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Purchase quantity discounts and open order rescheduling in an assemble-to-order environment: The hidden economic tradeoffs
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH European Journal of Operational Research 110 (1998) 261-271
Theory and Methodology
Purchase quantity discounts and open order rescheduling in an assemble-to-order environment: The hidden economic tradeoffs Rajesh Srivastava a, W.C. Benton b3* a Air Force Institute of Technology, AFITILAL, 2950 P Street, Bldg 641. WPAFB, OH 45433-7765, USA b Department
of Management
Sciences, Fisher College of Business, The Ohio State University, 3087 Hagerty Hall, I775 College Road, Columbus, OH 43210, USA
Received 1 August 1996; accepted 1 June 1997
Abstract
In manufacturing systems, raw materials and components are purchased from outside suppliers. The purchasing decision consists of quantity and timing decisions. An added dimension to the purchasing decision is the availability of purchase quantity discounts. At the same time, order rescheduling is aimed at revising due dates of orders such that the planned schedule matches the actual schedule over time. Such revisions in quantity and timing affect the purchase decision. In this study, the impact of order rescheduling on various purchase quantity discount lot size models is evaluated under different operating environments. The findings of this research provide evidence for implementing dynamic purchase quantity discount lot sizing procedures when order rescheduling is incorporated into manufacturing systems. 0 1998 Elsevier Science B.V. All rights reserved. Keywords:
Purchasing; Manufacturing
planning and control; Open order rescheduling; Quantity discounts
1. Introduction
The purpose of materials management is to support the transformation of raw materials and component parts into shipped or inventory goods. The function of inventory in general is to decouple the entire transformation process. During the transformation process, materials are combined with labor, information, technology and capital.
Corresponding benton. [email protected]. l
author.
Fax:
+l-614-292-1272;
e-mail:
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The materials planning system is central for the acquisition of part and component needs in an assemble-to-order environment. Materials Requirements Planning (MRP) and just-in-time (JIT) systems are directed toward planning and controlling the important characteristics of material flow: how much of what materials flow and when. Since materials flow is at the heart of all manufacturing firms, these are powerful tools that could determine the success or failure of an entire manufacturing operation. The MRP system is the means in which the production will be carried out. The most important element of the MRP system is data
262
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Research 110 (1998) 261-271
of end item value
RM = Raw Materials FG- Finished Goods CP = Component Parts
A =Inventory
Storage
Fig. 1. Manufacturing process (197&1980). RM, Raw materials; FG, Finished goods; CP, Component parts; d, Inventory storage.
Division about the evaluation of various discount schedules. From his vantage point he suggested that the discount acceptance decision cannot be made independently from the open order rescheduling decision. He went on to suggest that record accuracy and order rescheduling were key inputs into determining whether to accept or reject a specific discount schedule. ’
The JIT approach is based on efficiently moving material through the productive system. Although many successful companies have embraced JIT philosophies they continue to use concepts to enhance the effectiveness of the manufacturing mission. Perhaps the most significant change in the past decade has been the purchasing function. During the time period 19701980 most American manufacturing firms fabricated 6&80% of the product’s value (see Fig. 1). Alternatively in the past decade a large number of manufacturing firms purchased between 60% and 80% of the product’s value (see Fig. 2). Since this impressive shift in percentages, the scope of the manufacturing system has shifted to increased outsourcing. As can be seen in Fig. 2, the complexity in the fabrication operation has been shifted up stream to the supplier. Under the traditional model the firm transformed significantly more raw materials and labor into the end product. Today since industrial firms are buying more and more subassemblies (component parts) the manufacturing focus is shifted downstream to the assembly operation. This significant shift has elevated the importance and profile of purchasing professionals. The purchasing function has become a key cost reduction center.
Thus the purpose of this study is to investigate the impact of order rescheduling and quantity discounts. In manufacturing systems, raw materials and components are purchased from suppliers to efficiently transform the inputs into finished products. The purchasing decision consists of the quantity and timing of purchased items. The decision also involves the basic tradeoff between ordering in bulk, i.e. fewer orders in the year and lower associated ordering costs, but higher inventory carrying costs; and frequently ordering in smaller quantities to minimize inventory carrying costs, but higher ordering costs. This is an important decision since inventories often represent a substantial portion of the investment made by a firm. Purchase quantity discounts add another dimen-
Recently one of the authors had a conversation with the former vice president of purchasing for the Westinghouse Appliance
’ Conversation with Mr. Harry L. Johnson, 20 February 1995, Columbus, OH 43229, USA.
accuracy.
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Research 110 (1998) 261-271
263
fizz\ cn ‘o%nd N
item value
jsembly /
I
RM - Raw Materials OPR 1 - Operation
1
FG= Finished Goods CP = Component Parts
A =Inventory Fig. 2. Manufacturing Inventory storage.
process
(198&1990).
Storage
RM, Raw materials:
sion to the decision making since they allow for reductions in material cost for large orders. Moreover, order rescheduling may be an important consideration in this new component-based manufacturing systems since actual production often differs from planned production. This leads to revisions in the schedules from the Master Production Schedule (MPS) to the purchase schedules. A revision in a schedule may imply both a change in quantity as well as in the timing of the orders. Order rescheduling affects a firm’s customer service measures as well as its inventory levels [1,2]. Order rescheduling may also affect the purchase quantity, leading to changes in the discount schedule and fi-
OPR 1, Operation
1; FG, Finished
goods; CP, Component
parts; d,
nal item price [3]. Thus the purpose of this research is to investigate the economic and customer service impact of accepting or rejecting various discount schedules when orders are rescheduled.
2. Background When a manager plans the acquisition of materials, whether raw materials or component parts, quantity discounts must be considered. Even though manufacturing complexity has been reduced, the nature of the complexity has shifted to supply chain and demand management.
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Manufacturing planning systems have several stages/levels of requirements. At each stage in the purchasing system, quantity decisions must be made. There has been extensive research on the general lot sizing problem. Considerations have ranged from simple applications of single stage lot sizing procedures in static planning horizons to complex capacitated multi-level lot sizing applications in rolling planning horizons. There has also been a substantial amount of literature on how buyers and suppliers react to quantity discounts. Hadley and Whitin [4] found that it is sufficient to check only the largest EOQ and all price breaks greater than the EOQ and ignore the price breaks less than the EOQ. Furthermore, Rubin et al. [5] also found that if the EOQ for the lowest unit price is not valid and if it falls within a quantity interval associated with the unit price, it is sufficient to check the EOQ based on the unit price as the next candidate EOQ and ignore any EOQs associated with the discount price lower than the unit price. Numerous studies have dealt with the buyer’s lot sizing problem [6,7,5]. Krupp [S] considered the returns on investment for the EOQ and all price break quantities. The traditional models for the quantity discount problem assume that the demand is known and constant. Abad [9] developed a procedure for determining the optimal selling price and the optimal lot size assuming that the demand function is price dependent. Benton [lo] considered quantity discount procedure under condition of multiple items, resource limitations and multiple suppliers. Later Rubin and Benton [l l] extended the work of Benton [lo] by offering a more general solution methodology. Later research has focused on analyzing quantity discount decision making under uncertainty in demand [6]. Such research has, however, failed to address concerns such as the effect that the rescheduling of orders already placed with the supplier (i.e. open orders) has upon the buyers’ purchase quantity discount decision. The performance of alternative discount lot sizing models under the open order rescheduling conditions still remains unknown. This is important since generally the results reported in literature are based on static snapshot views of the system and do not, there-
Research 110 (1998) 261-271
fore, consider the dynamics of order rescheduling due to changes in customer orders or shop status. The effect of order rescheduling in MRP systems has also been explored extensively. However, most of such research focuses on the effect on the overall MRP system [6], under various order rescheduling procedures [6,1,2]. The issues of stability versus nervousness in MRP systems due to frequent order rescheduling has also been examined [12,2]. However, none of the research specifically examines the effect on purchase schedules and on purchase quantity discount models. This is important to the firm since rescheduling orders may lead to situations of excess inventory or shortages. In either case, a change in the timing and quantity of the item ordered is necessary. Such a change in quantity might affect the discount schedule, leading to a change in prices and thus, overall systems costs.
3. Current study The purpose of this study is to investigate the impact of order rescheduling on various discount quantity lot sizing procedures in various manufacturing environments. There are no known studies which examine this important interaction effect. Yet such an understanding is important from the buyer’s perspective in terms of minimizing total systems cost, as well as maintaining an adequate customer service levels. (Also see page 262 for comments by H. Johnson.) Previous research into purchase quantity lot sizing rules has evaluated the performance of different lot sizing rules under deterministic and uncertain demand schedules. This study will extend such research further to include the uncertainty in demand, and changes in production schedules which result from order rescheduling, which is faced daily by materials managers. Inclusion of such factors will allow for direct examination of the effect that the firm’s order rescheduling policy has on the performance of alternative quantity discount lot size models. This study specifically considers the purchase discount decision from the buyer’s philosophy and excludes situations such as the one time buy decision or blanket orders. It
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also allows for the buyer to have multiple suppliers and for changes in the order schedules and quantities. Earlier research on discount quantity lot sizing in MRP systems [10,6] has shown that rules such as modified McLaren’s Order Moment (MMOM) and modified Least Unit Cost (MLUC) perform better than other rules such as the traditional Purchase Discount Quantity (PDQ) rule under fixed demand schedules. Research on open order rescheduling [7,1,2] shows that under certain conditions filtered rescheduling heuristics such as Orlicky’s heuristic perform better than fixed (no rescheduling) or dynamic ( 100°/ rescheduling) rules. Filtered rescheduling implies that only a certain percentage of all due date change notices generated for the existing orders are implemented. This study also focuses on the interaction between lot sizing procedures and various rescheduling policies. What is more several realistic alternative manufacturing environments will be evaluated.
4. Research plan This section presents the research plan for evaluating different purchase discount quantity lot sizing models under the various rescheduling environments. A discussion of these two factors as well as other environmental factors which impact upon the lot size decision is presented first. Next, the simulation model is described. The experimental design is then presented. Finally, the results and conclusions will be presented.
4.1. Experimental factors The manufacturing environment is characterized by various environmental and operational factors, such as the coefficient of variation of demand, uncertainty in requirements, the time between orders, the lot sizing procedures employed [6] and the level of rescheduling implemented. Certain environmental factors (coefficient of variation [ 10,6,13], requirement uncertainty [ 10,6], order rescheduling classification [1,2]) found to be signifi-
Research 110 (1998) 261-271
265
cant in terms of system performance in previous studies [10,6] are used in this study. Other factors, such as the time between orders, purchase lead times, and uncertainty in lead times are kept fixed, so that these issues do not confound the study. The specific factors used in this study are described next. A specific description of the environmental factors is given below: 1. Coejicient of variation (CV): The CV is the standard deviation of the planned requirements divided by the average planned requirements per period. Requirements are generated to meet three specific levels of CV: zero, low and high. High CV values tend to increase the lumpiness of the requirements, which has been observed to have an effect on the lot sizing procedures. This factor has been found in previous studies [10,6] to have a significant impact on the systems performance. The specific values of CV used are taken from previous research [ 10,6]. 2. Requirements uncertainty (RU): RU measures the difference between the planned and the actual requirements for a period. Uncertainty in requirements is generated assuming a normal distribution of requirement errors around the planned requirements. The specific levels of the factor are shown in Table 1. Again, this factor has been reported to significantly affect system performance in previous discount quantity lot sizing related research [6]. The specific levels of RU used in this study are also taken from previous research PWI. Besides the environmental factors discussed above, which affect the performance of the discount quantity lot sizing procedures, there are also operational factors which are included in the study. These are discussed next. 3. Lot sizing procedures (LS): The most effective discount quantity lot sizing procedures will be used in this study. Detailed results in other environments are available for these [10,6], therefore they are selected to analyze the impact of order rescheduling. The specific lot sizing procedures used are the standard purchase discount order quantity (PDQ), the MLUC, and the MMOM procedures. These three procedures have been shown to outperform all others in previous research [10,6].
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Table 1 Factor levels for the experimental design
5. Simulation model
Coefficient of variation (CV) CV = 0.00 No variation CV = 0.29 Low degree of lumpiness CV = 1.85 High degree of lumpiness
The simulation model represents a realistic manufacturing system. The planned requirements are generated from a modified uniform distribution and the requirement errors are generated from a normal distribution. Reschedule notices are determined by generating changes in customer requirements, which in turn generates a change in the planned requirements of the purchased items, in terms of timing or quantity or both. A preliminary empirical analysis revealed that 10 replications of the experiment are provided to obtain observations for the experiment. The performance criteria used are the service level performance and the total cost of the solution. The total relevant cost of the solution is the sum of ordering, material, and inventory holding costs. The three heuristic lot sizing procedures used for determining purchase discount lot sizes have been rigorously tested against a variety of competing lot sizing procedures [10,6]. The best performing lot sizing procedures are the discount order quantity (PDQ), the MLUC and the MMOM procedure. These procedures are based on the underlying principles of the traditional economic order quantity, the least unit cost and McLaren’s order moment heuristics [ 10,6,14]. The specific criterion used in this study is the percent deviation of the given discount lot size rule from the standard PDQ procedure. The simulation model was validated by carrying out a number of verification checks. The run length was kept at 500 periods, which was observed to provide stabilization in the model. The planning horizon was kept at 100 periods which has been shown to be effective in literature [10,6]. The model was run for 50 periods before collection of the data for the next 450 periods. In addition, starting inventory was provided to avoid stockouts. The start up period of 50 was observed to eliminate transient conditions. Further, to eliminate the effect of differing service levels with the different rules, sufficient safety stock was provided to achieve a minimum service level of 99.99% [10,6]. Changes in order quantity and timing are initiated at the MPS level in the simulation, with sufficient lead time, thus
Requirements uncertainty (RU) RU = 0 No uncertainty RU = 40 Low uncertainty RU = 80 High uncertainty Lot sizing procedures (LS) PDQ: Purchase Discount Order Quantity MLUC: Modified Least Unit Cost MMOM: Modified McLaren’s Order Moment Order rescheduling (OR) Fixed: No rescheduling of orders Filtered: Orlicky’s heuristic (with 50% filtering) Dynamic: 100% rescheduling
4. Order rescheduling (OR) : Order rescheduling can be classified as dynamic, fixed, or filtered [14]. A dynamic procedure implements all indicated due date changes. A fixed procedure is one where due dates are never changed from their original values. Filtering implies revising a subset of the due dates. In this study, Orlicky’s heuristic [14,1] is used for filtering orders. The heuristic considers both the magnitude and the position of the due date in the planning horizon. This heuristic has been shown to be effective in earlier research [1,15], and details on this heuristic are provided elsewhere [14,1]. Fixed and dynamic rescheduling can be considered as extreme cases for any filtering procedure. With any filtering heuristic is the associated issue of degree of filtering, i.e., what proportion of the due date change notices are implemented. Again, previous studies [14,2] show that medium levels of filtering appear to be most effective. In this study, fixed, Orlicky’s heuristic with approximately 50% filtering, and dynamic rescheduling are used. The threshold value used in Orlicky’s heuristic to determine whether to reschedule or not is set such that approximately 50% of all rescheduling notices are implemented. Further, rescheduling does not affect delivery times since only those changes which have sufficient lead time are implemented.
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changes in the purchase schedule will not degrade customer service levels. Once the model was validated, an experimental design was set up to examine the relationship between order rescheduling and purchase quantity discount lot sizing procedures under various experimental conditions. The experimental design is discussed next.
6. Experimental design A full factorial design is used for the four factors with the levels shown in Table 1. The given design results in a total of (3 x 3 x 3 x 3) 81 problems. With 10 replications, a total of 810 observations are obtained.
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Table 2 Average percent deviation system costs
from PDQ by factor settings on total
Lot sizing procedures (LS) Coejicient of variation (CV) cv = 0.00 CV = 0.29 CV= 1.85 Requirements uncertainty SIGMA = 0.00 SIGMA = 40.00 SIGMA = 80.00 Order rescheduling Fixed Filtered Dvnamic
Mean value
MMOM
MLUC
-1.98
-3.32
-2.62
-2.26 -1.99 -1.69
-3.74 -3.34 -2.87
-3.03 -2.63 -2.19
-2.97 -1.64 -1.32
-4.49 -3.14 -2.32
-4.43 -1.79 -1.63
-1.52 -1.44 -2.98
-2.49 -2.97 -4.49
-2.06 -1.34 -4.45
(RU)
(OR)
6. I. Research questions
The major issue of interest is the impact of order rescheduling on the performance of purchase discount quantity schedules. Specifically, we are investigating the economic impact of the alternative lot sizing methods. In addition, interaction among the factors under various experimental conditions is also of interest. The formal research hypotheses are given below: HOI
Ho2
Order rescheduling (OR) does not affect the purchase quantity discount lot size procedure. The lot sizing procedures which work best in fixed OR environments work just as well in filtered or dynamic OR environments.
7. Experimental results
The marginal means are presented in Table 2 and the ANOVA results are presented in Table 3. All factors except CV (p = 0.07, marginally significant) had a significant main effect in terms of the performance criterion (Table 3). The most significant main effect was OR, followed by the RU and LS factors.
The highly significant OR factor, on the performance criterion of percent deviation from the standard PDQ lot size rule, implies that the degree of rescheduling of orders does have a significant impact on the performance of alternate lot sizing procedures. The marginal means shown in Table 2 show that in the dynamic rescheduling environment, the MMOM and MLUC (dynamic) proce-
Table 3 Analysis of variance results (Criterion: Average percent tion from the PDQ procedure on total system costs) Factor
effects
F
Level of significance
Main effects Coefficient of variation (CV) Requirements uncertainty (RU) Lot size procedures (LS) Order rescheduling (OR)
2.63 24.71 24.12 97.93
0.07 0.000 d 0.000 * 0.000 il
Two way interactions CVxRU cv x LS CVxOR RUxLS RUxOR LSxOR
3.48 0.66 4.45 1.30 6.41 7.88
0.008 0.621 0.001 0.000 a 0.000 * 0.000 a
ap < 0.001
devia-
@)
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dures are significantly better than the traditional PDQ lot sizing procedure. The implication is that the dynamic discount lot sizing procedures can better adapt to changes in the timing and quantity of orders than the standard PDQ procedure. Table 2 shows that as uncertainty (RU) increases, the performance of the dynamic lot sizing procedures tends to converge (see Fig. 3). This result is consistent with previous findings in literature. Fixed rescheduling implies that no changes are made in the ordering schedule. Under low RU, the difference between planned and actual require-
-
PW MLUC MYOM
-
I
I
I
,
1
2
3
4
Order
Fig. 3. Interaction procedure.
between
Rescheduling
order
Method
rescheduling
and
discount
Research 110 (1998) 261-271
ments is low, the dynamic lot sizing procedures perform better than standard PDQ lot sizing procedures. When RU is high, the difference between planned and actual requirements is high, causing the performance of dynamic lot sizing procedures to deteriorate. All of the two way interactions, except for the CV/LS interaction were significant. The strongest two way interactions are for LS/ OR and LS/RU. Interaction effects higher than two way are intractable and should not be reported in simulation experiments [16]. In terms of the research hypothesis investigated in this study, Tables 2 and 3 show that the level of order rescheduling greatly impact the performance of the lot sizing procedures. The LS/OR interaction is significant (p < 0.001); the analysis of the marginal means in Table 2 and Fig. 3 shows that both MMOM and MLUC are significantly better than the standard PDQ under both filtered and dynamic rescheduling. To flesh out a more thorough explanation of this finding we analyzed the fixed OR/LS and the dynamic OR/LS separately (see Fig. 4(a) and (b)). As uncertainty increases the lot sizing procedures converge (Fig. 4(a)). In Fig. 4(b), under dynamic rescheduling the dynamic lot sizing procedures are significantly more effective at all levels of uncertainty. This result clearly shows that in a filtered or a dynamic rescheduling environment dynamic quantity discount rules should always be implemented. Further, there is little difference in the performance of the two dynamic lot sizing rules. In filtered environments, the MMOM procedure is notably better than the standard PDQ procedures while the MLUC procedure is only marginally better than the standard PDQ procedure. A clear conclusion can be drawn that for purchased items, fixed OR is not a good managerial choice, there is always improvement in total system costs from utilizing filtered or dynamic rescheduling. Furthermore, use of dynamic lot size procedures is preferred to the static standard PDQ procedures. Similar results for these two factors have been obtained elsewhere under different environments. Dynamic discount lot sizing procedures have been shown to be better than the standard PDQ under the fixed OR scenario [6]. In a shop environment (as opposed to purchased items), filtered and dynamic OR have been shown
269
R. Srivastava. W. C. Benton I European Journal of Operational Research 110 (1998) 261-271
Fixed
Rescheduling
Dynamic
Rescheduling
-
POD YLUC MMOY
a
-51 -20
0
-5 20
40
Requirements
60
60
100
Uncertainty
1
0
0
1
-
I
-
20
8.
40
Requirement
(a)
I.
60
1.
60
I
100
Uncertainty (b)
Fig. 4. Fixed rescheduling (a); dynamic rescheduling (b).
to be better than fixed OR [2,15]. Here, it is clearly shown that such results hold true in a purchased items environment, and that the interaction of the two is significant; such decisions should not be made in isolation. An earlier study [6] has shown that various environmental factors affect the performance of discount lot sizing procedures, and that the MMOM procedure performs better than the others under some conditions. This study shows similar results for the two environmental factors used, namely, CV and RU. CV has a much lesser impact on lot sizing procedures performance. As shown in Fig. 4(a), RU affects the performance
of the procedures significantly; as the uncertainty increases, the MMOM procedure becomes clearly better than the MLUC procedure; both being better than the standard PDQ procedure. Again, these findings are consistent with the earlier study
Fl. Another issue addressed in this study is the interaction between OR and the two environmental factors (CV and RU). These results are shown in Table 4. The ANOVA results in Table 3 show that both CV and RU have significant interactions with OR. This indicates that these environmental factors will also impact the managerial decision of the level of rescheduling to implement. The results
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Table 4 Average percent deviation from PDQ on total system costs by factor settings Order rescheduling (OR) Fixed
Filtered
Dynamic
SIGMA = 0.00 SIGMA = 40.00 SIGMA = 80.00
-2.94 -1.19 -0.42
-3.01 -0.73 -0.58
-2.98 -3.01 -2.95
Coejlicient of variation (CV) cv=o.OO CV = 0.29
-1.80 -0.82
-1.57 -1.71
-3.41 -3.43
CV= 1.85
-1.93
-1.04
-2.09
Requirements
uncertainty
(RU)
in Tables 2 and 4 also show that in most environments it may be preferable to use dynamic rescheduling if these dynamic discount lot sizing procedures are used. Filtered rescheduling is preferable for fixed environments but not for dynamic environments. However, earlier studies [ 1,2] have shown that filtering the rescheduling messages can lead to the same levels of customer service and inventory levels as dynamic rescheduling, without the system nervousness and higher costs/ complexity associated with dynamic rescheduling. Thus it may be preferable to implement filtered rescheduling along with dynamic discount lot sizing rules to achieve better system performance than fixed rescheduling, or using standard PDQ, and without the system nervousness which accompanies dynamic rescheduling.
8. Conclusions The complexicity in manufacturing has been shifted upstream to the supplier. This significant shift to increased outsourcing has elevated the importance and profile of purchasing professionals. This study has examined a managerially significant problem which purchasing and materials managers often face, that is, the issue of rescheduling orders, and the associated changes in the quantity discount schedule. Specifically, the effect of rescheduling orders on the PDQ decision was examined. The performance criterion used was the percent deviation of the dynamic discount lot siz-
Research I10 (1998) 261-271
ing rules from the standard static PDQ rule in terms of system costs. The findings of this research provide evidence for implementing dynamic purchase quantity lot sizing procedures when order rescheduling is incorporated into manufacturing systems. The research explicitly shows the conditions under which a particular lot sizing rule should be selected, and also the level of rescheduling appropriate from a purchasing decision standpoint in various operating environments. The linkages between the manufacturing system rescheduling decision and the purchasing decision are established. This should aid the practicing manager in grappling with a difficult problem. As an example, this research has shown that it may be preferable to implement filtered rescheduling with dynamic discount lot sizing rules in order to maximize systems performance.
References (11 R.J. Penlesky, U. Wemmerlov, W.L. Berry, Filtering heuristics for scheduling open orders in MRP systems, International Journal of Production Research 29 (11) (1991) 2279-2296. VI R.J. Penlesky, W.L. Berry, U. Wemmerlov, Open order due date maintenance in MRP systems, Management Science 35 (5) (1989) 571-584. [31 C. Ho, P.L. Carter, S.A. Melnyk, R. Narasimhan, Quantity versus timing change in open order: A critical evaluation, Production and Inventory Management 27 (1) (1986) 122-136. [41 G. Hadley, T.M. Whitin, Analysis of Inventory System, Prentice Hall, Englewood Cliffs, NJ, 1993, pp. 62-68, 3233 345. PI P.A. Rubin, D. Dilts, B. Barron, Economic order quantities with quantity discounts: Grandma does it best, Decision Sciences 14 (1983) 270-28 1. WI W.C. Benton, D.C. Whybark, Material requirements planning (MRP) and purchase discounts, Journal of Operations Management 2 (2) (1982) 137-143. [71 P. Kuzdrull, R.R. Britney, Total set up lot sizing with quantity discounts, Decision Sciences 13 (1982) 101-l 12. PI J.A.J. Krupp, ROF analysis for price breaks, Journal of Purchasing and Materials Management (1985) 23-25. [91 P. Abad, All unit quantity discounts, Decision Sciences 19 (3) (1988) 622634. 1101 W.C. Benton, Multiple priced breaks and alternative purchase quantity lot sizing procedures, International Journal of Production Research 23 (5) (1985) 1025-1054.
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[1l] P.A. Rubin, W.C. Benton, Jointly Constrained Order Quantities with Ail Units Discounts, Naval Research Logistics 40 (1993) 255-278. [12] D.P. Christy, J.J. Kanet, Open order rescheduling in job shops with demand uncertainty: A simulation study, Decision Sciences 19 (1988) 801-818. [13] W.L. Berry, R.J. Penlesky, T.E. Vollmann, Critical ratio scheduling: Dynamic due date procedures under demand uncertainty, I.I.E. Transactions 16 (1984) 81-89.
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[14] J.A. Orlicky, Reschedule with tomorrow’s MRP system, Production and Inventory Management 17 (2) (1976) 3% 48. [15] R.J. Penlesky, R. Srivastava, Open Order Rescheduling Heuristics in Alternative Operating Environments, AFITLA-TM-94-4, Air Force Institute of Technology, WPAFB, OH, October, 1994. [16] H.R. Lindman, Analysis of Variance in Complex Experimental Designs, Freemand, San Francisco, CA, 1974.
Theory and Methodology
Purchase quantity discounts and open order rescheduling in an assemble-to-order environment: The hidden economic tradeoffs Rajesh Srivastava a, W.C. Benton b3* a Air Force Institute of Technology, AFITILAL, 2950 P Street, Bldg 641. WPAFB, OH 45433-7765, USA b Department
of Management
Sciences, Fisher College of Business, The Ohio State University, 3087 Hagerty Hall, I775 College Road, Columbus, OH 43210, USA
Received 1 August 1996; accepted 1 June 1997
Abstract
In manufacturing systems, raw materials and components are purchased from outside suppliers. The purchasing decision consists of quantity and timing decisions. An added dimension to the purchasing decision is the availability of purchase quantity discounts. At the same time, order rescheduling is aimed at revising due dates of orders such that the planned schedule matches the actual schedule over time. Such revisions in quantity and timing affect the purchase decision. In this study, the impact of order rescheduling on various purchase quantity discount lot size models is evaluated under different operating environments. The findings of this research provide evidence for implementing dynamic purchase quantity discount lot sizing procedures when order rescheduling is incorporated into manufacturing systems. 0 1998 Elsevier Science B.V. All rights reserved. Keywords:
Purchasing; Manufacturing
planning and control; Open order rescheduling; Quantity discounts
1. Introduction
The purpose of materials management is to support the transformation of raw materials and component parts into shipped or inventory goods. The function of inventory in general is to decouple the entire transformation process. During the transformation process, materials are combined with labor, information, technology and capital.
Corresponding benton. [email protected]. l
author.
Fax:
+l-614-292-1272;
e-mail:
0377-2217/98/%19.000 1998 Elsevier Science B.V. All rights reserved. PIZSO377-2217(97)00258-O
The materials planning system is central for the acquisition of part and component needs in an assemble-to-order environment. Materials Requirements Planning (MRP) and just-in-time (JIT) systems are directed toward planning and controlling the important characteristics of material flow: how much of what materials flow and when. Since materials flow is at the heart of all manufacturing firms, these are powerful tools that could determine the success or failure of an entire manufacturing operation. The MRP system is the means in which the production will be carried out. The most important element of the MRP system is data
262
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of end item value
RM = Raw Materials FG- Finished Goods CP = Component Parts
A =Inventory
Storage
Fig. 1. Manufacturing process (197&1980). RM, Raw materials; FG, Finished goods; CP, Component parts; d, Inventory storage.
Division about the evaluation of various discount schedules. From his vantage point he suggested that the discount acceptance decision cannot be made independently from the open order rescheduling decision. He went on to suggest that record accuracy and order rescheduling were key inputs into determining whether to accept or reject a specific discount schedule. ’
The JIT approach is based on efficiently moving material through the productive system. Although many successful companies have embraced JIT philosophies they continue to use concepts to enhance the effectiveness of the manufacturing mission. Perhaps the most significant change in the past decade has been the purchasing function. During the time period 19701980 most American manufacturing firms fabricated 6&80% of the product’s value (see Fig. 1). Alternatively in the past decade a large number of manufacturing firms purchased between 60% and 80% of the product’s value (see Fig. 2). Since this impressive shift in percentages, the scope of the manufacturing system has shifted to increased outsourcing. As can be seen in Fig. 2, the complexity in the fabrication operation has been shifted up stream to the supplier. Under the traditional model the firm transformed significantly more raw materials and labor into the end product. Today since industrial firms are buying more and more subassemblies (component parts) the manufacturing focus is shifted downstream to the assembly operation. This significant shift has elevated the importance and profile of purchasing professionals. The purchasing function has become a key cost reduction center.
Thus the purpose of this study is to investigate the impact of order rescheduling and quantity discounts. In manufacturing systems, raw materials and components are purchased from suppliers to efficiently transform the inputs into finished products. The purchasing decision consists of the quantity and timing of purchased items. The decision also involves the basic tradeoff between ordering in bulk, i.e. fewer orders in the year and lower associated ordering costs, but higher inventory carrying costs; and frequently ordering in smaller quantities to minimize inventory carrying costs, but higher ordering costs. This is an important decision since inventories often represent a substantial portion of the investment made by a firm. Purchase quantity discounts add another dimen-
Recently one of the authors had a conversation with the former vice president of purchasing for the Westinghouse Appliance
’ Conversation with Mr. Harry L. Johnson, 20 February 1995, Columbus, OH 43229, USA.
accuracy.
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263
fizz\ cn ‘o%nd N
item value
jsembly /
I
RM - Raw Materials OPR 1 - Operation
1
FG= Finished Goods CP = Component Parts
A =Inventory Fig. 2. Manufacturing Inventory storage.
process
(198&1990).
Storage
RM, Raw materials:
sion to the decision making since they allow for reductions in material cost for large orders. Moreover, order rescheduling may be an important consideration in this new component-based manufacturing systems since actual production often differs from planned production. This leads to revisions in the schedules from the Master Production Schedule (MPS) to the purchase schedules. A revision in a schedule may imply both a change in quantity as well as in the timing of the orders. Order rescheduling affects a firm’s customer service measures as well as its inventory levels [1,2]. Order rescheduling may also affect the purchase quantity, leading to changes in the discount schedule and fi-
OPR 1, Operation
1; FG, Finished
goods; CP, Component
parts; d,
nal item price [3]. Thus the purpose of this research is to investigate the economic and customer service impact of accepting or rejecting various discount schedules when orders are rescheduled.
2. Background When a manager plans the acquisition of materials, whether raw materials or component parts, quantity discounts must be considered. Even though manufacturing complexity has been reduced, the nature of the complexity has shifted to supply chain and demand management.
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Manufacturing planning systems have several stages/levels of requirements. At each stage in the purchasing system, quantity decisions must be made. There has been extensive research on the general lot sizing problem. Considerations have ranged from simple applications of single stage lot sizing procedures in static planning horizons to complex capacitated multi-level lot sizing applications in rolling planning horizons. There has also been a substantial amount of literature on how buyers and suppliers react to quantity discounts. Hadley and Whitin [4] found that it is sufficient to check only the largest EOQ and all price breaks greater than the EOQ and ignore the price breaks less than the EOQ. Furthermore, Rubin et al. [5] also found that if the EOQ for the lowest unit price is not valid and if it falls within a quantity interval associated with the unit price, it is sufficient to check the EOQ based on the unit price as the next candidate EOQ and ignore any EOQs associated with the discount price lower than the unit price. Numerous studies have dealt with the buyer’s lot sizing problem [6,7,5]. Krupp [S] considered the returns on investment for the EOQ and all price break quantities. The traditional models for the quantity discount problem assume that the demand is known and constant. Abad [9] developed a procedure for determining the optimal selling price and the optimal lot size assuming that the demand function is price dependent. Benton [lo] considered quantity discount procedure under condition of multiple items, resource limitations and multiple suppliers. Later Rubin and Benton [l l] extended the work of Benton [lo] by offering a more general solution methodology. Later research has focused on analyzing quantity discount decision making under uncertainty in demand [6]. Such research has, however, failed to address concerns such as the effect that the rescheduling of orders already placed with the supplier (i.e. open orders) has upon the buyers’ purchase quantity discount decision. The performance of alternative discount lot sizing models under the open order rescheduling conditions still remains unknown. This is important since generally the results reported in literature are based on static snapshot views of the system and do not, there-
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fore, consider the dynamics of order rescheduling due to changes in customer orders or shop status. The effect of order rescheduling in MRP systems has also been explored extensively. However, most of such research focuses on the effect on the overall MRP system [6], under various order rescheduling procedures [6,1,2]. The issues of stability versus nervousness in MRP systems due to frequent order rescheduling has also been examined [12,2]. However, none of the research specifically examines the effect on purchase schedules and on purchase quantity discount models. This is important to the firm since rescheduling orders may lead to situations of excess inventory or shortages. In either case, a change in the timing and quantity of the item ordered is necessary. Such a change in quantity might affect the discount schedule, leading to a change in prices and thus, overall systems costs.
3. Current study The purpose of this study is to investigate the impact of order rescheduling on various discount quantity lot sizing procedures in various manufacturing environments. There are no known studies which examine this important interaction effect. Yet such an understanding is important from the buyer’s perspective in terms of minimizing total systems cost, as well as maintaining an adequate customer service levels. (Also see page 262 for comments by H. Johnson.) Previous research into purchase quantity lot sizing rules has evaluated the performance of different lot sizing rules under deterministic and uncertain demand schedules. This study will extend such research further to include the uncertainty in demand, and changes in production schedules which result from order rescheduling, which is faced daily by materials managers. Inclusion of such factors will allow for direct examination of the effect that the firm’s order rescheduling policy has on the performance of alternative quantity discount lot size models. This study specifically considers the purchase discount decision from the buyer’s philosophy and excludes situations such as the one time buy decision or blanket orders. It
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also allows for the buyer to have multiple suppliers and for changes in the order schedules and quantities. Earlier research on discount quantity lot sizing in MRP systems [10,6] has shown that rules such as modified McLaren’s Order Moment (MMOM) and modified Least Unit Cost (MLUC) perform better than other rules such as the traditional Purchase Discount Quantity (PDQ) rule under fixed demand schedules. Research on open order rescheduling [7,1,2] shows that under certain conditions filtered rescheduling heuristics such as Orlicky’s heuristic perform better than fixed (no rescheduling) or dynamic ( 100°/ rescheduling) rules. Filtered rescheduling implies that only a certain percentage of all due date change notices generated for the existing orders are implemented. This study also focuses on the interaction between lot sizing procedures and various rescheduling policies. What is more several realistic alternative manufacturing environments will be evaluated.
4. Research plan This section presents the research plan for evaluating different purchase discount quantity lot sizing models under the various rescheduling environments. A discussion of these two factors as well as other environmental factors which impact upon the lot size decision is presented first. Next, the simulation model is described. The experimental design is then presented. Finally, the results and conclusions will be presented.
4.1. Experimental factors The manufacturing environment is characterized by various environmental and operational factors, such as the coefficient of variation of demand, uncertainty in requirements, the time between orders, the lot sizing procedures employed [6] and the level of rescheduling implemented. Certain environmental factors (coefficient of variation [ 10,6,13], requirement uncertainty [ 10,6], order rescheduling classification [1,2]) found to be signifi-
Research 110 (1998) 261-271
265
cant in terms of system performance in previous studies [10,6] are used in this study. Other factors, such as the time between orders, purchase lead times, and uncertainty in lead times are kept fixed, so that these issues do not confound the study. The specific factors used in this study are described next. A specific description of the environmental factors is given below: 1. Coejicient of variation (CV): The CV is the standard deviation of the planned requirements divided by the average planned requirements per period. Requirements are generated to meet three specific levels of CV: zero, low and high. High CV values tend to increase the lumpiness of the requirements, which has been observed to have an effect on the lot sizing procedures. This factor has been found in previous studies [10,6] to have a significant impact on the systems performance. The specific values of CV used are taken from previous research [ 10,6]. 2. Requirements uncertainty (RU): RU measures the difference between the planned and the actual requirements for a period. Uncertainty in requirements is generated assuming a normal distribution of requirement errors around the planned requirements. The specific levels of the factor are shown in Table 1. Again, this factor has been reported to significantly affect system performance in previous discount quantity lot sizing related research [6]. The specific levels of RU used in this study are also taken from previous research PWI. Besides the environmental factors discussed above, which affect the performance of the discount quantity lot sizing procedures, there are also operational factors which are included in the study. These are discussed next. 3. Lot sizing procedures (LS): The most effective discount quantity lot sizing procedures will be used in this study. Detailed results in other environments are available for these [10,6], therefore they are selected to analyze the impact of order rescheduling. The specific lot sizing procedures used are the standard purchase discount order quantity (PDQ), the MLUC, and the MMOM procedures. These three procedures have been shown to outperform all others in previous research [10,6].
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Table 1 Factor levels for the experimental design
5. Simulation model
Coefficient of variation (CV) CV = 0.00 No variation CV = 0.29 Low degree of lumpiness CV = 1.85 High degree of lumpiness
The simulation model represents a realistic manufacturing system. The planned requirements are generated from a modified uniform distribution and the requirement errors are generated from a normal distribution. Reschedule notices are determined by generating changes in customer requirements, which in turn generates a change in the planned requirements of the purchased items, in terms of timing or quantity or both. A preliminary empirical analysis revealed that 10 replications of the experiment are provided to obtain observations for the experiment. The performance criteria used are the service level performance and the total cost of the solution. The total relevant cost of the solution is the sum of ordering, material, and inventory holding costs. The three heuristic lot sizing procedures used for determining purchase discount lot sizes have been rigorously tested against a variety of competing lot sizing procedures [10,6]. The best performing lot sizing procedures are the discount order quantity (PDQ), the MLUC and the MMOM procedure. These procedures are based on the underlying principles of the traditional economic order quantity, the least unit cost and McLaren’s order moment heuristics [ 10,6,14]. The specific criterion used in this study is the percent deviation of the given discount lot size rule from the standard PDQ procedure. The simulation model was validated by carrying out a number of verification checks. The run length was kept at 500 periods, which was observed to provide stabilization in the model. The planning horizon was kept at 100 periods which has been shown to be effective in literature [10,6]. The model was run for 50 periods before collection of the data for the next 450 periods. In addition, starting inventory was provided to avoid stockouts. The start up period of 50 was observed to eliminate transient conditions. Further, to eliminate the effect of differing service levels with the different rules, sufficient safety stock was provided to achieve a minimum service level of 99.99% [10,6]. Changes in order quantity and timing are initiated at the MPS level in the simulation, with sufficient lead time, thus
Requirements uncertainty (RU) RU = 0 No uncertainty RU = 40 Low uncertainty RU = 80 High uncertainty Lot sizing procedures (LS) PDQ: Purchase Discount Order Quantity MLUC: Modified Least Unit Cost MMOM: Modified McLaren’s Order Moment Order rescheduling (OR) Fixed: No rescheduling of orders Filtered: Orlicky’s heuristic (with 50% filtering) Dynamic: 100% rescheduling
4. Order rescheduling (OR) : Order rescheduling can be classified as dynamic, fixed, or filtered [14]. A dynamic procedure implements all indicated due date changes. A fixed procedure is one where due dates are never changed from their original values. Filtering implies revising a subset of the due dates. In this study, Orlicky’s heuristic [14,1] is used for filtering orders. The heuristic considers both the magnitude and the position of the due date in the planning horizon. This heuristic has been shown to be effective in earlier research [1,15], and details on this heuristic are provided elsewhere [14,1]. Fixed and dynamic rescheduling can be considered as extreme cases for any filtering procedure. With any filtering heuristic is the associated issue of degree of filtering, i.e., what proportion of the due date change notices are implemented. Again, previous studies [14,2] show that medium levels of filtering appear to be most effective. In this study, fixed, Orlicky’s heuristic with approximately 50% filtering, and dynamic rescheduling are used. The threshold value used in Orlicky’s heuristic to determine whether to reschedule or not is set such that approximately 50% of all rescheduling notices are implemented. Further, rescheduling does not affect delivery times since only those changes which have sufficient lead time are implemented.
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changes in the purchase schedule will not degrade customer service levels. Once the model was validated, an experimental design was set up to examine the relationship between order rescheduling and purchase quantity discount lot sizing procedures under various experimental conditions. The experimental design is discussed next.
6. Experimental design A full factorial design is used for the four factors with the levels shown in Table 1. The given design results in a total of (3 x 3 x 3 x 3) 81 problems. With 10 replications, a total of 810 observations are obtained.
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Table 2 Average percent deviation system costs
from PDQ by factor settings on total
Lot sizing procedures (LS) Coejicient of variation (CV) cv = 0.00 CV = 0.29 CV= 1.85 Requirements uncertainty SIGMA = 0.00 SIGMA = 40.00 SIGMA = 80.00 Order rescheduling Fixed Filtered Dvnamic
Mean value
MMOM
MLUC
-1.98
-3.32
-2.62
-2.26 -1.99 -1.69
-3.74 -3.34 -2.87
-3.03 -2.63 -2.19
-2.97 -1.64 -1.32
-4.49 -3.14 -2.32
-4.43 -1.79 -1.63
-1.52 -1.44 -2.98
-2.49 -2.97 -4.49
-2.06 -1.34 -4.45
(RU)
(OR)
6. I. Research questions
The major issue of interest is the impact of order rescheduling on the performance of purchase discount quantity schedules. Specifically, we are investigating the economic impact of the alternative lot sizing methods. In addition, interaction among the factors under various experimental conditions is also of interest. The formal research hypotheses are given below: HOI
Ho2
Order rescheduling (OR) does not affect the purchase quantity discount lot size procedure. The lot sizing procedures which work best in fixed OR environments work just as well in filtered or dynamic OR environments.
7. Experimental results
The marginal means are presented in Table 2 and the ANOVA results are presented in Table 3. All factors except CV (p = 0.07, marginally significant) had a significant main effect in terms of the performance criterion (Table 3). The most significant main effect was OR, followed by the RU and LS factors.
The highly significant OR factor, on the performance criterion of percent deviation from the standard PDQ lot size rule, implies that the degree of rescheduling of orders does have a significant impact on the performance of alternate lot sizing procedures. The marginal means shown in Table 2 show that in the dynamic rescheduling environment, the MMOM and MLUC (dynamic) proce-
Table 3 Analysis of variance results (Criterion: Average percent tion from the PDQ procedure on total system costs) Factor
effects
F
Level of significance
Main effects Coefficient of variation (CV) Requirements uncertainty (RU) Lot size procedures (LS) Order rescheduling (OR)
2.63 24.71 24.12 97.93
0.07 0.000 d 0.000 * 0.000 il
Two way interactions CVxRU cv x LS CVxOR RUxLS RUxOR LSxOR
3.48 0.66 4.45 1.30 6.41 7.88
0.008 0.621 0.001 0.000 a 0.000 * 0.000 a
ap < 0.001
devia-
@)
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dures are significantly better than the traditional PDQ lot sizing procedure. The implication is that the dynamic discount lot sizing procedures can better adapt to changes in the timing and quantity of orders than the standard PDQ procedure. Table 2 shows that as uncertainty (RU) increases, the performance of the dynamic lot sizing procedures tends to converge (see Fig. 3). This result is consistent with previous findings in literature. Fixed rescheduling implies that no changes are made in the ordering schedule. Under low RU, the difference between planned and actual require-
-
PW MLUC MYOM
-
I
I
I
,
1
2
3
4
Order
Fig. 3. Interaction procedure.
between
Rescheduling
order
Method
rescheduling
and
discount
Research 110 (1998) 261-271
ments is low, the dynamic lot sizing procedures perform better than standard PDQ lot sizing procedures. When RU is high, the difference between planned and actual requirements is high, causing the performance of dynamic lot sizing procedures to deteriorate. All of the two way interactions, except for the CV/LS interaction were significant. The strongest two way interactions are for LS/ OR and LS/RU. Interaction effects higher than two way are intractable and should not be reported in simulation experiments [16]. In terms of the research hypothesis investigated in this study, Tables 2 and 3 show that the level of order rescheduling greatly impact the performance of the lot sizing procedures. The LS/OR interaction is significant (p < 0.001); the analysis of the marginal means in Table 2 and Fig. 3 shows that both MMOM and MLUC are significantly better than the standard PDQ under both filtered and dynamic rescheduling. To flesh out a more thorough explanation of this finding we analyzed the fixed OR/LS and the dynamic OR/LS separately (see Fig. 4(a) and (b)). As uncertainty increases the lot sizing procedures converge (Fig. 4(a)). In Fig. 4(b), under dynamic rescheduling the dynamic lot sizing procedures are significantly more effective at all levels of uncertainty. This result clearly shows that in a filtered or a dynamic rescheduling environment dynamic quantity discount rules should always be implemented. Further, there is little difference in the performance of the two dynamic lot sizing rules. In filtered environments, the MMOM procedure is notably better than the standard PDQ procedures while the MLUC procedure is only marginally better than the standard PDQ procedure. A clear conclusion can be drawn that for purchased items, fixed OR is not a good managerial choice, there is always improvement in total system costs from utilizing filtered or dynamic rescheduling. Furthermore, use of dynamic lot size procedures is preferred to the static standard PDQ procedures. Similar results for these two factors have been obtained elsewhere under different environments. Dynamic discount lot sizing procedures have been shown to be better than the standard PDQ under the fixed OR scenario [6]. In a shop environment (as opposed to purchased items), filtered and dynamic OR have been shown
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Fixed
Rescheduling
Dynamic
Rescheduling
-
POD YLUC MMOY
a
-51 -20
0
-5 20
40
Requirements
60
60
100
Uncertainty
1
0
0
1
-
I
-
20
8.
40
Requirement
(a)
I.
60
1.
60
I
100
Uncertainty (b)
Fig. 4. Fixed rescheduling (a); dynamic rescheduling (b).
to be better than fixed OR [2,15]. Here, it is clearly shown that such results hold true in a purchased items environment, and that the interaction of the two is significant; such decisions should not be made in isolation. An earlier study [6] has shown that various environmental factors affect the performance of discount lot sizing procedures, and that the MMOM procedure performs better than the others under some conditions. This study shows similar results for the two environmental factors used, namely, CV and RU. CV has a much lesser impact on lot sizing procedures performance. As shown in Fig. 4(a), RU affects the performance
of the procedures significantly; as the uncertainty increases, the MMOM procedure becomes clearly better than the MLUC procedure; both being better than the standard PDQ procedure. Again, these findings are consistent with the earlier study
Fl. Another issue addressed in this study is the interaction between OR and the two environmental factors (CV and RU). These results are shown in Table 4. The ANOVA results in Table 3 show that both CV and RU have significant interactions with OR. This indicates that these environmental factors will also impact the managerial decision of the level of rescheduling to implement. The results
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Table 4 Average percent deviation from PDQ on total system costs by factor settings Order rescheduling (OR) Fixed
Filtered
Dynamic
SIGMA = 0.00 SIGMA = 40.00 SIGMA = 80.00
-2.94 -1.19 -0.42
-3.01 -0.73 -0.58
-2.98 -3.01 -2.95
Coejlicient of variation (CV) cv=o.OO CV = 0.29
-1.80 -0.82
-1.57 -1.71
-3.41 -3.43
CV= 1.85
-1.93
-1.04
-2.09
Requirements
uncertainty
(RU)
in Tables 2 and 4 also show that in most environments it may be preferable to use dynamic rescheduling if these dynamic discount lot sizing procedures are used. Filtered rescheduling is preferable for fixed environments but not for dynamic environments. However, earlier studies [ 1,2] have shown that filtering the rescheduling messages can lead to the same levels of customer service and inventory levels as dynamic rescheduling, without the system nervousness and higher costs/ complexity associated with dynamic rescheduling. Thus it may be preferable to implement filtered rescheduling along with dynamic discount lot sizing rules to achieve better system performance than fixed rescheduling, or using standard PDQ, and without the system nervousness which accompanies dynamic rescheduling.
8. Conclusions The complexicity in manufacturing has been shifted upstream to the supplier. This significant shift to increased outsourcing has elevated the importance and profile of purchasing professionals. This study has examined a managerially significant problem which purchasing and materials managers often face, that is, the issue of rescheduling orders, and the associated changes in the quantity discount schedule. Specifically, the effect of rescheduling orders on the PDQ decision was examined. The performance criterion used was the percent deviation of the dynamic discount lot siz-
Research I10 (1998) 261-271
ing rules from the standard static PDQ rule in terms of system costs. The findings of this research provide evidence for implementing dynamic purchase quantity lot sizing procedures when order rescheduling is incorporated into manufacturing systems. The research explicitly shows the conditions under which a particular lot sizing rule should be selected, and also the level of rescheduling appropriate from a purchasing decision standpoint in various operating environments. The linkages between the manufacturing system rescheduling decision and the purchasing decision are established. This should aid the practicing manager in grappling with a difficult problem. As an example, this research has shown that it may be preferable to implement filtered rescheduling with dynamic discount lot sizing rules in order to maximize systems performance.
References (11 R.J. Penlesky, U. Wemmerlov, W.L. Berry, Filtering heuristics for scheduling open orders in MRP systems, International Journal of Production Research 29 (11) (1991) 2279-2296. VI R.J. Penlesky, W.L. Berry, U. Wemmerlov, Open order due date maintenance in MRP systems, Management Science 35 (5) (1989) 571-584. [31 C. Ho, P.L. Carter, S.A. Melnyk, R. Narasimhan, Quantity versus timing change in open order: A critical evaluation, Production and Inventory Management 27 (1) (1986) 122-136. [41 G. Hadley, T.M. Whitin, Analysis of Inventory System, Prentice Hall, Englewood Cliffs, NJ, 1993, pp. 62-68, 3233 345. PI P.A. Rubin, D. Dilts, B. Barron, Economic order quantities with quantity discounts: Grandma does it best, Decision Sciences 14 (1983) 270-28 1. WI W.C. Benton, D.C. Whybark, Material requirements planning (MRP) and purchase discounts, Journal of Operations Management 2 (2) (1982) 137-143. [71 P. Kuzdrull, R.R. Britney, Total set up lot sizing with quantity discounts, Decision Sciences 13 (1982) 101-l 12. PI J.A.J. Krupp, ROF analysis for price breaks, Journal of Purchasing and Materials Management (1985) 23-25. [91 P. Abad, All unit quantity discounts, Decision Sciences 19 (3) (1988) 622634. 1101 W.C. Benton, Multiple priced breaks and alternative purchase quantity lot sizing procedures, International Journal of Production Research 23 (5) (1985) 1025-1054.
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[1l] P.A. Rubin, W.C. Benton, Jointly Constrained Order Quantities with Ail Units Discounts, Naval Research Logistics 40 (1993) 255-278. [12] D.P. Christy, J.J. Kanet, Open order rescheduling in job shops with demand uncertainty: A simulation study, Decision Sciences 19 (1988) 801-818. [13] W.L. Berry, R.J. Penlesky, T.E. Vollmann, Critical ratio scheduling: Dynamic due date procedures under demand uncertainty, I.I.E. Transactions 16 (1984) 81-89.
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[14] J.A. Orlicky, Reschedule with tomorrow’s MRP system, Production and Inventory Management 17 (2) (1976) 3% 48. [15] R.J. Penlesky, R. Srivastava, Open Order Rescheduling Heuristics in Alternative Operating Environments, AFITLA-TM-94-4, Air Force Institute of Technology, WPAFB, OH, October, 1994. [16] H.R. Lindman, Analysis of Variance in Complex Experimental Designs, Freemand, San Francisco, CA, 1974.