similar attributes such as, fast movers, slow movers, turnover rates, lead times, etc.
132
9.
Parts Management Models and Applications
CONCLUSION
This research case study provides a conceptual framework for "eDesign" component management decision support system for strategic product development in order to build a basis for its technical feasibility. An example of a leading transport refrigeration unit manufacturer is used to illustrate a three level decision making hierarchy with economic optimization for levels 1 and 2 representing standardization of system modules and capacity decisions for a product line respectively and thermodynamic optimization for level 3 representing control systems to keep the system dynamically balanced with changing environments. The principal objective of the study is to present a detailed economic justification for implementing such a system in a product development environment. The proposed component management system can be utilized and customized to support three levels of formalized standardization, facilitate in compressing time to market cycle for new and upgraded products and also control design proliferation. The study identifies other potential applications for classification.
Adapted from the paper by authors: Kumar, Sameer and Chandra, Charu, (2001), "Economic Viability of Component Management for a New Design - A Case Study", The Engineering Economist, Vol. 46, No. 3, pp. 205-219.
Chapter 7 MANUFACTURING OPERATIONS EFFECTIVENESS THROUGH KNOWLEDGE BASED DESIGN^
1.
INTRODUCTION
Increasing global competition, rapid technological development, customization and speed to market of products and services are driving firms to maintain complex, yet efficient manufacturing capabilities. A growing number of firms are becoming multinational enterprises in order to strategically position themselves to serve global markets with worldwide manufacturing operations. It is a dynamic business environment with fast changing market and consumer needs. These conditions have prompted manufacturers to design equipments to accommodate new products without expensive retooling. It has enabled them to move into new markets rapidly and leave just as quickly. These new markets impose demands for products to match specific consumer needs that require customizing products or even altering an entire product line. Facilities are now being utilized for new products, which enable manufacturers to create rapid prototypes in short duration. Flexible manufacturing is assisting firms to offer lower costs with faster turnaround time and better utilization of production facilities and equipment. Quality of products is more uniform and predictable with low wastage on scrap and rework. It is increasingly becoming evident to manufacturers that through integration, standardization and 133
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Parts Management Models and Applications
proceduralization there are tremendous opportunities for, (1) improvements in product quality, and material handling, and (2) reduction in product design time, manufacturing set-ups, and factory and office overheads. By organizing cumulative knowledge and expertise of the manufacturing enterprise to aid decision-making, knowledge bases can be catalysts for achieving these improvements (Anonymous 1999:93, Boisot and Griffiths 1999:662, Fisher 1999:6, Steinacher and Lattig 1999:65). The focus of this chapter is on classification as one of the tools for organizing knowledge bases for manufacturing operations. According to McCarthy (1995:37), "Classifications enhance knowledge and understanding and will enable predictions to be made about manufacturing system behavior." A discussion has been presented on how classification techniques can be employed for the purpose of knowledge representation to convert data into similar classes based on similarities. The chapter is organized as follows: • Outline the purpose of a knowledge base in decision-making for manufacturing operations through elaboration of the knowledge representation process; • Review manufacturing classifications to identify essential attributes of a knowledge base; • Describe a classification based methodology utilizing a KMEANS algorithm in organizing knowledge base for manufacturing operations; • Present an industrial case study based on application of the above methodology to a flexible manufacturing system at a leading transportation refrigeration unit manufacturer; • Identify potential applications of the proposed knowledge base development technique to improve productivity and efficiency in a manufacturing environment.
2.
THE PURPOSE OF A KNOWLEDGE BASE IN DECISION-MAKING
Developing a knowledge base means organizing firm's data so that required information can be retrieved easily and flexibly in readily usable formats for various operational management, planning and general problem solving activities. Figure 7-1 depicts the knowledge representation process described below.
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f
Envtronme "" "
" '
A%i>^iit^^m
'2 L
Knowledge Bas«
Erprrt Syslerris \Hmy'ii^V>A(<X'\A ^ '
D
r\
A Figure 7-1. Knowledge representation process
Explicit models are created and used to assist in the definition and resolution of decision situations (scenarios) that arise in the planning, operation, and co-ordination of activities during manufacturing operations. A model is an accumulated statement of decision-makers' collective knowledge about a system. A model utilizes a firm's memory, which is organized as data and / or knowledge base, and represents relationships among its variables. A firm's memory does not stay static and is continually updated. New knowledge is generated through information processing and with off- and on-line experimentation. Knowledge bases help in improving communication, quality of decisions and in providing firm wide integration. This is achieved through development of models that study specific behavior of the system under different environments of firm's manufacturing operations. Problem solving techniques are applied through design and implementation of algorithms to solve a model. Results of the model are analyzed in reference to domain specific problem and to make inferences and judgments about it under various decision scenarios. Thus, models for forecasting management, inventory management, production planning and
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Parts Management Models and Applications
control, operations scheduling address specific decision-making needs for various manufacturing operations. A forecasting model may be designed to address a specific manufacturing problem impacted by seasonality of products, for which a special forecasting algorithm is developed. This algorithm can examine relationships between various variables related to demand, inventory, capacity, etc. under different scenarios through experimental design. An important objective of a knowledge base is to facilitate standardization and relieve Management of routine decision-making tasks. Classification forms the basis for standardization, proceduralization, and automation of manufacturing operations. It has the potential for improving activities in design, maintenance, cellular manufacturing planning, and achieving simplification and standardization of processes, procedures and operations (Dove 1998:18, Inkpen 1998:223). Standards and procedures, when fully developed and adapted are assimilated as rules in a firm's knowledge base. Full scale implementation of a manufacturing knowledge base, first as a pilot, and eventually as an operational system is carried out through expert systems which capture the essence of decision-making environments, i.e., goals and objectives, courses of action, resources, constraints, technology and procedures. The evolution of knowledge bases occurs as decision-makers experiment with the models to seek improvements in operational systems.
3.
MANUFACTURING CLASSIFICATIONS IDENTIFY KNOWLEDGE BASE ATTRIBUTES
Differences within manufacturing systems are primarily due to operational characteristics, levels of technology and flow structures. Manufacturing classifications facilitate identification of attributes that help determine and understand behavior of a manufacturing system. This enables organizing knowledge for decision-making. Manufacturing classifications emphasize development of manufacturing systems based on, (a) similar technological and behavioral attributes, and (b) storage and retrieval of information to facilitate generalizations of manufacturing operations across multiple problem domains (McCarthy 1995:37). Manufacturing classifications have been performed on the basis of a variety of generic manufacturing attributes. A sampling of these is as follows:
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•
Operational objectives - Wild (1989) has defined following basic types of manufacturing firm according to their operating structure: 1) from stock, to stock, to customer; 2) from source, to stock, to customer; 3) from stock, direct to customer; 4) from source, direct to customer. • Operational flow structure can be classified into following: 1) flow lines; 2) group technology; 3) material conversion classification. • Materials flow types classification are: l)job; 2) batch; 3) one of a kind; 4) continuous. • Type of organization classification are: 1) process organization (process layout); 2) product organization (product layout); 3) group technology. One of the challenges in introducing manufacturing classification in firms is the difficulty of weaving a common thread across the organization. Integration and standardization are concepts that have relevance for the entire organization. Their role in developing a common organizational knowledge base utilizing manufacturing classifications is described below.
3.1
Integration
In a manufacturing set-up, integration is usually identified with Computer Integrated Manufacturing (CIM). Integration relates to technical and social issues confronting manufacturing organizations (O'Sullivan 1989). Technical integration comprises integration of equipment, data and information. Equipment information is concerned with customization of equipment. Data integration is concerned with communication between various sub-systems in the organization. Information integration relates data flowing through the system in order to exercise control over manufacturing processes and contribute to an effective management of resources. Social integration involves integration of people, ideas and the decision making process. Management integration involves integration of management philosophy in order to facilitate effective problem solving.
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Parts Management Models and Applications
System integration requires various functional groups to be integrated. User integration aims at integrating users within technical and social environments. One of the obstacles to integrated manufacturing is the fact that manufacturing systems are invariably run on an informal basis. In an informal system, information is used from isolated databases, developed in an ad-hoc manner for planning and decision-making functions. A formal system, however, is run on common data accessed from a common database. Integration within a firm is achievable through a common policy, a common action plan and most importantly, through shared information used in various decisions, being based on common knowledge bases (Kosanke et al. 1999:83, Wyderka 1999:16). Thus, formal systems are needed in firms. A CIM is a type of formal system.
3.2
Standardization
In a typical firm, decision-making is hierarchically distributed. Detailed decisions are implemented at lower levels within the framework of macro decisions made at higher levels. For the operational level, the goal is to achieve standardization and automation of operations, whereas for the strategic level, it is to outline policies for smooth functioning of operational activities. Achieving standardization in a manufacturing environment entails identifying commonalties within, (a) operations, (b) processes, and (c) services. Standardizing operations entails enforcement of common manufacturing strategies and techniques for similar operations, e.g., sheet metal fabrication operation performed at different locations may be based on a common methodology, while allowing flexibility to recognize unique needs of different markets. Similarly, process standardization should be carried out on a corporate basis, allowing flexibility to recognize differences in markets. In the sheet metal fabrication example, the process of shearing would require cuts made with the same geometry, stress and tolerances (Dooley et al. 1998:281). A knowledge base for a manufacturing enterprise should be developed to meet firm wide needs for standardization. Such a system should be developed bottom up within a top down planned design configuration. The development of the knowledge base will occur in incremental steps. One of the reasonable ways to schedule development is to select among current problems, maximize incremental benefits to cost ratio locally, if choices are
Manufacturing Operations Effectiveness
13 9
available, and undertake smaller projects initially. The optimal design would require a common database with preplanned tools to convert data into information, ready for use as input to various operational procedures and other decision support systems (Culpepper 1998:58, Methlie and Sprague 1985).
4.
CLASSIFICATION METHODOLOGY FOR ORGANISING KNOWLEDGE BASE
The proposed classification methodology emphasizes integration and standardization concepts for manufacturing operations described in the previous section. Guidelines involved in development of a knowledge base utilizing the proposed schemes are • Define potential functions to be supported; • Formulate decision processes; • Identify information needs for various functions; • Identify list of objects in the system that needs to be classified; • Identify attributes for various objects and defining their measurement; • Develop procedures for grouping of objects; • Define structure of the knowledge base; • Retrieval of knowledge. A discussion on above steps follows. Step 1. Define potential functions to be supported Planning the development of classification schemes should be done with total organizational needs in mind rather than using a piecemeal approach of taking one function at a time. Accordingly, the first step is to define detailed functions within each functional area. Step 2. Formulate decision processes This step represents the formulation of a decision situation by identification of problems, or rather opportunities for improvements in the current decision behavior. The problem requiring planning and decision-making is defined by identifying its elements in terms of needs and constraints. This is done, by capturing data on current decision-making process using techniques of interviewing, observation, questions and historical records (Sawaragi et al. 1987).
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Parts Management Models and Applications
Next, attributes of outcomes and alternative courses of action are identified. This is followed, by arranging objectives in their order of importance and presenting these to the decision-maker for evaluation. Methods such as Critical Success Factor (CSF) analysis are used that focus on identifying information needs from an organizational perspective. By linking decision-maker's personal goals to specific goals of the organization through factors that are critical for success, unambiguous interrelationships between factors and goals are established. This helps in focusing decisions for both primary (organizational) and secondary (decision-maker's personal) goals (Methlie and Sprague 1985). Through this exercise, a comparison is carried out of how decisions are currently made in relation to how these ought to be. Step 3. Identify information needs for various functions This step concerns identifying specific information needs for above functions and defining underlying similarities embedded within the needed information. The information base will be used by the decision-maker in analyzing alternative courses of action in the decision process. Step 4. Identify list of objects in the system that need to be classified All objects within the system should be identified. The term object is used in a generic sense. It includes all types of items such as, raw materials, parts, component, equipment, failures, idle times, etc. If within a set of objects, there is a hierarchical categorization, the identifying code should reflect this relationship among categories and subcategories. Also, objects have other characterizing attributes. An important decision concerns what portion of characteristic attributes should become a part of the identifying code. Sometimes, the intention is to classify objects straight away employing the identifying code. If numbers of categories within the classification being planned are not too many, then using identifying code for classification is appropriate. However, if numbers of categories are too many, then the identifying code will become unduly complicated. A tradeoff decision is involved between its simplification and being the basis for classification (Park and Lee 1998:17). Step 5. Identify attributes for various objects and defining their measurement Most classification schemes are attribute based. Attributes used in defining classes for a given purpose are called 'criterial' attributes. The number of criterial attributes for a class should be as few as possible. These should be highly discriminatory and not related to each other otherwise the
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measurement will be redundant. Criterial attributes for different purposes will be different. If the cost of misclassification is low, a reduction in their numbers is justified. Principal component analysis techniques are usually employed in searching for criterial attributes. Such a possibility implies that low dimensional hyperplanes can reasonably fit the data. The measurement of all attributes is in standardized units so that intra-distances between objects are not affected by a change of scale (Spath 1980). Step 6. Develop procedures for grouping of objects Clustering is grouping of objects on the basis of certain specified similarities. Mutual homogeneity within objects is implied with their being in a group. On the other hand, objects being in different groups are an indication of heterogeneity between them. The objective is to classify a given subset of N objects based on values of their attributes into n classes (the value of n is not fixed a-priori). One of the measures of effectiveness commonly used is the value of the ratio (R), of between and within variances. Variances between the means of the classes Average variance within classes A variety of cluster analysis techniques are available in the literature. Since yardsticks for measuring clustering performance are different for different purposes, there is no unique scheme that is optimal for all purposes (Gordon 1981, Arabic et al. 1996). Any clustering scheme involves basic steps shown in Figure 7-2.
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Given Objects and their Attributes
Define distance measure between any
two objects and mfor purposes
Define Clustering Techniques
Figure 7-2. Clustering methodology
Clustering techniques will be independent of the way distances are measured. There is no consensus either on the definition of distances or on the clustering techniques. A KMEANS cluster analysis technique is described below for classification purposes in a manufacturing environment. In the case study to follow in a later section, the KMEANS method is used for grouping of objects.
4.1
KMEANS Cluster analysis algorithm (Spath 1980)
The method starts with k clusters initially. It uses minimum inter-cluster distance around the mean as criterion. As an object is assigned to a cluster, means are updated. Objects are shuffled from one cluster to another minimizing the ratio R mentioned in the previous section. The process is continued until no more improvements in R can be realized.
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In this algorithm, only cases where the cluster Cj consists of at least one object are used. The initial assignment of the vectors Xi's representing m objects with ^attributes, to n clusters is given by the array p, and pi, the cluster number of the i*^ vector. Thus each pi must be such that l
m
m, m.
m J+ 1
x^-x.
(P, =r;j^r)
...(1)
then Xj is allocated to the cluster v for which the right hand side of inequality (1) is minimized, which means that Cr+Cy becomes m. m. •1
Xr-xJ
m.
+e,+m„ +1
Xv - X -
...(2)
(where Cj is the sum-of-squared distances of objects from respective means Xj of each cluster, and mj is the number of objects in cluster Cj) and accordingly, the total sum d = Ecj is reduced as much as possible. If this is not the case, the next object is considered. As many passes are performed through the objects i = l,...,m as are needed, until there are no more changes. Means Xj's are modified, each time one object is transferred from one cluster to another. Results generally depend on the sequence in which objects are considered. Any object Xi which forms a cluster on its own is not taken into account since with cluster of one object, the algorithm no longer functions. This often prevents very good or fully optimal partitions from being found, when m/n > 5. If m/n is large, this problem does not normally appear. The KMEANS algorithm is stepwise optimal. Step 7. Define structure of the knowledge base The knowledge base (Sol 1983) is a composite of database of quantitative and qualitative facts; set of algorithms of quantitative inferences. These algorithms are designed for extracting information from databases in useful formats. It is essential that the set of algorithms supports all levels
144
Parts Management Models and Applications
of the management hierarchy and is flexible to accommodate different styles of management with minimal changes. Despite all the flexibility desired, there are constraints on information that can be extracted from the knowledge base and this has to be planned on a-priori basis. Any information within the above planned set is extractable by employing appropriate operator (or algorithms) with the operand data within the databases. Figure 7-3 displays this process in concept.
Qpe^TfncL ^DataBase , Operator
t
o
\
)
Algorithms
Knowledge Base Figure 7-3. Knowledge acquisition process
Relating this concept to example discussed in an industrial case study, operand within data set is a set of fans, operator the KMEANS algorithm, and useful information class of fans, similar to the proposed design. Step 8. Retrieval of knowledge For retrieval, two basic categories of information usage may be identified for the total system. First, information that is generated and retrieved on demand by the user. Second information that is retrieved on a-priori basis and is stored in the knowledge base. The information in this category is of the type that is frequently used and requires effort for retrieval. In principle, storing too much of information on a-priori basis is avoided as it unduly complicates data updating.
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Expert system constitutes a very important part of information technologies. It is software that interfaces a decision support system with the user. It may provide decisions in a prescriptive form for lower levels and in a suggestive form for higher levels. Expert systems also interpret and update knowledge bases. The expert systems technology is starting to find usage in the manufacturing sector although it is far from being popular yet (Park and Lee 1998:17). As manufacturing gets more and more automated, human feedback will decrease. This requires finer classification and more prescriptive solutions. Expert systems technology holds out promise to fulfill this role. If properly designed, these systems will offer more consistent solutions than traditional systems. Expert systems have the potential of satisfying many routine and moderately complex decision situations within the manufacturing sector. However, their development is still in infancy compared to their potential applications in the manufacturing sector. The next section briefly outlines various models for classification of objects.
4.2
Models for Classifying Objects
There are two approaches for classification of objects: 1. Classification of objects directly by Experts on the basis of their similarity judgments. 2. Development of classification capabilities based on weighting of relevant attributes. Following steps are involved in planning for classification: • Identify types of objects in the system that need to be classified. • Identify purposes, and define similar class for each purpose. • Identify attributes for objects and define their measurements. • Develop procedures for generation of similar classes for various purposes. It is important that planning for the development of classification schemes should be for the entire firm's needs rather than using a piecemeal approach, taking one business function at a time. Approach 2 is subdivided into two types of classification models:
146
Parts Management Models and Applications
(i) Principal component analysis based classification. Salient features of this technique include: • Defining new coordinates, whereby a fewer number of these can explain a sizeable fraction of variance in a given data. • Representing each object geometrically by a point in an n-dimensional space. The principal component analysis technique involves the rotation of coordinate axes to a new set of orthogonal coordinate axes, wherein each of the "n" original attributes is described in terms of the "n" new principal components. These components are uncorrelated. • Basis for classification of objects will be fewer components, instead of original "n" attributes, if these account for a large percentage of the total variance. (ii) Clustering algorithms based classification. There are two types of clustering algorithms - partitioning and hierarchical. A number of books provide comprehensive details on various classification models (Spath 1980, Arabic et al. 1996, Gordon 1999).
5.
INDUSTRIAL CASE STUDY
Developing a firm wide integrated information system (knowledge bases and design support systems) is a large undertaking (Boisot and Griffiths 1999:662, Dvorak 1999:868). An industrial case study of implementing integrated manufacturing and design support systems, at a leading transport refrigeration unit manufacturer reveals, issues, problems and opportunities of designing advanced knowledge bases. The classification methodology described in the preceding section is utilized. For this case study two independent, yet, highly interconnected systems are described below: • A Flexible Manufacturing System, to provide production flexibility, and • A Design Support System for controlling proliferation of unnecessary new parts where reasonable substitutes are available within existing parts.
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5.1
147
Background for the Flexible Manufacturing System
The firm's Manufacturing Engineering units in Europe are designing refrigeration units along with manufacturing processes required by a unique market segment of Europe. Processes involve sheet metal fabrication for chassis and mechanical and electrical assemblies. In order to optimize the product and process design within constraints of marketability, costs and lead times, the Engineering department is obliged to seek solutions that facilitate manufacturability as far as possible within firm-wide standardized parameters. The test case pertains to the problem of controlling design proliferation in components and in finished refrigeration units. This problem falls in Design Engineering within the functional area of Engineering. Planning for production requires decisions at strategic, tactical, and operational levels. Strategic level decisions are aimed at reducing refrigerant emission to help support the corporate mission of alleviating environmental pollution. Tactical level decisions focus on areas whose impact is felt across functional boundaries, e.g., product design, product development, engineering change control, material planning, inspection and quality control, marketing, warranty management, procurement, and cost accounting. Operational level decisions are directed towards ensuring that the unit's engineering specifications match its proposed design. Interviews with decision-makers established that the current decision process focuses mostly on the operational level and it must be extended to reflect the unified needs of the total organization. Information needs of decision-makers were identified as falling under three categories: • Physical • Process • Functional The firm has been experiencing an enormous expansion in its global operations. Markets in Far East and Europe offer good growth prospects. In order to stay competitive, a more rational and formalized approach to product design, manufacturing operations and customer service has become essential. Co-operative designing and manufacturing are becoming critical to realize economies of scale and product integration. The proposed "enterprise manufacturing model" being implemented for producing a refrigeration unit is shown in Figure 7-4.
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148
Firm-Wide Knowledge Repository Corpor.3te Models Manufacturing Marketing
inventory'
Matenal Plannincj
Design Engineering
European Models Manufactur ing
UrMn^\ Oesrgn Planning j gngneenng
kti
Tool Library Mac-nine inierface Raw Matenal Cost Model
PartProqrarnrrang CAD/NC
Figure 7-4. An Enterprise Manufacturing Model for the case study
This enterprise model recognizes a common firm-wide knowledge repository to be used in each of the sub-models, e.g., manufacturing, marketing, inventory management, etc. for fostering integration in decision making throughout the firm. In the example under study, the Manufacturing Engineer specifies criterial attributes for physical, process and functional characteristics of the unit. The grouping being sought is on the basis of design similarity, in order to support the decision process and alleviate design proliferation either at the unit or component level. The starting point is the existing offerings of refrigeration units by the firm. The aim is to identify a unit similar to that, proposed to be designed. This process continues sequentially until the search has been narrowed down from a unit, to a component level.
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The next section reviews the design support system for components.
5.2
Background for the Design Support System
A Design Engineer planning to add a new part is supplied with a list of parts similar to the one being considered for addition. In order to determine the group to which the proposed design belongs, rules for associating it to one of the groups are needed. It seems reasonable to associate the proposed design to the group for which its distance to the mean of the group is minimum. In order for the Design Engineer to add the new part, it will have to be certified that none of the available similar parts is an acceptable substitute. The similarity needed in this code is the one based on design and functionally oriented features.
5.3
Test Case
The test case pertains to the problem domain of design proliferation in fans (a component in any standard transport refrigeration unit that the firm manufactures). This problem is a subset of Design Engineering, a part of the functional area of Engineering depicted in Figure 7-4. The family of parts considered in this case is fan. The firm currently uses 126 types of fans as components in its product range. These are grouped into similar classes based on their design-oriented attributes under three broad information categories identified in section 5.1. The grouping being sought is on the basis of design similarity, in order to support the decision process to alleviate the design proliferation of parts. When designing a fan for evaporator and condenser sections used in a transport refrigeration unit, the design engineer determines the amount of airflow needed and how much space is available to house the fan. The rotational speed of fan is determined from the amount of airflow required. For the evaporator section, the firm has been using 3600 revolutions per minute (rpm) speed fans and for the condenser section, 1200-rpm speed fans. The amount of space available helps in estimating the size of the fan. Also, amount of airflow needed and pressure drop in the evaporator or condenser section dictates the motor power rating for the fan. The "bearing type" has no impact on fan design, and it is picked depending upon operating environment considerations. The "bearing type" is dictated by the supplier of the motor and, if need be, bearings (size, seals, and grease) are modified to fit the operating environment. Typically, "drive type" has no direct influence on fan design, other than, if the fan is engine driven,
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Parts Management Models and Applications
material strength considerations, such as, type of material and its thickness come into play to deal with vibration concerns due to engine. For a given rotational speed and power rating for the new fan, a design engineer would like to ascertain values of other important key design attributes, such as, number of blades, diameter of fan, blade tip angle, rotation direction, hub type, and material. Hub is a device, which makes the transition between the fan blades and the shaft. Design based attributes for fans used in the classification are - number of blades, diameter of fan to the nearest inch, blade tip angle in degrees, direction of rotation, hub type and material. The selected attributes and their values and measurement are as shown in Table 7-1. Data in regards to objects and their critical attributes is arranged in the table given in Appendix A. The mean and standard deviation for attribute values are given in Table 7-2. Principal component analysis revealed that attributes such as material, hub-type, direction of rotation, and blade tip angle in that order account for 85% of total variance of all attributes.
Manufacturing Operations Effectiveness Table 7-1. Attributes for fans - value and measurement criteria Attribute
Measurement
Blades
Number
Diameter of Fan
Inches
Blade tip angle
Degrees
Rotation
Hub
Matenal
Value
Description of attribute values
1
11 to 15 degrees
2
16 to 20 degrees
3
21 to 25 degrees
4
26 to 30 degrees
5
31 to 35 degrees
6
36 to 40 degrees
7
41 to 45 degrees
8
46 to 50 degrees
Direction
Type
Type
1
Clockwise
2
Counter clockwise
1
Split block
2
Keyed
3
Set screw
4
Pinned
5
Belt drive
1
Steel
2
Aluminum
3
Plastic
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Parts Management Models and Applications
J 52
Table 7-2. Mean and standard deviation for categorical values of attributes
Attributes Number of blades Diameter of fan (inches) Blade tip angle (degrees) Rotation direction Hub type Material
Mean 4.4286 15.1190
Standard deviation 0.7422 4.0291
26.4127
7.26
1.5873 1.7619 1.0873
0.4943 0.8526 0.3103
The starting matrix is a heterogeneous group of objects with attributes measured on a separate scale. The Design Engineering had, (a) assigned to each attribute the level of importance, (b) determined arbitrarily size of the cluster and, (c) assigned each object to one of the cluster. The initial data was sorted hierarchically on the basis of level of importance of attributes. Attribute values from the initial matrix are transformed so as to have all the values represented on the same scale with standard deviation equal to 1 and mean equal to 0. This is done using the following transformation rule. (Xik - X.k) Xik
Sk
2 Sk
E(xik-X.k) i=\
m-1
where, Xik is the new standardized value for each attribute. Using this standardized data as input, the KMEANS clustering program was applied to the output of principal component analysis (which was hierarchical grouping of objects), which generated clusters of objects grouped into similar classes. In this example, the expert decided to group 126 types of fans into 28 clusters. The largest cluster is a group of 12 objects and the smallest has just one object in it. Cluster 1 make-up is depicted in Table 7-3. KMEANS clustering program minimizes intra distance within groups and inter distance between groups. Table in Appendix B shows intra subset and within subset heterogeneity and homogeneity. This table shows mean distances of various objects within a subset from their subset means
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and between various subset means on the new coordinate system based on principal components. The distance measure used is city block distance (Spath 1980, Gordon 1999). Consider that the Design Engineer is planning to design a new fan. The feature vector for this fan is [4 12 20 1 2 1], corresponding to the same attribute sequence as depicted in Table 7-1. The Design Engineer ought to review a set of similar fans that might be suitable substitutes for the fan under planning. In order to find out which set is closest to the feature vector of the proposed design, intra-distances are determined between the feature vector and vectors of group means for various groups. Table 7-3. Cluster T breakdown of fan types Attributes Objects
1—•
Number of
Diameter
Blade tip
Blades
of Fan
angle
Rotation
Hub Type
Material
(Fan Type)* 21
4
12
19
3
43
4
14
16
2
44
4
14
17
3
45
4
14
18
2
49
4
14
21
3
62
4
16
21
3
(B
4
16
21
3
66
4
16
22
2
61
4
16
22
2
82
4
22
27
3
The feature vector is identified as similar to cluster 1 of the original group. Besides examining the possibility of finding a suitable substitute for the proposed design in cluster 1, the Design Engineer is also advised to look at fan types 62, 63, and 66, 67 which are similar in their attributes. Perhaps, one fan within each of the above pairs can be eliminated from the current inventory of fans. The above analysis of clustering and classification of data was performed using SAS statistical software (from SAS Institute, Carey, North Carolina, USA) to demonstrate the usefulness of the proposed design support system for new product design.
154 6.
Parts Management Models and Applications CONCLUSION
Decision-making is information intensive that requires sharing of knowledge among various units within the organization. The extent to which information is communicated and used depends on how well knowledge is represented and organized. Knowledge is represented to follow the decision hierarchy - visions, concepts at strategic and tactical levels and guidelines at operational level. Representing knowledge is a complex task. Classification as a tool seems to hold out promise, but experiences of its application to manufacturing are still very limited. The automated factory of the future cannot be designed without elaborate knowledge bases. It is high time that firms make an earnest start in the development of knowledge bases.
Adapted from the paper by authors: Chandra, Charu and Kumar, Sameer, (2003), "Enhancing Manufacturing Operations Effectiveness Through Knowledge Based Design", Integrated Manufacturing Systems, Vol. 14, No. 3, pp. 278-292.
Chapter 8 SERVE YOUR SUPPLY CHAIN, NOT OPERATIONS^
1.
INTRODUCTION
This chapter describes a successfully completed proof of concept supply chain integration pilot project started in February 1997 and completed in August 1998 at Noramco, a manufacturing division of General Pump Corporation. Much has been written in the last decade to promote the abandonment of MRP II systems (Costanza 1998, Dibono 1997, Studebaker 1997, Gumaer, 1996, Stein 1996, Copacino 1996, Steudel and Desruelle 1992, Gunn 1987, Goldratt 1984) and encourage such alternative production planning and control practices as Lean Production, Demand Flow Management, Theory of Constraints and Synchronous Manufacturing. It presents results of research and implementation of such alternative methods of production planning and control. These alternative methods were evaluated for their ability to support products manufactured by Noramco. The main focus of this project effort was to establish characteristics of Noramco's supply chain and implement process changes to meet optimized requirements of their supply chain (Michel 1997, Poirier and Reiter 1996, andMaynard 1996).
155
156
1.1
Parts Management Models and Applications
Company Background And Operational Issues
General Pump Corporation was founded in 1982 as a privately owned distributor of high pressure positive displacement plunger pumps to the US marketplace. In 1985, it added an engineering staff to transition design changes requested by their customers to their vendors. This engineering staff also began to design products, specific to General Pump that complemented products offered through their distributorship. In 1988, the company acquired Noramco, a job shop manufacturing operation, which by 1994 became a captive manufacturing operation producing only General Pump products. The two most notable products were, high pressure spray tips (nozzles) and pump thermal protectors (PTP's). Noramco also became a custom assembler for General Pump's customers producing pump and accessory sub-assemblies and kits. In 1998, General Pump was acquired by Interpump Group, an Italian manufacturing company. Noramco guaranteed fast deliveries to its customers, while its suppliers continued to have long and inconsistent lead times causing former to carry a costly volume of inventory. In 1996 their average inventory turns were less than two. Even with this level of inventory, their delivery was less than satisfactory, since stock-outs were common and expediting was the norm rather than the exception. In 1996, General Pump installed a new Enterprise Resource Planning (ERP) system from Data Works Corporation. This system utilizes MRP II to plan and execute production of product and was set up to run on a multi plant platform, with General Pump being in one plant and Noramco in the other. The Forecasting was done at General Pump plant, whereas inter plant orders were processed to pull products from Noramco to General Pump. Production planning at General Pump was done in the master production schedule (MPS) module. This module used a frozen monthly requirement for 90-day period as input and did not utilize inventory or forecast when establishing demand. It used the larger of forecast or demand quantity for that period to create requirements. At that time, all products were expected to ship on the same day. Material requirements planning (MRP) was being run at the Noramco plant to process demand from interplant orders. However, finished goods inventory was kept in the General Pump plant, therefore, MRP was only netting work in process (WIP) and raw material (RM) inventory from actual requirements. If the product was already in stock at General Pump to cover this demand, MRP still generated production requirements. This system had many weaknesses one of which was that it did not respond to changes in the demand from what was forecast. When the
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demand was higher, it placed additional orders and when it was lower, it still ordered to forecast. Thus, it increased demand on manufacturing and raised inventory levels. Since, neither MPS nor MRP reports were netting finished goods inventory from actual requirements, it grew unchecked. An excess inventory report was used to track overstock conditions and cut back on future deliveries. Adjustments to the forecast generally allowed the system to respond, however, by that time Noramco was already missing deliveries. In order to correct the problem. General Pump tried to improve its forecasting process. It was not long, before the sales force was spending more time on forecasting, than visiting with customers. This resulted in even less accurate forecasts and the problems continued to worsen. Often demand not covered by the forecast was handled by placing more interplant orders. However, interplant orders were usually not canceled for products that experienced a drop in demand from expected and forecasts were also not adjusted down when the market declined. All forecast adjustments by the sales department were intended to increase demand. The result was an ever increasing demand on the manufacturing capacity. It became extremely difficult to differentiate the demand to satisfy customer orders, from the demand causing unnecessary inventory. In addition, lead times grew longer and the hot list grew bigger each day. Noramco was soon looked at as the worst supplier of General Pump. Noramco's product line consisted of a mixture of low sales volume with high product variety and high sales volume with low product variety. The efforts in manufacturing were geared towards quick response to customer requests. Shorter throughput times had been achieved through setup time reduction, automation, and better component availability with their vendors. However the MRP system did not utilize this improved throughput time. It was actually working against it since there was no visibility to what customers were actually buying. In order to gain control of the planning system and be able to respond to the changes in customer demand it meant manually overriding the system. At first a cross-functional team of representatives from customer service, manufacturing, purchasing and planning met each week to review the schedule, inventories and open orders. Work orders were canceled for all items that had inventory and no open orders within next four weeks. The team reviewed remaining work orders to assure that all sales orders were covered and these work orders were then prioritized. This soon reduced overload on manufacturing capacity but placed the company in a reactive rather than planning mode while deliveries improved negligibly. Early in 1997, executives at General Pump were asking following questions:
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Parts Management Models and Applications •
Was it a mistake for General Pump and other companies to invest in an MRP II system? • Were other manufacturing philosophies better for Noramco's products than MRP? • Could the MRP system be modified to use these new philosophies? • Should the MRP II system be replaced? The order fulfillment rate was less than 30 % of delivery commitments. The production requirements continued to go from feast to famine and financial performance continued to be poor. ERP system from Data Works offered a Kanban alternative to its MRP I planning tool. In order to improve delivery, Noramco piloted Kanban on their most repetitive product, "nozzles". However, most of their other products consisted of a large variety and complexity with little consistency in demand, therefore, limiting this alternative to the nozzle product. The company was unable to use Kanban with their key vendor due to their lengthy response time of 90 days. Noramco needed to use the MRP module for purchasing their components. One of the drawbacks with the planning system at Noramco was the inability for the MRP and Kanban modules to communicate, thus creating manual conversion from one system to the next (Millard 1998). Higher levels of inventory were required to maintain customer service.
2.
INFLUENCING THE MANUFACTURING ENVIRONMENT
The following section describes the effects of Acceleration Principle, process changes and total cost based systems on the manufacturing environment. The acceleration principle Jay Forester at MIT created a management training exercise in the 1950s called "The Beer Game" (Sherman 1997). It is designed to simulate how product and information flow through multi-echelon supply chains. The result of this simulation is what has been called the "Forester's Effect", or the acceleration principle. Simply stated, a ten percent change in the rate of sale at the retail level can result in a forty percent change in demand for the manufacturer. Figure 8-1 shows the results of the game using Noramco's supply chain lead times for a pressure wash nozzle.
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Figure 8-1. Illustrates the Inventory results from the Production Game performed at General Pump in January of 1997.
Customer orders were released into the system at a steady rate, changing only once after the third week. This slight change sent a ripple back through the supply chain. By the time it reached the stage of raw material supplier it was magnified by 400%. This ripple effect (the Acceleration Principle) had following effects on Noramco: Effect #1: For products that Noramco builds to order, periods of heavy backorders and periods of excess capacity were created. The manufacturer needed more capacity available to handle the surge in demand. Effect #2: For products that Noramco builds inventory on, a higher level of inventory was required to avoid stock-outs during the peak demand portion of the cycle. This resulted in higher inventory costs. Effect #3: Management's reaction to ups and downs in inventory, added to the size of humps. When inventory was high, reduction efforts drove the resulting downside lower. Then expediting efforts drove the resulting upside higher. Effect #4: Using history for forecasting assures the cycle would continue.
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The acceleration principle was a result of slow reaction times and batch processing from one organization to the next. Panic started an overreaction to the current state of inventory, increasing the amplitude of the effect. The effect became cyclical with periods of high backorders switching to periods of high inventory. The effect could be minimized, if retail sales information was shared throughout the supply line, at the same time reducing reaction time to respond to fluctuation in demand. However, it was appropriate to turn the focus on to your business organization within the supply chain. This is where most control can be exercised, and for which organization should be in place, prior to working on supply chain improvements. All business organizations involve two flows: material and information (Plossl, 1991). The production game was only exposing the top layer of problems manufacturing firms face today with managing these flows. Functional silos within each company affect the flow of information and materials in the same manner, as multi companies do in the supply chain. Batch processing of information creates acceleration principles within the organization. Distorted demand data and delayed information become commonplace, creating several other conditions. The first is a reaction typical of purchasing personnel and production planners. This reaction is referred to as the "Lead Time (or Safety Stock) Syndrome" (Plossl, 1991). This syndrome is illustrated in Figure 8-2. The effect continues to escalate and soon leads to the fatal mistake of increasing capacity based on this condition. This capacity increase is not without a corresponding cost increase.
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Figure 8-2. The Lead Time/ Safety Stock Syndrome
Eventually the overload is relieved since increased capacity floods the supply chain causing the second effect from distorted demand data, "The Inventory Reduction Syndrome" as shown in Figure 8-3. This effect is the result of the organization addressing excess inventory created by the first syndrome. Without process change these two syndromes feed each other in a continuous loop. Eventually, another silo is established in the organization specifically chartered to run promotions, targeted at reducing excess inventory with the hope of increasing market share. This action is equally as fatal as increasing capacity. The organization has now combined perpetual reductions in sales prices from the Inventory Reduction Syndrome with increasing production costs from the Lead Time Syndrome.
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Figure 8-3. Inventory Reduction Syndrome
In a growing market the combination of these two effects is consumed by the growth in demand. Companies can survive and even flourish during this growth period, in spite of the oscillating cycle to focus on reducing inventory during one time period, then expedite product regardless of cost during the next period. When the market experiences a plateau or drops off at this time, than the organization can spiral themselves right out of existence. Process changes Noramco's tendencies in 1996 were to implement process changes in textbook form. When implementing a Kanban system, the company followed the exact process successful in an unrelated industry. However the requirements of company's supply chain were not understood and the Kanban system fell short of expectation. The company could not afford the capacity investment required to respond to seasonal peeks using Kanban, nor could their vendors respond to erratic increases and decreases in demand. Noramco could no longer use MRP in the traditional form. They had to respond to actual demand rather than forecast and schedule constraints instead of final assemblies. The company needed a different approach. They changed their focus to understanding the needs of their supply chain and fitting their processes to those needs. They also had to find solutions which could be supported by limited capital financing and little change in their suppliers' and customers' practices.
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Total cost based systems The traditional standard cost system approaches are still used by most US manufacturers today. In such a system direct labor drives costs which promotes cost reduction efforts focused in isolation. In most cases, overhead and material costs are a significant portion of the product cost. Costing decisions, based on the traditional cost system often spread higher overhead costs to fewer direct labor hours without synchronizing total output of the plant with total demand. The system encourages optimization of cycle times and volumes making it virtually impossible for the organization to maintain flexibility and small lot sizes, thus creating minimum order quantities which in turn creates ever higher overhead costs (Umble et al, 1990). The only exception to this condition is if the cost reductions provide an increase in production supported by an equivalent increase in demand. Traditional cost systems use an established value for both efficiency and utilization. The former being the ratio of standard hours eatned and actual hours consumed while the latter is a measure of how intensively a resource is being used (direct time charged versus clock time scheduled). They suggest that higher the utilization and efficiency, lower the part cost which uses the resource. Goldratt (1984, 1986) perhaps was the first to argue that using these measures to evaluate manufacturing performance is actually causing companies to lose money. The use of utilization and efficiency measures encourage actions that adversely affect overall performance of the plant. These measures encourage managers to concentrate more on needs of manufacturing operations than on needs of customers. Conventional executive wisdom maintains that expensive machinery should never be idle. This wisdom consumes capacity with unwanted product. The high utilization of capacity leads to poor response times. Unresponsiveness to changes in demand feeds lead time and inventory reduction syndromes, thus leading to poor profit margins. Goldratt (1986) provided an easy to apply method of focusing on total cost based on organizations changing to three basic performance measurements that should reflect such critical functions as, sale of finished goods, purchase of raw materials, and transformation of materials into finished goods. These measurements include: throughput (revenue generated by the firm through sales, over a specific period of time), inventory (investment in materials that the firm intends to sell), and operating expense (investment by the firm to convert inventory into throughput over a specific period of time). Each measurement has a different effect to the bottom line. An increase in throughput has a direct increase to the bottom line. Decreases in inventory have an indirect increase to the bottom line through operating
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expense reduction. Finally, operating expense reductions directly increase the bottom line. Decisions evaluated with these simple measurements provide direct impact to the profitability of the company. The need to measure the effectiveness of manufacturing processes then fall into two categories: operating cost control and manufacturing planning effectiveness. Operating cost control can be measured by productivity. Productivity is measured as the output at cost, divided by wages and salaries. Goldratt suggests measuring manufacturing planning effectiveness through inventory (measured in turns). This is a result of finishing manufacturing early and late shipments in dollars, which is a consequence of manufacturing the product too late. Another important measure is the throughput time. This is the time to convert inventory to actual sales. Shorter throughput time provides better delivery potential. Throughput time to be effective must end with the actual sale of the product. Simply pushing inventory to another functional area is also contrary to goals of the company. An example of this is manufacturing, moving product from WIP to finished goods. The finished goods now become someone else's inventory. This event is not desirable because of what Plossl (1991) calls value subtracting, a loss of material value from processing due to loss of flexibility. The inventory should be maintained in the location, where it is most flexible, and yet be easily convertible into product when the customer requires it.
3.
NORAMCO'S SUPPLY CHAIN
The following section describes Noramco's supply chain. Figure 8-4 shows an information and product flow diagram of company's total supply chain linking immediate suppliers and customers. This flow diagram is further broken out to represent the supply chains for the top four product lines at Noramco: Modified Product, Nozzles, PTP (the main protector product) and Chemical Injector (one of the main accessory products).
Serve Your Supply Chain, Not Operations 30 Days
_DnBctShip_ 25 days
Italian Rjnrps 35 Days
165 OEM Consumer P/W 14 Days
Dealers/ Dstributor
Stock 10 Days lOcJays Fotgngs 60 Days Italian Axessories 40 Cays 5Davs
RM 10 Days
25 days
5 days
OEM GonTrerdal P/W 14 Days
25dayd
GP IDay
Scfeys Iday
ODays
OEM car V\teh 90 Days
Noramco 14 Days
M
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5 days
Molded Rastic 60 Days 25 days
Machine Barks 10 Days
Sdaysi
-Same d a y OEM Industrial 60 Days
Sub Contractor 65 Days
Dealer/ Dstributer
Estimated Supply Chain Inventory
Total
Inventory
$5,200,000
$7,800,000
$5,200,000
$7,800,000
$26,000,000
Cost of Inventory
$ 89,180
$191,100
$728,000
$1,560,000
$2,568,100
Figure 8-4. Represents the supply chain model for Noramco.
The supply side for the company consisted of nine groupings of suppliers. Eight of these were direct suppliers. For the purpose of simplifying this study, it was elected to only show the main supply chain link for the overall supply chain. Extended supply chains are provided for individual product lines. The remaining supplier is General Pump (GP). All of the non-Noramco components present in modified products were requisitioned from General Pump, essentially, a supplier as much as a customer. On the demand side all of Noramco's products were distributed through General Pump. General Pump distributed to original equipment manufacturers (OEM's) that provided pressure-washing equipment to retailers. This segment consisted of mainly four channels: Consumer, Commercial, Car Wash and Industrial. Each of these segments then sold their products through retailers, contractors or distributors.
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Noramco's total supply chain appeared complex. Efforts required to meet the needs of the nozzle supply chain in Figure 8-5 were different from the needs to satisfy the accessory supply chain. The individual supply chains were less complex and allowed to individualize supply chain requirements.
Paper IVf III 90 Days
Resin Supplier 60 Days
- 5 days -
Packaging 30 Days
- 5 days -
Molded Hastic 30 Days
-25 days -
2 days
—»|
Bar Stock Distributer 10 Days
-•I
}ar Stock Distributer 10 Days
5 days Steel Mill! 90 Days
Noramco 14 Days
Sub Contractor 20 Days 5 days
I - 5 days -
Machine Blanks 10 Days
-Same Day
OEM Consumer P/W 14 Days
Dealers/ Distributor 10 days
5d lys
' GP 1 Day
GEM Commercial P/W 14 Days
Retailer
OEM Car Wash 90 Days
Contractor
OEM Industrial 60 Days
Dealer/ Distributer
Consumer
5 days
Figure 8-5. Represents the supply chain for nozzles only.
Supply chain inventory Adequate information was not available on the total amount of inventory in the supply chain. After reviewing the supply chain some conclusions on where the inventory was stored in the pipeline could be drawn. Noramco's suppliers were typically building to order. They had small amounts of inventory in raw materials. The bar stock used by Noramco was purchased from a local distributor. Their inventory was large but served many supply chains. For this study it was assumed that the suppliers carried one month's usage for the company.
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Since most of Noramco's components were built to order with lead times that exceeded what the it's customers would accept, Noramco had to carry inventory to meet their customers' demands. Likewise inventory was also held at the original equipment manufactures and retailers to meet their customers demand. The carrying cost at each location for $100,000 worth of final product can be calculated producing following results: (assuming 20 % annual carrying cost and 30 % markup at each link in the chain) Retailer's cost ($100,000 x .2) = $ 20,000 (1 turn) OEM's Cost ($ 70,000 x .2) = $ 14,000 (1 turn) Distributor's Cost ($ (49,000/4) x .2) = $ 2,450 (4 turns) Manufacturer's Cost ($ (34,300/4) x .2) = $ 1,715 (4 turns) This example illustrates benefits of carrying the inventory as far upstream as possible. This also illustrates the advantage to the retailer that consignment inventory managed by the distributor offers. The percentage of inventory carried at each location was about 30% at the retailer's, 20% at the OEM's, 30% at the distributor's and 20% at the manufacturer's. The cost of inventory in the whole system is $9,535 for every $100,000 of sales or 9.5 percent. The emphasis should be to optimize the number of turns in the system, since it has the greatest effect on reducing carrying costs. Figure 8-4 shows the estimated amount of inventory in the system based on the above assumptions. Noramco inventory Noramco's highest level of inventory at the beginning of 1997 was double that of annual cost of goods sold for nozzles in 1996. It only turned half of their nozzle inventory in 1996. Other product lines performed better than nozzles. The nozzle product line was chosen for the pilot study because of their significant inventory level and simplicity of the supply chain. Understanding the flow of information and materials through the supply chains helped identify where the waste was in Noramco's systems. The next step was to evaluate process changes that would eliminate this waste. Product analysis It was important to understand Noramco's products and their individual supply chains in order to identify opportunities to improve the information and material flows through such chains. Figure 8-6 represents a Pareto chart of sales by products. The modifled product line provided highest level of sales in 1997. The modified product is the assembly of pressure wash components such as a pump, unloader, hose, gun, lance and the safety
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devices. The product was then set to customers' operating performance specifications. This product line was not very stable. The ultimate goal of offering these assembly services was to enhance sales of the actual Noramco products. Historically, customers assembled products themselves when their volume justified investing in their own equipment and as a result life cycles of the modified products were very short. Some customers acquired capabilities to make the assemblies in house they continued to buy the individual components made by Noramco. Other customers preferred to purchase a complete unit ready to install on a cart with a power unit as they believed it kept their overheads low and made them more competitive. 1st Half 1997
• 1997 Sales... i] 1997 YTD Profit
Modified Product
Nozzles
Parts and Kits
Figure 8-6. Represents the product sales in order of volume.
The second highest level of sales in 1997 came from Noramco's nozzle product line. This product was unique to the company and it made one of the components while purchasing others. There were one or two purchased components depending on specific product design. The assembly was done at Noramco. Historically the lead time on all the components was 90 days. It had a high level of sales and was the product line that required the most activity to fulfill orders. The repair parts and kits provided third highest level of sales which were sold through the OEM's to be used on their assembly line or sold at the retail
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level. These kits contained Noramco as well as other manufacturers' products and allowed their customers to minimize the number of components purchased by them. The remaining products were all Noramco specific products sold as components. These products consisted of three categories: Protector devices (PTP's and Safety Valves), Pumps and Accessories (Viper, Chemical Injectors. Etc.).
4.
THE TRANSFORMATION OF NORAMCO'S SUPPLY CHAIN
The following section describes the impact of integration and synchronization of activities onNoramco's supply chain.
4.1
Waste Reduction
Lean production focuses on the eliminating of waste throughout the organization (Womack 1996). As the first step to eliminate waste generated in the order fulfillment process, an information and materials flow diagram was developed for General Pump and Noramco. A cross-functional team analyzed the process steps and determined whether they added value to their customers. It was not surprising that only 15% of the activities being performed actually added value to the process. The non-value adding activities were targets for improvement or elimination. Noramco continued to use this team approach to identify and implement the process improvements to their nozzle line. They soon determined that the ERP system had to be re-implemented using only one plant. The goal was to combine the information into a common database so that MPS and MRP could be run using actual requirements by netting inventory from demand. The frozen period was reduced to one week so changes in demand would be reflected within a week's time. This change took effect on August 1, 1997. This same team continued to work on other targeted waste even after the reimplementation was complete. The process improvements were completed by September of 1997. The flow diagram of the current order fulfillment and planning processes for nozzles is shown in Figure 8-7. Twenty six non-value added steps were eliminated from the process since January of 1997.
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Parts Management Models and Applications Order Fullfilment
Figure 8-7. Represents the process flow for fulfilling orders after the changes in 1997
4.2
Forecasting Process
The nozzles were perishable components which were not customer specific. There were 264 different varieties of nozzles and although the gross sales were fairly predictable, the actual usage by part was not. The demand for nozzle product was seasonal and most of this product was sold during the construction months of summer. However the production level had to be maintained year round since Noramco was limited by its capacity. For these reasons the team implemented an accurate response process
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similar to the one used by Obermeyer (Fisher et al, 1994). This process enabled the company to predict the probability of sales by nozzle and utilized enough of its capacity during the off-season while using the available capacity during the season to respond to actual demand. The nozzle and the modified products did not fit the same forecasting and demand conditions. Modified products were customer specific assemblies. The risk of carrying inventory was much higher for modified products than it was for nozzles requiring a much different approach. The approach Noramco implemented was to pull production planning from actual assembly line consumption at the customer. Noramco approached its two biggest customers and asked them to provide monthly updates of their production schedule and inventory levels. Customer cooperation was even higher than expected. Noramco guaranteed an agreed upon level of inventory to meet their schedule. If they did not need to make that product, Noramco would carry the inventory into the next month. If they did take the product, Noramco would replace it. This worked like a Kanban system but Noramco used actual consumption to determine the lot size instead of the normal card system. Noramco called it their SO-WO (sales order to work order) process. At first they used an e-mail generated by the order entry representative to the manufacturing planner. The planner then entered a work order to replace the inventory being consumed. This process was later automated to let the order entry person actually release a work order from the sales order, even though the sales order would be filled by finished goods inventory. Supplier relationships Nozzle products provided a significant opportunity to improve Noramco's supplier relationship. There were only two suppliers and the relationship between them and the suppliers were ripe to introduce a partnering approach. The program was presented to the suppliers in May of 1997. The first step was to discuss the intentions and establish goals for the partnering program. A supplier of injection molded component made the same component in four different colors. This supplier was able to work off a blanket order with monthly releases. It appeared to be the best solution with this supplier. They were able to manage their production schedule and inventory without being forced to respond to fixed lead time orders. They could take advantage of setup and run efficiencies with this process. Another supplier provided 66 different parts. These parts were not as predictable and both the vendor and Noramco were suffering from too much of the wrong inventory. The approach used here was similar to the process
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put in place with the modified products customers. Only this time Noramco shared monthly forecasting, production scheduling and inventory amount with the vendor. The vendor in turn shared its inventory condition and production schedule to Noramco. The changes discussed to this point had been to improve the information and material flow to and from Noramco. These changes would not accomplish much without improving the process of planning and carrying out production at Noramco. The process being used in 1996, and early 1997 was too unstable to provide consistent information to Noramco's vendors thus jeopardizing the programs with both vendors and customers. Process and capacity analysis Noramco's production processes and flow for nozzles are shown in Figure 8-8. The processes consisted of two acme screw machines each capable of making 2,000 parts per day. Noramco's supplier had the capacity to machine the inserts at a rate of 10,000 per day. Finally the assembly process could assemble 8,000 nozzles per day. The MRP process scheduled the product assemblies. Thus the lead time and commitments were based on the 8,000 nozzles per day output capabilities of the final assembly process. The lead time was based on the total time to order material from the vendor, machine the components and assemble the final product. This lead time totaled 90 days.
•
Material Supplier
Q Body 2000 day Assembly 8000 per day
M, S, F Body's 2,000 day
i i
Insert 10,000 per day
Protectors 50,000 per day
Figure 8-8. Represents the nozzle product process flow
Two major flaws were present in the existing planning process. One, the 90 day lead time would require an unacceptable level of inventory to meet the actual demand during the season. Two, the planning rate of 8,000
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nozzles a day could not be achieved when the system constraint was 4,000 nozzles per day. It is known that throughput is equal to the output of the constraint (Goldratt, 1984). Therefore, the highest level of production would not exceed 2,000 Q nozzles per day and 2,000 of either M, S or F style nozzles per day. Inventory in finished and semi-finished forms One of the biggest mistakes Noramco made in the past was to produce finished goods based on forecast. This led to producing parts that were or were not selling. Once assembled, the insert, body and deflector were no longer capable of being sold in any other product configuration. This caused disassembling some finished goods to meet an unexpected customer order for another assembly, that used the same component not in stock. The safety stock syndrome led to high levels of safety stocks and surges in capacity requirements. The lead time to assemble the finished products was less than a day. Noramco's assembly capacity far exceeded the demand. To remedy this condition, inventory was maintained in semi-finished and finished forms for maximum flexibility and delivery. Each component of a nozzle could be used in multiple products. Realizing this fact, it made sense to keep the inventory in components and not finished goods to improve Noramco's response to changes in demand. However, it was not that simple. The first issue was that the sales force felt extremely uncomfortable when they did not see a large quantity of finished goods inventory. How could they promise delivery, if it was not in stock? The second issue was that the orders would come in sizes of 50,000 pieces. Noramco had not yet impressed upon its customers to more frequently place orders in smaller quantities. Management decided to pursue it anyway and felt that with the correct scheduling process the finished goods inventory would stabilize at the correct level to eliminate the sales group's concerns. Scheduling process A great deal of criticism has been targeted at MRP II recently, largely because of three reasons: The MRP II and ERP cost accounting systems focus on manufacturing efficiency instead of synchronizing manufacturing with demand. It puts production ahead of customers which leads to higher inventory, manufacturing inefficiencies and poor quality goods and services (Dibono 1997). MRP II and ERP cannot plan, execute and redirect manufacturing processes in real time (Gumaer, 1996). They use batch processing updates
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that are slow to reflect change. The system pushes the product through the plant, using the finished assembly schedule and standard lead times to plan components. The system is slow to react to changes in customer demand. MRP II and ERP use the infinite capacity model often creating overcapacity conditions which encourage large buffer stocks and lead times. The following alternative methods of production scheduling were investigated to make up for the limitations of MRP. Upgrade MRP to use Finite Requirements Planning (FRP) or Manufacturing Executive Systems (MES) (Fulcher 1997). Implement Kanban and Lean Production (Womack 1990, 1996 and Millard 1998). Apply Drum Buffer Rope (DBR) and Theory of Constraints (TOC) (Goldratt 1984, 1986, Gardiner, Blackstone and Gardiner 1994, and Umbleetal 1990). Implement Demand Flow Manufacturing (DFM) (Dibono 1997, Hase 1997). Apply Synchronous Manufacturing (Grasson 1998, Slater 1998, Stein 1996, Copacino 1996, Smith 1994, and Umble et al 1990,). No standard process could fit the requirements to schedule nozzles. The MRP process resulted in the delivery and inventory problems discussed earlier. The Kanban process could not respond to extreme changes in demand. Noramco could not increase its capacity levels to extremes experienced in actual sales. It needed to capitalize on the accurate forecast process in order to produce product during the off season. Combining the accurate forecast and the MRP process together works well during this time. During the period from October to February, constraint capacity was scheduled to run components. A fifty percent forecast accuracy was used to determine the estimated variability in annual volume. Final assembly was scheduled to target the level of inventory that would be sure to sell in the following year. MRP was run off this final assembly schedule to order vendor product during this time and also free up their capacity during the season. During the season from March through September, Noramco switched the planning system to drive off actual demand trends. A process was established to analyze sales for the previous month. These results were then fed back into the planning system. MRP was still used to release shipments for Noramco's suppliers and schedule the constraints, but actual assembly was driven off demand much like a build to order with a shipping buffer. The schedule was based on replacing the actual amount sold. In order to accomplish this, Noramco implemented a process referred to as the SO-WO
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(sales order to work order). When a sales order was released, it automatically established a work order to replace the product sold. The rate of production was set by the constraints to be 4,000 nozzles per day. In 1998, the level of demand exceeded constraint capacity. Noramco responded by applying Goldratt's Theory of Constraints. First, it subordinated all activities to the constraint minimizing downtime and running through breaks. All overtime was focused on the constraint. Finally, in order to meet demand they outsourced some production to offload the constraint. In order to achieve best results from this action, Noramco provided the first set of tooling and the process instructions for the vendor. Purchasing these components increased Noramco's material costs by 30 percent. However, the level of additional throughput dollars it provided was more than double the increased material costs, thus creating a positive impact on total profit. As discussed earlier, modified products were now being scheduled by actual consumption as well using the SO-WO process. The only issue that needed to be addressed was how to assure correct inventory of components. The decision was to continue to use the MRP process plan components, thus creating a highbred system. In order to use MRP, the system required some changes. The first change was to eliminate the frozen period. This allowed the system to react to actual demand. The other step was to eliminate forecasts since the expected demand was given to Noramco by its customers. The company also set up buffer stocks of components prior to assembly. It would have been preferred to use buffer time instead of stock but its system was not yet able to accommodate this condition. Management was concerned however that work in process inventory would increase. However, as was the case with nozzles, modified products also used the same components in multiple assemblies. The effect was the production inventory did not increase at all but actually was declining (see Figure 10). Organizational issues The flow of information could no longer be batch processed through the organization. In August of 1997, the MRP II system was re-implemented to a single plant. All functional departments shared the same data base and sales, production planning and inventory systems were linked together. The task of order entry now played a bigger role in production planning. Training was required to get customer service personnel capable of performing this task. The system was set up to flow with a minimum number of steps in order to eliminate batch processing of information.
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Where batch processing of information could not be eliminated, the frequency was increased to simulate continuous flow. Sales personnel needed to work with customers to change their buying habits in order to minimize the Acceleration Principle. Purchasing changed from the normal reviewing of reports, getting quotes and placing orders for these products. It now focused on sharing information and continuous improvement concerning supplier's delivery and costs. Noramco's management required a change in thinking about equipment utilization, efficiencies and inventory management. At the same time, cost accounting must change its approach to focus on and measure total costs. If the standard costing and performance measuring systems would have been used to make the decisions during this pilot, most of the actions taken to increase throughput would have been avoided.
5.
RESULTS FROM THE PILOT PROJECT
The following section outlines the contributions made by the pilot study to Noramco's and its trading partners operations.
5.1
A New Beginning
Faced with poor financial performance and declining product sales in 1996, Noramco either had to change the way it operated, or soon be out of business. As described earlier, it put great efforts in improving its condition and also made a large investment in a new Enterprise Resource Planning (ERP) system. However, its sales decline continued into 1997. The problem was not the lack of efforts exerted by Noramco's associates, but with its systems. Noramco's efforts were put toward optimizing the manufacturing environment to achieve maximum efficiency and reduced variances. It was not synchronizing its efforts with the needs of their supply chain. Noramco changed to focusing on increasing its throughput while maintaining existing operating and material costs. Today, Noramco has been transformed into a major profit contributing division of General Pump. Although, General Pump has been experiencing a downsizing of its main market segment and distributed product line, Noramco's delivery of nozzle product continues to set the pace in the market. This delivery capability combined with fair pricing is providing a continuous flow of new customers. At the same time, its profitability
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continues to trend upward, as a result of lower operating and inventory expenses. Figure 8-9 shows the profit trends since 1996.
Noramco Monthly
$0
Profits
Ja Fe M Ap M Ju Ju Au Se Oc No De Ja Fe M Ap M Ju Jul Au Se Oc No De n- b- ar- r- ay n- I- g- p- t- v- c- n- b ar- r- ay n- - g- p- t- v- c97 97 97 97 97 97 97 97 97 97 97 97 98 98 98 98 98 98 98 98 98 98 98 98 - Profit
Figure 8-9. Noramco's Nozzle Profit Trend
Process changes have fundamentally improved the way Noramco operates today. It is no longer experiencing the cycle from safety stock to inventory reduction syndromes. Though the demand continues to come to Noramco in wave patterns, it is successfully minimizing the amplitude of this wave and decreasing its effect on downstream suppliers. The key to operational improvements was to simultaneously use bits and pieces of lean production practices such as Kanban, Drum, Buffer, Rope (DBR), Theory Of Constraints (TOC) and Demand Flow Technology (DFT) that fit the supply chain to achieve continuous flow of products. Noramco made following changes to their production scheduling processes. They implemented the accurate forecasting process. This allowed Noramco to utilize their excess capacity in the off season building product, without building the wrong inventory. They used the constraint in the process to establish the production rate and maintained inventory where it is most flexible without compromising response time. Noramco made changes to MRP programs to schedule constraints and respond to demand trends and
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used T, I, and OE to make decisions, while focusing on achieving maximum throughput not minimizing throughput time and creating long term partnership arrangements with suppliers. This allowed Noramco to share forecasting information, production schedules, inventory information and jointly work on improvements to both total cost and delivery. Finally, they streamlined the information flow by establishing common database, reducing and eliminating batch processes and eliminating any wasted efforts. The existing production processes for nozzles changed depending on the season. During the season of high sales the assembly was based on actual demand. The planning was based on the output of constraints. The priority given to schedule the assembly process was to fill backorders, followed by open orders, and if there was any constraint capacity left, it was used to built inventory of finished goods in order of highest percentage of sales for the previous month. During the off season, the constraint product was produced at full capacity. Inventory was accumulated on this product and used to extend Noramco's capacity to 8000 units per day, when backorders and non-filled future orders exhausted the capacity. If all three conditions were met: no back orders, no unfilled open orders and all previous months' sales had been replenished; then no product was assembled. As already stated earlier, the revised MRP system was used to schedule constraints and release purchase parts. Among modifications included: frozen periods were reduced to zero, relevant data files were updated every night, and the forecast driving the MRP system was updated monthly, instead of annually to reflect changing demand trends for total sales and product mix. During months when sales were slow (the off season), MRP was triggered by the accurate forecasting process, instead of recent sales. Production was still scheduled at constraints. During this time, assembly activity was only used to replenish finished goods inventory of products being sold. The inventory was progressively built between the constraint and assembly operations. This philosophy did not facilitate maintaining low work in process and reducing throughput times. However, in Noramco's case where capacity was constrained to less than average sales during the season, efforts to increase this capacity resulted in a higher quality and delivery risk than increasing work in process (WIP) inventory. As shown in Figure 8-10, the WIP inventory actually declined. This was an unexpected result for Noramco. The make-up of the WIP was analyzed in an attempt to explain this result. It was found that less efforts were being put forth in building non-constraint inventories, therefore, reducing the overall
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inventory, which enabled Noramco to avoid the Throughput Time Trap (TTT). It was acceptable to use throughput time to identify and eliminate waste in the system. However, the use of Throughput Time measurements which discourages storing flexible WIP resulted in poor use of inventory. Many software measure throughput time as the time from picking raw material to the transfer of product to finished goods inventory. Noramco achieved large delivery and inventory benefits from maintaining inventory in WIP, instead of completing the product to finished goods. The rules to avoid TTT became: • Manage the inventory level after the constraint and long lead time items. • Use demand to pull this inventory to finished goods. • Do not produce product after the constraint, until required. • Do not make more than required after the constraint.
NOZZLES $
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Figure 8-JO. Inventory Results from Changes
Figure 8-10 shows effects, the planning system changes had on Noramco's inventory. Analysis by product showed that all of the inventory reductions were in the nozzle and pump assembly products. Inventories for other product lines showed little improverhent or increase during this time.
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Parts Management Models and Applications
Inventory turns for nozzles increased to three times the original amount. Clearly, inventory reductions can be attributed directly to process changes.
5.2
Sales Results for Products
In 1998, the order of sales volume changed and nozzles became number one (see Figure 8-11). Noramco believed this condition occurred for two reasons. First, increased competition in pumps had caused Noramco to lose some modified business. A more significant influence had been large increase in nozzle sales. Noramco attributed this to improvements discussed above. In 1997, stock-outs of nozzles were common. In most cases, it took 20 to 30 days to fill these outages. This condition was not the result of low levels of inventory but the result of having the wrong inventory. Noramco's customers could get similar products from competition. Thus, it lost sales because of not having the right product on the shelf However, improved conditions in 1998 have resulted in few backorders, which were being filled within a week. Noramco won back several customers that it had lost in 1996 due to delivery and price issues. It won back these customers because it could consistently deliver when the competition was missing its promised dates. For this reason combined with a stable sales price, it can be assumed that the additional $100,000 monthly sales increase was a direct result of the process changes put in place in 1997. Perhaps an even bigger improvement was the change in profitability. Although the sales volume had less than doubled, the profits had increased to three times the 1997 amount. The same result occurred in the modified product line. In this case the total sales had diminished to two thirds that of 1997, yet the total profit dollars had increased almost one third as much.
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181
1998 Product Results • • 98 Sales Ez3 98 profrt ^ * ~ 97 Sales " ^ 97 orofIt
$ 0 •
Nozzles
Modified Product
Private Label Kits
PTPs
Accessories
Figure 8-11. 1998 Product By Sales Volume
5.3
Standard cost versus throughput, inventory and operating expense
To evaluate the effectiveness of the pilot project, Noramco measured results in two formats. The first was traditional standard cost comparisons where process efficiency and utilization were used to measure production. The operations performance was measured in terms of standard versus actual variances As shown in Figure 8-12, no direct relationship was achieved between efficiency and profits. When decisions were made using the standard cost system and these performance measures, the operations group tended to pay more attention to the need of manufacturing rather than the need of the customer. Therefore these measures were not used in making decisions during this pilot project.
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182
150%
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Figure 8-12. Efficiency and Utilization
Performance measures used in making decisions were: throughput, inventory and operating expense. Throughput was considered the same as actual sales for the month. Inventory measured the actual cost of materials waiting to be sold or converted to product. Operating Expense, had been removed from the historical inventory measure. Operating Expense was the actual expenses incurred by Noramco for all activities. Results of this tracking are illustrated in Figure 8-13. Here, it is easy to see that increasing throughput and decreasing inventory while maintaining operating expense led to higher profits.
Serve Your Supply Chain, Not Operations
>f
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183
^^^ ^^ Month
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- Operating Expense — A — Inventory
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Figure 8-13. Represents Throughput, Inventory and Operating Expense Performance
5.4
Proof is in the Profits
As a result of changes implemented to production scheduling processes and other aspect of the supply chain, Noramco achieved following results: • Non-value added steps were decreased by 26. • Finished goods inventory has dropped to 20% from 1996 levels. Finished goods turns have increased from 2 to 8.7. • Work in process inventory has declined to 75% from 1996 levels and turns increased from 1.7 to 4.9. • Delivery has improved from 90 days to 2 days. • Nozzle throughput has increased by 33%. • Operating expense has increased less then 3 %. • Profitability in dollars has increased to 200%) of 1997 amounts. For the purpose of comparison, impact of these changes were measured with the previous measurement system used by Noramco, and the results are given below: • Efficiency declined from 110% to 80 %. • Utilization followed the trend of throughput, falling off during the off
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Parts Management Models and Applications
season. The only work centers being fully utilized during slow demand was the constraint. • Profit margin declined by 5 %. Historically these three measurements were used to measure operations. With these measurements having poor performance, it was a difficult struggle to stay on the course. Although upper management supported changes and understood their value, they continued to question the impact on efficiency, equipment utilization and profit margin percent. During the off season pressure was on to run more equipment. This would bring up the utilization and decrease the capacity variance. This action would also create inventory that may or may not sell during the season at the same time it would consume more of Noramco's constraint product, leaving less for responding to demand changes during the season. In 1996 and 1997 the excess inventory syndrome described earlier led to selling off the excess inventory at almost cost. At the same time, the safety stock syndrome required increasingly high demand on Noramco's capacity during the season raising manufacturing cost for overtime and outsourcing of all products. During the season when efficiencies declined to 80 %, it was Noramco's work force and engineering personnel who applied the pressure. The lower efficiencies came from running less than the lot size required in the standard cost. The fear of not meeting standards was so great on the manufacturing floor that they fought efforts to fill orders in order to achieve these efficiencies. In the past, Noramco would have continued to run long production runs on all equipment and deliveries would not have been achieved. The final result was lost customer orders, thereby reducing throughput. The profit margin percent decline was the result of two factors. First in 1996, the competition was driving down pricing in the market. Noramco needed to respond to this by reducing the price for nozzles. Second, suppliers were raising their prices because the purchasing volume was declining. This resulted in a higher standard cost with lower selling prices. It was easy to see standard reactions to these three measurements would have surely perpetuated Noramco's decline in nozzle sales and profits. By ignoring these measurements and concentrating on throughput, inventory and operating expense, Noramco was able to regain a profitable financial position and win back customers when their competition could not deliver during the season. Therefore, the only important measure was increase in total profit dollars.
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185
Fundamental Organizational Change
The effect of acceleration principle (Layden, 1998) on Noramco was apparent in its constant demand fluctuations. The most difficult task of this project was to get the organization to understand the effect of this principle. Operations group were interested in better forecasts and longer lead times, whereas sales group wished to see higher inventory levels to eliminate stock-out potential. Because of this, the lead time and inventory reduction syndromes were alive and well. Finally, placing blame on the current process or misapplied technique combined with the pursuit to implement the next craze, allowed executives to continue to implement tools improperly. These activities pulled efforts away from: doing the basics well, sharing information, and concentrating on actual demand. In order to get the sales group comfortable with low finished goods inventory, they had to be educated on steps taken to improve reaction time. They also had to trust the system and communicate unexpected customer increases in volume. It took some time before trust in the new system would unleash the true potential of the sales force. The unexpected reaction came from the assembly personnel. They no longer had a long list of future orders to build. It basically appeared as if they would run out of work in three days. They began to slow down to maintain workload and avoid layoffs. A result of past messages sent by management that slow times result in letting people go. They had to be educated in the new approach. Noramco involved them in managing the process and focusing on open orders. Constant exposure to throughput growth provided the information to ease their concerns. The whole organization efforts must be synchronized. Breaking up of responsibilities and applying ownership and accountability, segment processes into non-synchronized and isolated improvements. These improvements often are counter-productive to meeting customers needs. Tools and improvements must be shared by the entire organization. They must fit needs of all functions. Cross-functional teams are the only means to achieve this result. Finally throughput, inventory and operating expense (T, I, and OE) are relevant to measure operations efficiency. Noramco has not abandoned use of equipment utilization and efficiency measures. They continued to use them for applying the product cost and determine long term investment strategies, but, T, I, and OE are used to make decisions. Three simple questions need to be answered with each decision - whether this decision would (1) increase throughput, (2)decrease inventory, and (3) decrease operating expense? The addition of capital equipment and
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inventory investments should produce a greater increase in throughput. It is essential to avoid the trap of making decisions on the equipment utilization and efficiency, instead establish what the correct utilization and efficiency should be to establish a product cost that optimizes T, I, and OE.
6.
CONCLUSIONS
This pilot project was highly successful and yielded excellent profit results, however, it was not directly transferable to remaining Noramco products. Planning based on combination of Demand Flow Management, MRP and TOC approaches was unique to nozzle supply chain and not appropriate for other Noramco products supply chains. It was the process of analyzing nozzle supply chain and implementing the appropriate methods and processes to this chain that could be applied to various products supply chains. This was evident when the pilot project was extended to Noramco's modified products assembly processes. These do not follow the same process as the nozzle product line. The decisions to be made once the supply chain and process flows were understood included - locating inventory in the chain to optimize flexibility and delivery performance, identifying and scheduling constraints to pull the product based on demand after constraints, and also sharing of accurate and timely information across the supply chain to achieve optimum performance. Important lessons learned from this pilot study (many of them are applicable to organizations striving for ways to strengthen their business operations and that of their trading partners) were as follows. One, improving business operations that optimize T, I, and OE and results measured using these performance measures, is an approach to improve organization's supply chain. If measurements trend negatively, the supply chain should be reanalyzed and started over. Two, there is a need to involve both suppliers and customers in efforts to ensure that supply chain needs are met. Three, one should use as many of the existing systems as possible. Typically, it is beneficial to simplify existing systems with some modifications to incorporate new techniques as compared to starting with a whole new system. Four, it is important to use a cross-functional team and the continuous improvement process to implement change. Noramco is still improving its process today. Five, inventory reduction should not be a program but a result of a synchronized system. Six, a synchronized system can only result from all organizational functions understanding the supply chain requirements and working together to meet these requirements. Seven,
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only financial measurement that matters is total profit dollars. All other measurements should tie to this measure. Eight, understand the operation before simplifying it. Eliminate wasteful activities prior to automating the system. Nine, actual demand may be used to drive the production response. Ten, it is important to know constraints and ways to exploit them. Eleven, the correct scheduling method should be used to meet requirements of the supply chain, not needs of the manufacturing efficiency and utilization performance.
Adapted from the paper by authors: Kumar, Sameer, Chandra, Charu and Stoerzinger, Michael, (2001), "Serve Your Supply Chain, Not Operations - A Case Study", Industrial Management and Data Systems, Vol. 101, No. 8, pp. 414-425.
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Chapter 9 HOLISTIC VIEW OF PARTS MANAGEMENT
This chapter has two distinct parts. The first provides a summary of improvements in a Parts Management System derived from the models and their applications described earlier in the book. The second illustrates a wellknown Dell Computers Supply Chain which uses optimal ordering, inventory management, assembly and distribution methods. We begin with summary of suggested improvements in the Parts Management System. Impact of inventory miscount and non-incorporation of lead time variability in ordering decision rules is studied. As a result, ordering rules are revised, where new rules duly consider lead time variability. Audit procedures are developed to avoid inventory miscount. These procedures are based on the conservation of flow concepts at micro-level through their transient flow phase. Procedures for period physical counting of inventories are suggested on an ongoing cyclic basis. A model is developed which within a two-level distribution system divides the total set of items into company items and dealers' items. Market share to a large extent depends upon composite customer service level. The model duly incorporates this interdependence. Currently, these decisions as to which items are shelf inventory items are more dealers based. They keep inventory for items which on an individual basis are profitable to them. Quantitative rationale for subsidizing some of the marginal items which they ordinarily will not stock, is developed. 189
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Parts Management Models and Applications
New appropriate ordering rules for purchases from common suppliers are developed. Benefits from EDI in terms of lower cycle and safety stock inventories are studied. Controlling design proliferation holds a great potential for improving manufacturing productivity and reducing costs. Techniques of Principal Components Analysis is used to group items in similar classes based on their design similarities. Procedures are suggested for using these classes for controlling design proliferation. A conceptual framework is described for "eDesign" component management decision support system for product development in order to build a basis for its technical feasibility. A three level decision making hierarchy is illustrated with economic optimization for levels 1 and 2 representing standardization of system modules and capacity decisions for a product line respectively. Thermodynamic optimization for level 3 represents control systems to keep the system dynamically balanced with changing environments. The principal objective of the study is to present a detailed economic justification for implementing such a system in a product development environment. The proposed component management system can be utilized and customized to support three levels of formalized standardization, facilitate in compressing time to market cycle for new and upgraded products and also control design proliferation. A lot more work needs to be done before practical approaches in parts variety control are developed. Exploiting various similarities within items, which in the literature have been called "Group Technologies" seem to hold a promise in bringing improvements in several other areas such as • Grouping for cellular manufacturing. • Grouping of maintenance operations for better scheduling and worker training. • Promoting more standardization in general. Decision-making is information intensive that requires sharing of knowledge among various units within the organization. The extent to which information is communicated and used depends on how well knowledge is represented and organized. Knowledge is represented to follow the decisionmaking hierarchy - visions, concepts at strategic and tactical levels and guidelines at operational level.
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Representing knowledge is a complex task. Classification as a tool seems to hold out promise, but experiences of its application to manufacturing are still very limited. The automated factory of the future cannot be designed without elaborate knowledge bases. It is high time that firms make an earnest start in the development of knowledge bases. In order to affect whole supply chain of the company studied, the organization needed to rethink its historical means of measuring performance. This involved questioning validity of measures that management had held for generations and transforming thinking. The biggest benefit happens to come from improved capacity utilization among all trading partners, which results in increased sales and profits. In the rest of this chapter, Dell Computers and its nearly optimal supply chain are described in detail.
1.
DELL
When it comes to supply chain management in the computer industry today, Dell Computer sets the standard. Dell is the largest PC company in the world; over $31 billion in annual sales, and it is the most effective company at managing its supply chain. In order to appreciate what Dell has done in this industry, it is important to understand something about where things were prior to Dell's existence (Information Technology Association of Canada, 2001-2003).
1.1
DelFs Beginnings
Dell was founded in 1984, when Michael Dell hit on the idea of selling PC's over the phone from his dorm room. The simple difference this entailed was not having a sales team, and not having a middleman or distributor to whom a share of the profits would go. Dell focused on cutting costs and delivering quickly, and sales soared. Within three years, Dell was offering next-day, on-site service for its products, and it made its first foray into international markets by opening a subsidiary in the United Kingdom. The company continued to strive to cut its gross margin. On the face of it, this seems counter-intuitive, since that step should decrease profits. But with no other companies in the chain taking a cut, Dell could reduce its margins and under-price the competition
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Parts Management Models and Applications
while still making a profit, and therefore begin to take sales away from them. By 1988, sales had reached $159 million, and it was time to go public. Dell raised another $30 million through this process. By then, it had reduced gross margins to 30% because of its efficiencies, at a time when the competition had gross margins of 40%. The funding helped Dell expand further internationally by opening a manufacturing facility in Limerick, Ireland. This plant was designed to serve the European, Middle Eastern and African markets. Continuing its rapid growth, Dell launched its first notebook computer in 1991, and IBM and Compaq began to take notice. They in turn began to create new operating units with pared down staffing and reduced R&D, but they couldn't approach Dell's gross margins. By 1992, Dell entered the ranks of the Fortune 500, and by 1993 opened subsidiaries in Australia and Japan, with sales putting it into the top five PC manufacturers in the world (www.dell.com). During this time, large companies had infrastructures consisting of multiple enterprise resource planning (ERP) systems that could not communicate effectively amongst themselves or with external systems. They were slow and unable to respond proactively to business changes as they occurred. As PC manufacturing companies began to increase their outsourcing from outside suppliers, the need for visibility across the extended supply chain grew tremendously and the ERP structures of the large computer companies proved to be ineffective at delivering on that need. This supply chain communication problem persisted for many years. While costs slowly came down through focus on reducing operating expenses, inefficiencies continued to exist from the communication challenges that resulted from the high level of outsourcing (Harrington, 2002). During this time Dell wasn't much different from the rest. As late as 1994 it was considered a second-tier PC maker. This didn't stop Michael Dell from making rash predictions about increasing Dell's market share. In 1993 Dell held 4.1% of the market, and Michael Dell proclaimed that it would reach 18%. While many scoffed at this audacity, Dell reached this mark in 1999, and continues to grow (Pletz, 2002). At this time Dell still faced the inefficiencies created from ordering component parts from its suppliers in advance and then building inventories for sales. It was disadvantaged as the larger PC companies benefited from their size, i.e., lower fixed costs per unit. This forced Dell to completely reevaluate its supply chain. It needed to do something radically different if it was going to survive in the PC industry.
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1.2
193
The Dell Supply Chain Model
This is when Dell began to introduce a new business model (Court, 1998). It converted its operations to a built-to-order process, eliminated its inventories through a just-in-time system, and sold its products directly to consumers shown in Figure 9-1 below.
PC Component Supply
Partial Assembly
Customer Specific Configuration
Built-To-Order
Figure 9-1. The Dell Model
Dell attempted to develop a supply chain model that went beyond the pursuit of efficiency and asset productivity. It was attempting to displace the current model with one that made the supply chain more efficient AND delivered more value to consumers (Copacino and Byrnes, 2002). As we all know, Dell was successful in this endeavor. It achieved a high level of success by making supply chain capabilities the core of its business model, which can be explained through these five key steps as shown in Figure 9-2 (Wasserman, 2002; Copacino and Byrnes, 2002):
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Parts Management Models and Applications
Acfoimt
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Figure 9-2. Dell's Five Steps Approach to Attain Supply Chain Excellence
1.2.1
Account Selection
Dell started by establishing targeted accounts. It carefully defined both target accounts and accounts that did not fit with its supply chain strategy. Specifically, Dell targeted corporate relationship customers that had predictable, budgeted needs and that wanted a predetermined set of product models (Briody and Moskowitz, 2001). It also selected individual customers that were high-end, repeat purchasers with a preference for early technology adoption. Both account segments had the stable, predictable purchase patterns that Dell needed to make its built-to-order system work. 1.2.2
In-Customer Operations
Dell determined that it was crucial for it to operate within its customers' organizations. This requires powerful technical capabilities, deep customer knowledge, and the ability to fit into the customer's organization and work processes. What ultimately differentiated it from the competition was its ability to blend into its customers' day-to-day operations and culture. This unique customer knowledge has helped Dell create barriers to entry that others have not yet been able to penetrate. An example of this is how Dell developed a set of effective customerspecific intranet Web sites. Each Web site is highly tailored to the customer's individual station. Dell works with each customer to specify a particular set of product configurations that work best in the customer's network. Tailored offerings are specific and developed for each customer (Bearden, 1999). At the same time, Dell uses its direct links with both corporate and individual customers to get immediate, real-time insights about uncovered customer needs and identifies new generations of products and services. This enables Dell to deliver reliable customer service and innovation at the same time! (McSpadden, 2001)
Holistic View of Parts Management 1.2.3
195
Channel Strategy
There are many different ways in which a company can approach strategy. Some move along the Porter line, pursuing either low cost of production or highly specialized products. Others pursue a "solutions" approach, integrating their business systems with those of their customers', enabling them to "co-create" value and share in the gains (Kucharvy, 1997; Ojo, 2002). While others attempt to become the de-facto standard in the industry, effectively "owning" their link in the value chain. By developing its direct-to-consumer strategy, Dell created a channel that had never existed before (Burke, 2002). It combined its deep integration with its customers' businesses with its unique position in this new direct-to-consumer channel shown in Figure 9-3.
Component Production /ranacitv + Rp;ii Timp^ (Capacity + Real-Time)
r«„*:„„rpH m nm^r Configured-To-Order ^Qg gclty + Real-Time)
Customer Specific ^""X . Configuration Built-To-Order
Figure 9-3. Dell "Direct-To-Consumer" Supply Chain
By distinguishing a set of high-end customers that were ready for direct distribution and customer support from help lines, Dell became the only viable alternative for PC sales through its new channel (Fisher, 2002). As a
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Parts Management Models and Applications
result of this, Dell now has access to several crucial elements that help propel its business model (Teresko, 2001): • Real-time customer feedback and market insights • The ability to sell what they had, i.e., using day-to-day pricing and sales incentives to shift demand toward products that are currently marketable • Crisp product life cycle transitions • Elimination of the obsolete and excess dealer stock that plagues the non-direct competitors • The ability to control pricing on a real-time basis 1.2.4
Core Operations Capabilities
Before a company can be great at anything, it must be good at many things. It is necessary for companies to develop a set of core capabilities they can leverage to accomplish truly outstanding things. Early in Dell's rise to success, it developed a set of operations capabilities in five key areas: It created the flawless make-to-order system mentioned before It worked at length to build an effective supplier management function in order to shorten component lead times and maintain the absolute quality standards required by the just-in-time operation It developed the system needed to be able to sell what it has that is needed to match consumer demand It instituted an extraordinarily crisp set of product life cycle management capabilities that yield great cost reductions and strategic advantages It worked with its suppliers to shorten their product life cycles, extending its business model to the whole channel 1.2.5
Management/Organization Structure
Dell had to find a way to operate with no inventories in order to raise the cash needed to continue investing and developing this model. This required a complete change in management style and its success depended upon total commitment from the management team. There were many issues that surfaced and most of them revolved around two philosophical changes to the old way of conducting business operations: Built-to-order vs. Built-to-stock. Integrated with direct-to-consumer, Dell introduced a way for consumers to decide what features they want in their computer before manufacturing of the product was complete. This way, products were never built for stock; rather, they were built for the
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individual consumer and never gathered dust as inventory. This significantly lowered financing costs and increased customer satisfaction for Dell's chosen market segments (Economist, 2001a). Configured-to-order vs. Built-to-forecast. To manage its built-to-order system effectively, Dell pioneered the concept of configured-to-order (Bearden, 1999). It began using real-time information to make adjustments in the production cycle. Products were started based on what the market was saying it would need. In the past decisions about when and how much to produce had always been made using demand forecasting and planning. This was the answer the Just-in-time concept was looking for in this industry, but it was the most difficult for management to get comfortable with. Due to the complexity of the built-to-forecast concept, it is necessary to break it down to effectively explain how it works (Harrison, 2002). There are four key points that must be understood: Demand is managed at the supplier level. With no inventories to manage demand from, this model requires demand to be managed through capacity at the production facilities. Dell's supply chain depends upon the number of PC's produced being equal to PC's sold. Therefore, the supplier must know how many parts to produce and ship to the assembly line so that inventories will not be created. Demand forecasts determine capacity, not production. For suppliers to be able to produce only the number of components needed for actual sales, they need to know in real-time what demand is for their products. The traditional method of forecasting what demand will be and then producing that number of products is far too inefficient to be used in this type of supply chain. That is not to say, however, that there is no value in forecasting. Forecasting is used to determine the capacity of components needed so that supplies are available as demand calls for them. This allows suppliers to prepare for anticipated changes in demand by increasing capacity or selling a certain percent of their products through another channel. Operations are started based on expected rates of demand vs. manufacturing orders. Under the conventional method, manufacturing orders are released to produce specific items due on specific dates. When this is for make-to-stock, where finished products are sent to inventory, this works just fine. However, when this is for a specific customer order, which is needed to satisfy customers in the PC industry, problems often arise (Souza, 2000): Missing components delay the entire process Changes in customer requests require changes in the timing of the entire process
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Parts Management Models and Applications
Swapping of parts to satisfy orders complicates the entire process Rate-based planning establishes a rate of demand for finished products and the component suppliers build and assemble to match that rate. By doing this, Dell has computers half made when customer orders are taken, and it can deliver the final product very quickly: The average amount of time a customer has to wait for a Dell PC is only 5 days (McSpadden, 2001). Rates are determined through real-time demand information. This method of production is extremely risky. If rates are not accurately estimated, Dell could find itself short of needed inventories or full of unneeded supplies. To ensure that rate planning is done effectively, Dell relies on real-time demand information and communicates that back through the supply chain. Every two hours new information is passed through the system that can alter the manufacturing schedule, as needed, to adapt to changes in demand. Our assumption is that in the end this battle will be won and lost over price. While service is an issue, over time consumers will become more comfortable with the help line and as the processors and software improves, there will be less problems for consumers to worry about.
Appendices
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Parts Management Models and Applications
Appendix A Table showing values of attributes of fans Fan Type 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
1
44
Number of Blades 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4
_J
Diameter of Fan in inch 10 22 6 10 10 10 10 10 10 10 10 10 10 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 14 14 14
Blade tip angle in degrees 35 27 23 12 24 24 27 27 27 27 28 28 28 32 32 35 40 52 16 16 19 20 20 20 21 21 21 21 23 24 24 24 24 27 28 28 29 30 30 37 32 16 16 17
Rotation Direction 1 2 2 2 1 1 2 2 2 1 1 1 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 1 2 2 2 2 1 1 2 1 2 2 2 2 2 2 1 1
Hub Type 2 2 3 2 2 2 3 3 2 2 2 2 2 4 1 3 3 2 2 1 3 1 1 1 2 2 3 1 3 3 3 1 1 3 2 4 2 3 2 1 2 4 2 3
Material
Appendices
201
Table showing value of attributes of fans (continued)
Fan Type A5 46 47 48 49 50 51 52 53 54 55 56 51 58 59 60 61 62 63 64 65
tt 61 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88
Number of Blades
Diameter of Fan in inch
Blade tip angle in degrees
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5
14 14 14 14 14 14 14 14 14 14 14 15 16 16 16 16 16 16 16 16 16 16 16 16 18 18 18 18 18 20 20 22 22 22 22 22 22 22 24 14 14 14 14 15
18 19 21 21 21 24 24 26 26 36 40 38 20 20 20 21 21 21 21 22 22 22 22 28 16 16 22 27 31 19 19 21 21 21 27 27 27 27 15 26 26 26 26 31
Rotation Direction 1 1 2 1 1 1 1 2 2 1 2 2 1 1 1 2 2 1 1 2 2 1 1 2 2 1 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2
Hub Type 2 1 1 1 3 1 1 1 1 2 2 1 1 1 1 3 3 3 3 2 2 2 2 2
Material
202
Parts Management Models and Applications
Table showing value of attributes of fans (continued)
Fan Type 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
No. of Blades 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 4 4 4 5 5 6
Diameter of Fan in inch
Blade tip angle in degrees
Rotation Direction
Hub Type
15 15 15 15 17 17 18 20 20 20 20 20 20 24 24 7 15 16 18 18 18 18 18 18 18 18 20 20 20 20 20 10 10 10 14 14 14 24
31 40 41 41 29 31 17 19 23 23 23 25 33 45 45 21 31 35 30 36 36 36 36 36 36 36 21 21 22 23 23 27 27 40 30 30 30 22
2 2 2 2 2 2 1 2 2 2 1 2 2 2 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1 2 2 1 1 2 2 2 1 2
2 2 3 1 1 3 2 2 2 2 2 2 2 2 1 1 1 1 3 3 3 1 1 1 1
Material
2 2 2 2 2 2 2 2 2
Appendices
203
Appendix B Table showing intra subset and within subset heterogeneity and homogeneity Group Group 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
2
3
4
5
6
7
8
9
10
11
12
13
14
4.7
11.3
18.3
31.1
3.3
2.6
44.6
7.1
19.8
10.4
11.7
33.2
16.3
8.1 3.4
21.8
17.4
12.7
19.2
7.8
26.2
23.3
10.2
31.1
19.8
12.8
5.9
30.1
25 6.2 3.3
14.1
21 14 1.3
12.2
18.4
7 3.7
11 3.4 7.9
20.6
6 7
17 5.6 2.5
32.4
11.4
9.2 8.7
31.9
20.2
12.7
13.5
36.1
16
31.4
5.6
11
19.8
43.6
10
11.3
26.3
11.8
11.7
20.5
38.5
16.3 21.9
23 8 8.7 8.9
3.3 9.2 17 32.4
10.4
17.4
30.1
8.7 5.7 21
12.6
25
2.5 14
14.1
5.4 6.2 16
11.2
4.6
15.4
17.8
8.6
9.2
27.6
2.3
31.4
26.3
15.4
8.4
33.2
21.3
13.6
12.2
37.3
24.2
11.8
17.8
33.2
1.8
11,8
21.4
45.4
4.5
11.7
8.9 3.1
2.6 11
12.2
19.2
31.9
3.4
20.1
11.9
4.3
15.9
12.7
19.8
20.4
13.7
21.4
9.6
9.6 0.7
33.5
11.7
8.6 9.2
21.3
20.6
7.9 7.8
5.6 11
23.9
25.5
12.5
44.5
33.2
26.2
13.5
43.6
38.6
27.6
12.2
45.6
33.5
23.9
13.3
49.5
36.4
10 8
16.3
21.9
37.3
8.7
24.2
4.5 8.9
7.1 8.1
16.3
23.3
36.1
10.2
22.9
19.7
3.4 8.3
4.2
11.4
18.7
16.8
8.8 5.6
12.7
33.1
21.8
14.8
2.2
32.2
27.1
16.1
1.5
4 5.9
15.9
25.5
49.5
3.2
13.1
12.5
36.4
13.1
3.1
20.5
3.1 8.6
5.2
25.8
24.6
11.5
33.9
22.1
14.3
11.4
38.1
6.4
25 7.5 2.7 9.5 3.9
10.8
16.9
29.6
16
30.9
19.1
43.1
25.2
8.1
11.3
16.5
2.8 6.7
9.6
12.4
6.2 5.9
12.4
5.2
14.7
38.7
10.8
4.6
13.4
16.7
15.6
18.5
6.6
4.8
26.9
22,6
10.4
21.2
21
12.7
22.4
10.8
34.6
14.9
11.8
7.9
12.6
19.8
20.6
13.6
21.6
3.5 9.7
10.7
20.7
5.4 11 9.3
14.7
10.3
6.1 6.9 6.4
23.8
25.7
12.6
35.6
24.3
17.3
34.7
29.6
18.6
24.6
8.9
40.6
27.5
22.1
15.1
32.5
27.4
16.5
6.5 6.4
36.5
33.5
7.8 3.9
2 15
34.3
22.4
14.8
13.3
38.4
25.3
20.2
10.3
13.8
19.2
19
7.8
14.7
20.9
9
2.5
24.4
25.1
12
5.9
33.7
8.5
14.8
19.6
35
4
13.7
23.2
47.2
3.7
10.8
29.3
14 18
6.9 21 12.7
10.1
28.4
25.3
14.1
11.1
30.2
18.3
8.7
16.5
34.3
21.2
32.5
21.2
14.2
26.5
15.5
3.5
33.4
21.5
13.8
12.3
37.5
24.4
11.2
5.9
2.5 9.5
31.6
22.5
21.6
16.5
5.5
10.7
23.3
11.5
10.6
22.1
27.5
14.4
17.6
204
Parts Management Models and Applications
Table showing intra subset and within subset heterogeneity and homogeneity (continued)
Group Group
15
16
17
18
19
20
21
22
23
24
1 2 3 4 5 6 7 8 9
19.7
33.2
4
17.6
10.3
20.8
35.6
33.5
20.2 5.9
25
26
27
29.3
32.5 22.5
28
8.3
21.8
10.8
5.9 6.1
6.8
6.4
11.8
24.3
22.1
10.3 14
18
21.2 11.2
4.2
14.8
16.9
12.5
4.6
10.4
7.9
17.3
15.1
7
21.7
11.4
2.2
29.6
25.2
13.5
21.2
12.6
7.8
3.9
13.8 33.7
14.2 6 2.5 9.5
18.7
32.2
6.1
12.1
19.9
34.7
32.5
19.2 8.5
28.4
35.6 21.6
27.1
12.4
5.8 8.2
16.7
16.8
15.6
12.7
20.6
29.6
27.4
19
14.8
25.3
26.5 16.5
19.6
14.1
15.5 5.5
21
10.1
5.6
16.1
16
11.3
5.4
11
9.3
18.6
16.5
7.8
12.7
1.5 34
30.9
26.5
14.7
22.4
13.6
6.5
4.4
14.8 35
U.l 3.5
2.8
6.7
18.5
10.8
21.6
36.5
34.3
21
4
30.2
33.4 23.5
8.6
22.1
9.6
5.2
22.4
18.3
21.5 11.5
14.7
10.7
14.8
23.2
8.8
13.8 10.6
24.9
11.4
43.1
38.7
26.9
34.6
23.8
15 8.9
9.1 2.5
13.7
19.1
9.7 2
24.6
'l4.3
6.6 4.8
3.5
5.2
13.3
24.4 47.2
16.5
12.3 22
13 14
24.6
38.1
6.4
10.8
22.6
14.9
25.7
40.6
38.4
25.1 3.7
34.3
37.5 27.5
11.5
25
7.5
2.7
9.5
3.9
12.6
27.5
25.3
12
10.8
21.2
24.4 14.4
15 16
4.7
13.5
18.2
13.8
3.2
9.8
3.8
16
13.8
4
22.3
9.6
12.9 5.6
13.5
11.3
31.7
27.3
15.5
23.2
14.2
(^.9
15.4 35.8
11.8
3.1
17
18.2
31.7
2.4
4.7
16.2
8.5
19.3
34.2
4 32
18.7 4.1
27.9
31.1 21.1
18
13.8
27.3
4.7
1.1
11.7
6.1
14.8
29.8
27.6
14.3 8.6
23.5
26.7 16.7
19
3.2
15.5
16.2
11.7
5.4
7.7
5
18
15.8
3.4
20.3
11.7
14.9 6.9
20
9.7
23.52 8.5
6.1
7.7
4.6
10.8
25.7
23.5
10.2 12.6
19.4
22.6 12.6
21 22
3.7
14.2
19.3
14,8
4.9
10.8
2
14.9
14.7
2.1
15.9
6.9
34.2
29.8
17.9
25.7
14.9
7.8
10.9
15.5 38.3
8.6 8.2
9.9
17.3
23 24
13.8
4
32
27.6
15.8
23.5
14.7
10.9
0
15.8 36.1
12.2
2
10.9
4
15.4
18.7
14.3
3.4
10.2
2.1
15.5
15.9
0
9.2
14.9 9.8
25 26 27
22.3
35.8
4.1
8.5
20.3
12.3
23.4
38.3
36.1
22.8 0
11.7
27.8
23.58
11.7
19.4
8.6
12.2
9.2
12.8
3.1
31.1
26.6
14.9
22.6
13.7
8.2 10
32 0
35.2 25.2
9.7
2
14.9 35.2
11.2
28
5.6
10.6
21.1
16.6
6.9
12.6
9.3
17.3
10.9
8.8
14.1
0 10
10 11 12
20.5
23.4
22.8
32 25.2
10.7
10.6
13.7 9.3
11.2 14.1
10 0
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Index
Classification scheme 4, 5 Clustering 108, 123, 141, 142, 146, 206 Clustering algorithms 123, 146 Coding and classification 100 Coding scheme 2, 100 Component management 4, 118, 125, 132, 190 Components 3, 4, 8, 30, 42, 46, 55, 59, 70,78,79,80,88,95, 102, 103, 107, 108, 114, 117, 118, 120, 122, 123, 146, 147, 149, 153, 158, 165, 167, 168, 169, 170, 172, 173, 174, 175 Composite service level index 53, 59 Computer Integrated Manufacturing 137, 210 Conservation equation 2 Constant demand rate 3, 50, 69, 77, 78, 79,80,212 Control 4, 29, 31, 33, 34, 35, 36, 39, 40, 41,42,56,80,99,101, 114, 115, 117, 118, 119, 120, 122, 125, 130, 132, 136, 137, 146, 147, 155, 157, 160, 164, 190 Cost minimization 3, 69 Customer service 1,2, 27, 28, 29, 30, 49, 147, 157, 158, 175, 189 Customers' service level 1, 8 Cycle counting 29, 36, 78, 97
Acceleration Principle 158, 159, 176 Actual cost 182 Actual service level 8 Aggregate approach 57 Amortized capital cost 120 Audit procedure 189 Average demand 10, 11, 15, 79, 80, 88, 98 Average demand rate 9 Average inventory 30, 127, 156 Back order 50, 51, 178 Beer Game 158 Bottlenecks 130 Buffer stocks 174, 175 CAD 100 Capabilities 97, 99, 101, 123, 130, 133, 145, 168, 172 Capacity decisions 4, 132, 190 Capacity management 5 Capacity requirements 173 Carrying cost 80, 167 Cellular manufacturing 100, 136, 190 CIM 137, 138,212,214 Classification 4, 5, 38, 39, 99, 102, 103, 105, 115, 123, 124, 130, 132, 134, 136, 137, 139, 140, 142, 145, 146, 150, 153,206,213,214 Classification and Coding 214
219
220
Parts Management Models and Applications
Data-entry errors 29, 31, 37, 41 Data-input errors 41 DBR174, 177 Decision support system 4, 117, 132, 139, 145, 190 Delaycost51,55, 67, 68 Delivery cost 55, 57 Demand Elasticity Model 58 Demand Flow Manufacturing 174 Demand rate 9, 34, 37, 42, 52, 53, 54, 59, 65, 70, 77, 79, 82, 98 Demand variability 3, 56 Design characteristics 4 Design proliferation 4, 99, 114, 118, 122, 132, 147, 148, 149, 190 Design support system 146, 149, 153 Design variables 120 DFM 174 Discrete optimization technique 73, 84 Distribution planning model 58 Drawings Retrieval System 121 Drum Buffer Rope 174 Economic lot 37 Economic optimization 4, 119, 132, 190 Economic viabiHty 118 eDesign 122 EDI 190 Effectiveness 4, 29, 78, 141, 164, 181 Efficiency 5, 119, 134, 163, 173, 176, 181, 184, 185, 186, 187 Eigen values 103, 106 Eigen vector 103, 107 Eigen vectors 103 EM variables space 121 Energy 120 Enterprise Resource Planning 156, 176 EOQ3,57, 127 EOQ model 127 ERP 156, 158, 169, 173, 174, 176 Evaluation. Methods 140 Exergy 120 Exogenous market (EM) variables 120 Exogenous variables 120 Exogenous variables 120 Expected demand 175 Expected stockout quantity 86 Expert systems 136, 145
Exponential smoothing 8 Feedback 145 Finished goods 51, 156, 157, 163, 171, 173, 178, 179, 185 Finite Requirements Planning 174 Fixed order quantity 42 Flexible manufacturing system 134 Forecast accuracy 174 Forester's Effect 158 FRP 174 Group technology 100, 114, 130, 137210, 211,214,215 GTIOO, 102, 114 GT codes 100, 114 GT coding schemes 100 Heuristic ordering rules 3, 78, 81, 86, 97 Heuristicrules79, 80, 81,88 Historical inventory 182 Holding cost 18, 19, 42, 45, 51, 55, 56, 64, 67, 70, 80, 88, 90, 95 Incremental cost 88 Independent variable 120 Inentory 169 Inquiry 4 Internal audit procedure 41 Internal Inventory Control 33 Inventory 1,2,3,4, 5,8,9, 10, 11, 12, 19,23,24,27,28,29,30,31,33,34, 36, 37, 41, 42, 46, 51, 56, 57, 69, 70, 77, 78, 79, 80, 81, 87, 88, 95, 97, 98, 99, 127,128,129, 131, 135, 148, 153, 156, 157, 158, 159, 160, 161, 162, 163, 166, 167, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 189 Inventory cost 127, 159 Inventory count 2, 28 Inventory miscount 27, 28, 29 Inventory on hand 87 Inventory Reduction Syndrome 161 Investments 8, 28, 120, 186 Item-based approach 49, 55, 56, 57, 59, 60, 63, 64, 65, 67, 68
Index Item-based approaches 64 JIT 2, 41,42,205,213,215 Kanban 158, 162, 171, 174, 177 KMEANS clustering 124, 152 Knowledge acquisition 5, 211 Leadtime2, 8, 9, 10, 13, 19,20,22,23, 24, 27, 28, 29, 42, 45, 53, 56, 71, 80, 81,82,85,86,87,88,98, 131, 147, 156, 157, 158, 163, 167, 168, 171, 172, 173, 174, 179, 185, 189,217 Lead Time Syndrome 161 Lead time variability 2, 10, 189 Lean Production 155, 174 Lotsize2, 42, 43,44,45, 163, 171, 184 Lot-sizing 3 Macro-engineering variables 122 Mahalanobis distance 103, 110, 112, 113 Manufacturing classifications 136 Market elasticity factor 59 Market share 1, 3, 49, 50, 53, 58, 59, 61, 64,161 Master production schedule 156 Material conservation 2 Material requirements planning 156 MES 174 Monte-Carlo simulation 88 MPS 156, 157, 169 MRP 155, 156, 157, 158, 162, 169, 172, 173, 174, 175, 177, 178, 186. MRP Multi-level 50, 56 netting 156, 157, 169 Objectives 118, 130, 136, 137, 140 OIRMulti-M 100,214 On-handquantity 10, 29 On-order quantity 9 Operating and maintenance costs 120 Operating expense 5, 164, 181, 182, 184, 185 Operating expense 183 Optimal ordering procedures 3 Order entry 171, 175
221 Order quantity 80, 87, 127 Ordering cost 2, 3, 42, 43, 44, 45, 52, 56, 70, 78, 80, 81, 82, 86, 87, 88, 90, 95, 98, 127, 128 Ordering decision 1, 2, 9, 189 Ordering procedure 2, 3 Ordering rules 2, 3, 78, 79, 80, 88, 92, 93, 97,98, 190 Order-upto-level 78, 85 Overhead cost 163 Parity checking 2, 27 Part number 118 Parts distribution system 27, 49, 50 Parts proliferation 4, 101, 130 PDM 99, 208 Penaltycost37, 39, 41 Performance measures 5, 181, 186 Performance statistics 88, 90, 92, 93, 94 Physical count 28, 30, 41, 97, 189 Planning and fulfillment 5 Principal Components 4, 102, 114, 190 PRINCIPAL COMPONENTS ANALYSIS 102 Priority 178 Probability density function 9 Procurement Lead Time 212 Product Data Management 99, 115, 208 Product design 117 Product structure 118 Production processes 172 Production planning 51, 135, 155, 171, 175 Production rate 177 Projected 81, 127, 128, 129 Pull system 51, 56 Purchase order 70, 78, 82, 131 Purchase parts 178 Push system 50, 51 Qualitative 143 Quantitative 2, 29, 143 Randomdemand3,42, 51,77, 78, 81, 85, 97,98 Reorder point 8, 9, 10, 19, 23, 28, 29 Response variables 120
222
Parts Management Models and Applications
Robust design 120 SafetyStock 18,85, 160 Safety stock factor 9, 42, 52 Service level 8, 9, 10, 12, 14, 15, 19, 20, 22, 23, 24, 25, 27, 28, 30, 51, 53, 54, 59, 79, 80, 94 SKUs30,38 Standard costing 176 Standard deviation of demand over lead time, 9 Standardization 4, 100, 118, 121, 126, 127, 128, 129, 130, 132, 133, 136, 137, 138, 139, 190 Standardized module 121 Standardized modules 121 State variable 1 Staticmodel79, 81,92, 93 Stockout cost 3, 42, 45, 70, 74, 75, 79, 80,81,86,87,88,90 Stockout levels 3, 70, 79 Stockouts 2, 31, 69, 70, 74, 75, 78, 79, 80,81,205,210,211 Subsidization 3 Supply chain 155, 158, 159, 160, 161, 162, 164, 165, 166, 167, 169, 176, 177, 183, 186, 191 Synchronized system 5, 186
Synchronous Manufacturing 155, 174, 217 System-based approach 53, 55, 57, 58, 59, 60, 63, 64, 68 Theory of Constraints 155, 174, 175,216 Thermodynamic optimization 4, 132, 190 Throughput 5, 157, 163, 173, 175, 176, 178, 179, 181, 182, 183, 184, 185 Time-to-market 118 Total cost 3, 69, 71, 73, 74, 78, 80, 83, 84,90,94,96, 158, 163, 176, 178 Total market demand 56, 57, 59 Total variable cost 3, 71, 82, 88, 97 Unit cost 42, 52 Utilization 5, 130, 133, 163, 176, 181, 184, 185, 186, 187, 191 Variable lead time 2, 13 Variations 85 Variety control 101, 115, 122 Warranty cost 126, 127 WIP 156, 164, 178 Work in process 156, 175, 178 Work-in-process 29
