CENTRALIZED VERSUS DECENTRALIZED PRODUCTION PLANNING IN SUPPLY CHAINS

Transcription

1 CENRALIZED VERSUS DECENRALIZED PRODUCION PLANNING IN SUPPLY CHAINS Georges SAHARIDIS* a, Yves DALLERY* a, Fikri KARAESMEN* b * a Ecole Cenrale Paris Deparmen of Indusial Engineering (LGI), , saharidis,dallery@lgi.ecp.fr * b Deparmen of Indusrial Engineering, Koç Universiy, 3445 Isanbul, urkey , fkaraesmen@ku.edu.r Absrac: wo analyical models are developed o solve he producion planning problem in a mulienerprise supply chain. In he real operaional world, for compeiive reasons, frequenly each enerprise prefers o opimize is producion plan wih lile care abou he ohers members of he supply chain. his case is presened hrough a simple model of decenralized opimizaion. he aim of his sudy is o analyze he wo ypes of opimizaion (Cenralized-Decenralized) and compare hem. he iniial quesion is: wha is he gain of global (cenralized) opimizaion in conras o local (decenralized)? We characerize his gain by comparing he opimal profis obained in boh cases: he decenralized and cenralized cases. Keyword: Global-Local Opimizaion, Producion Planning, Cenralized-Decenralized models.. Inroducion Producion planning is he process of deermining a enaive plan for how much producion will occur in he nex several ime periods, during an inerval of ime called he planning horizon. Producion planning also deermines expeced invenory levels, as well as he workforce and oher resources necessary o implemen he producion plans. Producion planning is done using an aggregae view of he producion faciliy, he demand for producs, and even of ime (using monhly ime periods, for example). Producion planning is affeced by higher-level decisions ha consrain producion. Fixed resources limi producion. However, in some siuaion i may be feasible o change he amoun of equipmen Hax []. Moron Kamien & Lode [5] propose, a model in which subconracing can be explicily considered as a producion planning sraegy; also possible marke and no marke subconracing mechanisms and heir coss are discussed. Elsayed & homas [6] presen he purpose of he aggregae producion planning and Lee & Kim [7] develop wo models for planning, he firs one for producion planning and he oher one for disribuion planning in a global approach. Finally Riane, Ariba and Iassinoviski [8] propose a model for a sysem called Hybrid Flow-shop which is close o our model. We are unaware of any paper ha explicily compares he effecs of decenralized opimizaion in producion planning. Aggregae producion planning has been reviewed several imes before. Hax & Candea [] give a review of lieraure up o he mid 7 s. Gelders & Van Wassenhove [3] review many differen soluion procedures and homas and McClain [4] give a complee overview of producion planning. In Secion we presen he sudied sysem and he modeling assumpions as well as he main research quesion and he wo models ha are developed. Secion 3 presens our numerical and qualiaive resuls. Finally in Secion 4 he fuure research is presened.

2 . he Sysem and he Modeling Assumpions Our sysem consis of wo producion plans, Facory (F) and Facory (F), for which we would like o obain he opimal producion plan, wih wo oupu socks and wo exernal producion faciliies called Subconracor and Subconracor (Subconracor gives final producs o F and Subconracor o F). We have a finie horizon divided ino periods. he producion lead ime of each plan is equal o one period (e he facory or q he subconracor). In he following figure we presen our sysem. Subconracor Subconracor Facory Sock Facory Sock D Figure :he ow-sage supply chain We assume ha he above sysem produces a single produc. Facory (F) produces semi-finished componens for F which produces he final produc. Backorders are no allowed and all demand have o be saisfied wihou any delay. Each facory has a nominal producion capaciy and he role of he subconracor is o provide addiional exernal capaciy if desirable. For simpliciy, we assume ha boh iniial socks are zero and also ha here is no demand for he final produc during he firs period. he capaciy of socks and subconracors are assumed o be infinie. he producion and subconracing coss are fixed during he enire period and proporional o he quaniy of producs produced or subconraced respecively. Finally he producion capaciy of F is equal o he capaciy of F. In he decenralized approach we have wo inegraed local opimizaion problems from he end o he beginning. Namely, we firs opimize he producion plan of F and hen ha of F. On he oher hand, in global opimizaion we ake ino accoun all he characerisics of he producion in he F and F simulaneously and hen we opimize globally our sysem. he iniial quesion is: Wha is he gain obained by Global opimizaion in conras o local? Below (Figure -3), we analyze and compare hese wo ypes of opimizaion and we presen our resuls in secion 3.

3 Subconracor Subconracor Facory Sock D Facory Sock D Local Opimizaion Local Opimizaion Figure : Local Opimizaion schema Subconracor Subconracor Facory Sock Facory Sock D Figure 3: Global Opimizaion schema wo linear programming formulaions are developed o solve he above problems and hey are presened in he appendix. Model gives he soluion for global opimizaion and model for local opimizaion. We uilize he wo models o invesigae cerain qualiaive behavior in erms of producion, invenory and subconracing levels. Our iniial quesion is presened by he following example: Consider a supply chain wih a seasonal demand and idenical nominal producion capaciy a he wo facories as presened in he figure 4 below:

4 Demand - Producion Capaciy Quaniies Periods Figure 4 In order o saisfy he demand during he enire period and wih he hypohesis ha we have periods during which he demands are greaer han he capaciy producion, we mus find a soluion for hese periods hrough invenories or subconracing. In he local opimizaion approach, we firs opimize he producion plan of F and hen ha of F. he policy adoped for F, in his example, is o subconrac he supplemenary demand and for F o consiue an invenory. he whole cos in his case is 4 (8 for F and 4 for F). On he conrary in he global opimizaion when we ake ino accoun all he characerisics of producion of he F and F he policies changed compleely and became invenory for F and F follow he demand (he reason ha F can saisfy his demand only wih his own producion is ha demand is always lower han is capaciy). In his case he oal cos is 37 ( for F and 6 for F). We found ou a difference of 5. he reason for his significan difference beween he wo resuls is ha in he second opimizaion we ake ino accoun all sysem coss simulaneously. In he following figures (5-8) we presen he resuls of his example. he black curve depics demand, he disconinuous black he producion, and he horizonal whie he producion capaciy and he whie wih black poins he subconraced producs. Local Opimizaion Producion Plan Facory Local Opimizaion Producion Plan Facory Quaniies Periods Quqniies Periods Figure 5 Figure 6

5 Global Opimizaion Producion Plan Facory Global Opimisaion Producion Plan Facory Quaniies Periods Quaniies Periods Figure 7 Figure 8 In he nex secion we presen numerical resuls and he characerisics we found in our sysem. Deails and proof can be found in [7] 3. Resuls 3. Qualiaive resuls We firs used he wo models o explore cerain qualiaive behavior. Firs of all we proved ha ha he sysem s cos of global opimizaion is less han or equal o ha of local opimizaion. In erms of each one facory s coss, he F s producion cos in local opimizaion is less han or equal o ha of global and F s is greaer han or equal in local han in global. We were also able o show ha he sysem s opimal producion plan is he same when he difference beween he producion cos and he subconracing cos says consan. Also he difference beween he coss of local and global opimizaion is consan. In addiion when he global opimizaion gives an opimal soluion for F o subconrac he exra demand regardless of he plan of F, he local opimizaion has exacly he same soluion. Finally we demonsraed ha when a he local opimizaion, he exra demand for F is saisfied from invenory, hen he global opimizaion has he same opimal plan. 3. Numerical resuls In his secion we presen some numerical resuls. In figure 9 he Relaive Difference (RD) beween he coss of he local and global opimizaions is presened in funcion of invenory cos h. For fixed h, RD increase as funcion of h and goes up o % when h is close o h. I becomes even greaer when h > h alhough his siuaion will no in general appear. Relaive Difference Relaive Difference Cos of Sock Relaive Difference Figure 9 : h 5

6 Also we found ha he RD increases when he subconracing cos for F increases also. We keep all cos fixed (excep csc ) and we sar wih a value of csc equal o zero and we examine he behavior of our sysem in global and local opimizaion. We found hree differen inervals: csc <5 (exra producs subconraced ) ; 5<csc <55 (exra producs subconraced and socked) ; 55<csc (exra producs socked). In he nex schema (figure ) he RD for he differen cos of subconracing is presened: Figure : Relaive Difference he following four schemas (figure -4) presen he comparmen of he DR when we keep he csc fixed and we change he h. Afer hese numerical examples we have found ha we have exacly he same form. In he firs space he DF is zero, in he second increases wih flucuaion and always wih he peak of he graph and in he hird space we have again zero. Figure : Relaive Difference h Figure : Relaive Difference h Relaive difference Relaive difference Relaive difference Relaive difference Relaive difference csc csc Figure 3 : Relaive Difference h Figure 4 : Relaive Difference h 5 Finally in he nex able we presen an example ha shows ha when he difference beween he cos of producion and he cos of subconracing say consan he opimal plans aken from he models is he same.

7 he Coss Invenory Producion Subconracor Facory Facory Facory Facory Facory Facory h 6 h Cp 4 6 csc cp 4 3 csc 6 49 Z * And when we change for example he cp and csc we ake exacly he same producion plan. he Coss Invenory Producion Subconracor Facory Facory Facory Facory Facory Facory h 6 h cp csc cp 4 3 csc 6 49 Z *

8 4. Conclusion: I is known ha decenralized planning resuls in loss of efficiency wih respec o cenralized planning. I is, however, difficul o quanify he difference beween he wo approaches wihin he conex of producion planning. We invesigaed his issue in he seing of a wo plan series producion sysem. In paricular, we explored a locally opimized producion planning procedure where he downsream plan opimizes is producion plan and he upsream plan follows his requess (while opimizing is coss). We hen compared his locally opimized (and decenralized) approach wih global opimizaion where a single decision maker plans he producion quaniies of he supply chain in order o minimize oal coss. Using a combinaion of analyical and numerical resuls, we characerized sysem srucures which lead o small (or large) efficiency loss. Fuure research focuses on he exension of hese ideas o demand processes wih random componens. Appendix: Variables: : ime horizon ( monhs) ; P, : producion in F during period ; I, : Invenory of F during period ; SC, : producs subconraced during period in F ; P, : producion in F during period ; I, : Invenory of F during period ; SC, : producs subconraced during period in F. Coss: cp : producion cos of F ; cp : producion cos of F ; h : Invenory Holding Cos of F ; h : Invenory Holding Cos of F ; csc : Cos of subconraced producs for F ; csc : Cos of subconraced producs for F.

9 GLOBAL OPIMIZAION he LP formulaion for F and F: Objecive funcion: MinZ cp P, + h I, + csc SC, + cp P, + h I, + csc Subjec o: Balance Equaions: I, I, + P, + SC, d for,.., I, I, + P, + SC, P, + SC, for,..., I, ; I., Producion capaciy: P,, P, producion capaciy for ; P ;,, P. SC, LOCAL OPIMIZAION he LP formulaion for F: Objecive funcion: MinZ cp P, + h I, + csc Subjec o: I, I, + P, + SC, d SC, for,, ; P, producion capaciy ; I, P.,, he LP formulaion for F: Objecive funcion: MinZ cp P, + h I, + csc Subjec o: SC, I, I, + P, + SC, P, SC, for,,-; P, producion capaciy ; I, P.,,

10 References: [] Hax, A.C. (978) Aggregae producion planning, in: J. Moder and S. Elmaghraby (eds.) Handbook of Operaions Research, Van Nosrand Reinhold, New York. [] Hax, A.C., and D. Candea (984) Producion and invenory Managemen, Premice Hall, Englewood Cliffs, NJ. [3] Gelders, L.F., and L.N. Van Wassenhove (98) Producion Planning: A review. European J. Oper. Res. 7, -. [4] L.J. homas and J.O. McClain (993) Handbooks in operaions research and managemen science Volume 4 Logisics of producion and invenory (S.C. Graves, A.H.G. Rinnooy Kan and P.H. Zipkin, Ediors), Chaper 7, Norh-Holland. [5] Moron I., Kamien and Lode Li (99) Subconracing, Coordinaion, Flexibiliy and producion smoohing in aggregae planning, Managemen Science Vol 36 No. [6] Elsayed A Elsayed, homas O. Boucher: Chaper 4 of Analysis and Conrol of Producion Sysems Published sep93 by Pearson Educaion (Series: Prenice Hall Inernaional Series in Indusrial and Sysems Engineering). [7] Saharidis Georges, Dallery Yves, Fikri Karaesmen Cenralized versus Decenralized Producion Planning in Supply Chains, echnical repor, Ecole Cenrale Paris, in preparaion.