EVALUATING THE PERFORMANCE OF SUPPLY CHAIN SIMULATIONS WITH TRADEOFFS BETWEEN MULITPLE OBJECTIVES. Pattita Suwanruji S. T. Enns

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1 Proceedngs of the 00 Wnter Smulaton Conference R.G. Ingalls, M. D. Rossett, J. S. Smth, and B. A. Peters, eds. EVALUATING THE PERFORMANCE OF SUPPLY CHAIN SIMULATIONS WITH TRADEOFFS BETWEEN MULITPLE OBJECTIVES Pattta Suwanruj S. T. Enns Dept of Mechancal and Manufacturng Engneerng Unversty of Calgary Calgary, AB TN N, CANADA ABSTRACT Smulaton s well suted to the development and analyss of supply chan models, snce the problems of nterest tend to be comple and encompass uncertanty. However, there are typcally multple performance objectves that tend to conflct. A major problem n supply chan studes s that assumptons need to be made about the performance tradeoffs nvolved. Therefore, the conclusons may not be general. In ths paper we develop an approach that allows both delvery performance and nventory levels to be consdered over a range of tradeoffs. By developng tradeoff curves and analyzng the area under each we are able to reach conclusons that are more general and can be shown to be statstcally vald. INTRODUCTION The comparson of supply chan performance results obtaned usng smulaton models s dffcult for several reasons. Frst, the performance s dependent on many assumptons regardng both the supply chan envronment and the replenshment control system. Second, there are numerous responses of potental nterest. At a mnmum, we are usually nterested n some measure related to nventory nvestment and some measure related to customer delvery performance. However, there s a trade off between such measures, wth one typcally mprovng as the other deterorates. One approach s to control the level of one or more output measure across eperments to be equal and then make comparsons on the bass of only one response measure. However, ths approach s dffcult to mplement effectvely. Furthermore, the resultng comparsons apply only under the restrcted assumptons regardng the other fed responses. Another approach s to weght the output measures and then aggregate them nto a sngle response, usually an economc measure. Ths approach s also lmted snce conclusons may be contngent on the weghts chosen. The ablty to effectvely compare supply chan performance results s mportant. In partcular, ths s requred to help understand the factors and nteractons whch affect the supply chan s performance. As well, t s becomng of ncreasng nterest to compare dfferent plannng and control strateges used n supply chans. For eample, t s not well understood under what condtons Dstrbuton Requrements Plannng (DRP), reorder pont (ROP) or Kanban systems are preferable. A good approach for makng comparsons s requred to develop a better understandng of the relatve strengths of these systems and provde gudelnes for selecton and mplementaton (Suwanruj and Enns 00). In ths paper we present an analyss approach that has recently proved effectve n comparng supply chan results generated usng dscrete-event smulaton. Ths approach s well suted where metrcs related to nventory and delvery performance are of nterest. Tradeoffs are systematcally evaluated wthn a gven supply chan envronment and then comparsons are made across dfferent envronments. The followng sectons descrbe and llustrate the steps n ths analyss approach. EVALUATION USING TRADEOFF CURVES An epermental desgn must be developed for the supply chan scenaros to be tested before smulaton results can be generated. Ths epermental desgn should nclude one factor that allows the tradeoff between nventory and delvery performance to be controlled. For eample, f reorder ponts are beng used as the replenshment strategy wthn the supply chan, the reorder pont should be treated as one factor. Ths factor must take on a seres of levels so that a tradeoff curve can be developed for each combnaton of the other factor settngs. Fgure llustrates two tradeoff curves, ndcatng results when one addtonal factor s beng run at two levels, A and B. In ths llustraton, mean tardness s beng used as the delvery performance measure and average nventory counts are beng used as the nventory nvestment measure. In Fgure t s clear that curve A domnates curve B. At any level of mean tardness, curve A results n a lower nventory level. Lkewse, at any nventory level, curve A

2 Suwanruj and Enns Delvery Mean Tardness (hours) 8 6 A B Total Inventory (unts) Fgure : Tradeoff Curves results n lower mean tardness. Therefore, the scenaro assocated wth curve A would be preferable to that of curve B. However, n many cases t s not clear f the dfferences n the resultng tradeoff curves are statstcally sgnfcant. In some cases, there may even be a slght crossover n the curves. Furthermore, we are typcally dealng wth many comparsons n supply chan eperments. Therefore relyng on tradeoff curves for analyss alone may be nsuffcent. Calculatng the area under each of the curves allows comparsons to be made across both delvery and nventory measures. If suffcent observatons have been run along each of the curves, a smple algorthm based on straght lne appromatons between ponts along the curves wll yeld good estmates of the area. Fgure llustrates the computaton of areas for each of two curves. The ponts X and Y llustrate bounds that can be used to restrct area computatons to the regon of relevance, based on acceptable performance lmts. Delvery Mean Tardness (hours) Y' A B under curve A under curve B Total Inventory (unts) Fgure : Tradeoff Curve Analyss If each curve s replcated multple tmes, t s readly possble to estmate the error assocated wth the area under each curve. Furthermore, we can apply Analyss of Varance (ANOVA) technques to determne the statstcal sgnfcance of dfferences between the mean results for curves across multple scenaros. Therefore, the statstcal X' sgnfcance of varous man and nteracton effects can be establshed. Furthermore, regresson coeffcents can be used to estmate the magntude and drecton of varous effects. Montgomery (00) s one good resource that provdes detals on epermental desgn and analyss. EXAMPLE USING TRADEOFF CURVES In ths secton we llustrate a smple eample of the use of the analyss approach beng presented.. Problem Scenaro Two supply chan scenaros are beng compared, as llustrated n Fgure. It s assumed that reorder ponts are beng used for replenshment across the supply chan. The method of generatng the tradeoff curves s llustrated by the followng equaton, ROP = D ( RT ) SF. () where: ROP - Reorder pont for echelon D - Average demand per unt tme at echelon RT - Epected replenshment tme at echelon SF - Safety factor for echelon In ths sample problem the average demand s per hour at each of most downstream echelons. Epected replenshment tmes are between each of the echelons. The tradeoff curves are generated by ncreasng the replenshment safety factor, SF, from.00 to.9 by ncrements of 0.0. Therefore, twenty ponts are generated to determne each tradeoff curve. Echelon Echelon Echelon Echelon Confguraton Confguraton Fgure : Supply Chan Confguratons. Epermental Desgn Downstream Upstream The epermental desgn nvolves fve factors, n addton to the safety factor, SF, used to generate tradeoff curves for every combnaton of the other factors. These fve factors are all run at two levels, resultng n a total of combna-

3 Suwanruj and Enns tons of eperments for the two-level factors. The model for ths desgn, ncludng only two-way nteractons s, yˆ = ˆ β + 0 g= h= ˆ β gh g h. Where: ŷ - Ftted area under trade off curve ˆ β 0 - Regresson constant ˆβ - Coeffcent for A, confguraton - (-) for Confguraton, (+) for Confguraton ˆβ - Coeffcent for B, lot sze - (-) for small lot sze, (+) for large lot sze ˆβ - Coeffcent for C, demand pattern - (-) for level demand, (+) for seasonal demand ˆβ - Coeffcent for D, demand uncertanty - (-) for low uncertanty, (+) for hgh uncertanty ˆβ - Coeffcent for E, transt tme uncertanty - (-) for low uncertanty, (+) for hgh uncertanty Note that the factor levels are shown only n terms of the coded values. The real values assocated wth each of the - and + levels are not of concern n ths llustraton.. Smulaton Results The eperments were run usng the test bed descrbed by Enns and Suwanruj (00). The dscrete-event smulaton component n ths test bed reles on the use of ARENA.0 (Kelton, Sadowsk, and Sadowsk 00). The length of each smulaton run was 000 unts of smulated tme, wth 080 unts of tme beng used for ntalzaton to reach steady state. Three replcatons were used. In other words, three tradeoff curves were developed for each of the combnatons of two-level factor settngs. Wthn group varance was qute low. An eample of one tradeoff curve s shown n Fgure. Ths tradeoff curve compares the two confguratons when lot szes are small (-), demand patterns are seasonal (+), demand uncertanty s hgh (+) and transt tme uncertanty s low (-). In ths stuaton t would appear Confguraton, represented by the lower curve, performs best.. Analyss of Results Analyss of Varance (ANOVA) was performed usng the area under each of the tradeoff curves as the response. Lower areas represent better performance. The ANOVA () Delvery Mean Tardness (hours) Confg. Total Inventory (unts) Confg. Fgure : Sample Tradeoff Curve results are shown n Table. Note that only the sgnfcant factors and nteractons are shown. Ths analyss was generated usng Desgn Epert 6.0 (Montgomery, 00). Table : ANOVA Results Analyss of varance table [Partal sum of squares] Source Sum of Squares DF Mean Square F Value Prob > F Model.86E+09.88E < A.6E+08.6E < B.E+08.E < C.E+09.E < D.68E+08.68E+08.7 < E.80E+08.80E < AC.9E+08.9E < AD.7E+06.7E BC.0E+07.0E < BE.E+07.E+07.7 < CD 7.88E E+07. < CE.7E+07.7E < ACD 9.87E E Resdual.78E E+0 LackOfFt 9.78E+06 9.E Pure Error.80E E+0 Cor Total.9E+09 9 The coeffcents for the regresson equaton are llustrated n Table. These coeffcents are partcularly useful n ths analyss snce all the factors take on only two levels. Therefore t s very easy to determne the drecton and pont estmates for both the man and nteracton effects. The ft of ths model was very good, wth an R value of 99.0%. Fgure shows that the plot of the resduals s normally dstrbuted. Therefore, we can conclude that ths model s sutable for evaluatng the epermental desgn.

4 Table : Regresson Coeffcents = * A 07 * B 680 * C * D 68 * E 908 * A * C - * A * D -68 * B * C 97 * B * E -906 * C * D - * C * E - * A * C * D Suwanruj and Enns DES IG N-EX PERT Plot 08 X = A: Confg Y = C: DmdPat Des gn Ponts C - C A ctual Factors B: LS = - D: DmdCV = - E: Trans CV = In teracton G raph C: Dm dpat DES IG N-EX PERT Plot Normal Plot of Resduals A: Confg Fgure 6: Sample Interacton Plot Normal % Probablty the eample gven, ths analyss approach s also applcable where factors take on more than two levels. ACKNOWLEDGMENTS Ths research was supported n part by a grant from the Natonal Scence and Engneerng Research Councl (NSERC) of Canada Studentzed Resduals Fgure : Normal Probablty Plot of Resduals Further analyss can provde nsghts nto partcular behavor that may be of nterest. For eample, Fgure 6 provdes one nteracton plot that may be of nterest. In ths graph the confguraton, Factor A, s plotted aganst the demand pattern, Factor C. When there s no demand seasonalty (C=-) there s lttle dfference n the performance of the two confguratons. When there s demand seasonalty (C=), the performance deterorates under both confguratons. However, Confguraton (A=) does not deterorate as much as Confguraton (A=). From ths we could conclude that, gven the other factor settngs, Confguraton s better than Confguraton f demand s seasonal. REFERENCES Enns, S.T., and P. Suwanruj. 00. A smulaton test bed for producton and supply chan modelng, Proceedngs of the 00 Wnter Smulaton Conference, S. Chck, P.J. Sanchéz, S. Ferrn, and D.J. Morrce, Ed., 7-8. Pscataway, New Jersey: Insttute of Electrcal and Electroncs Engneers. Kelton, W.D., R.P. Sadowsk and D.A. Sadowsk. 00. Smulaton wth Arena, nd Ed., McGraw-Hll Co. Montgomery, D.C. 00. Desgn and Analyss of Eperments, th Ed., John Wley and Sons, Inc. Suwanruj, P. and S.T. Enns. 00. Informaton and logc requrements for replenshment systems wthn supply chans, Internatonal Journal of Operatons and Quanttatve Management, Vol. 8, No., 9-6. CONCLUSIONS Ths paper has llustrated an approach that has proved useful n understandng factors that affect supply chan performance and n comparng supply chan scenaros. Key strengths are that ths approach allows multple crtera to be used n evaluaton and that results can be statstcally valdated. Ths approach s very practcal to mplement where structured epermentaton can be performed, such as when smulaton methodology s used. The approach can be especally useful when comparng dfferent plannng and control strateges, such as those usng DRP, reorder pont and Kanban systems. Although not llustrated n AUTHOR BIOGRAPHIES PATTITA SUWANRUJI s a PhD canddate at the Unversty of Calgary, Canada. She receved her BEng n Chemcal Engneerng from Kasetsart Unversty and her MEng n Industral Engneerng from Chulalongkorn Unversty, both n Bangkok, Thaland. Her research nterests le n modelng and analyss of supply chans. Her emal address s <psuwanru@ucalgary.ca>. SILVANUS T. ENNS s an Assocate Professor at the Unversty of Calgary, Canada. He receved hs PhD from the Unversty of Mnnesota. Hs research nterests le n

5 the development of algorthms to support enhanced MRP performance as well as varous aspects of job shop, batch producton and supply chan modelng and analyss. Hs emal address s <enns@ucalgary.ca>. Suwanruj and Enns