OPERTIONS ND SUPPLY CHIN MNGEMENT Vol. 4, No., January 20, pp. -20 ISSN 979-356 EISSN 979-387 Parner Selecon n Suppler-Buyer Relaonshp wh Inegraon of Leadme Decsons under Demand Uncerany Suaon Yos. Hdaya, Kasuhko Takahash 2, Kasum Morkawa 3, Kunhro Hamada 4, 2, 3 Deparmen of rfcal Complex Sysems Engneerng Deparmen of Socal and Envronmenal Engneerng 4 Graduae School of Engneerng,Hroshma Unversy, Hgash Hroshma 7397527, JPN Emal: akahas@hroshma-u.ac.jp 2, kmorkawa@hroshma-u.ac.jp 3,hamada@naoe.hroshma.u.ac.jp 4 Luca Dawa 5, nd Cakravasa 6, 5, 6 Deparmen of Indusral Engneerng InsuTeknolog Bandung, Bandung 4032, INDONESI Emal: yos@mal..b.ac.d, luc@ganesha.b.ac.d 5,and@mal..b.ac.d 6 bsrac We developed a procuremen decson model, whch akes no accoun parner selecon and opmal order quany wh he negraon of a planned producon leadme operaonal decson. Leadme s aken no accoun n me and cos performance o acheve on-me delvery of a supply chan (SC sysem. We conras he hree followng orgnal equpmen manufacurer (OEM condons, ( longer leadme o he buyer bu a a lower cos for he suppler, so he buyer has o add crashng cos o reduce he leadme; (2 less leadme o he buyer bu a a hgher cos for he suppler; (3 shorer leadme o he buyer by addng crashng cos o reduce he nvenory cos. Takng no consderaon he mpac of demand uncerany drecly o he buyers, we focus on smulaneous procedures n achevng an opmal soluon. Our model consders an objecve funcon conssng of operaonal coss and lead me decson under negraed supply chan enes (supplers, sub-assembly manufacurers (OEMs, and buyers. Based on our numercal resuls, by radng-off nvenory cos and leadme crashng cos, he bes possble combnaons of parners n fulfllng demand from he marke are B - 2 -S 2 and B 2 - -S 3. We found ha hese wo combnaons gve $4,02.95 oal prof per year o he SC sysem. We proposed approprae sraeges ha could be appled a OEM by consderng order arrval mng and leadme. Keywords: demand uncerany,opmum leadme decson, parner selecon, supply chan managemen.. Inroducon Supply chan managemen (SCM s he managemen of acves ha ransforms raw maerals no nermedae goods and fnal producs, and hen delvers hose fnal producs o cusomers. These supply chan acves nvolve purchasng, manufacurng, dsrbuon, and ransporaon o marke. From an operaonal perspecve, he goal of SCM s o negrae supplers, manufacurers, warehouses, and sores, so ha merchandse s produced and dsrbued a he rgh quanes, o he rgh locaons, and a he rgh me o mnmze sysem-wde cos whle sasfyng servce requremens n he mos effecve way (Smch-Lev e al., 2000. anmen of hs goal may be hndered when he approprae sraegc parner decson s separaed from mporan operaonal decsons due o demand uncerany, whch drecly mpacs buyers. *Correspondng uhor
2 Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 Consderng he fac ha he buyer mus buld dfferen knd of producs o mee ancpaed cusomer demand, and snce fuure demand s usually unceran, s dffcul o se plans a he rgh level n procurng he approprae maeral. Subsequenly, demand uncerany s one of he mos mporan facors sgnfcanly mpacng SC performance. Because procuremen can only be done once whn one perod, he opmal procuremen lo sze should be properly deermned. In a probablsc nvenory, he oversock nvenory sll can be used n he nex plannng perod, so only mpacs he holdng cos. Whle a he end of he sellng season, he produc s prce wll be decreased or dscouned because of he deeroraon of funcon, model, and echnology wll be oudaed (Hdaya e al., 2009. In fac, he on-me delvery of an assembly sysem generally dmnshes due o produc or componen shorages. The cos consdered n hs suaon s he under-sock cos. Shorages ofen resul n losses n producon capacy and/or cusomers goodwll nduced by mssed produc delvery daes. The prmary cause of componen shorage s he nheren uncerany assocaed wh procuremen and/or manufacurng leadmes, whch can be arbued o a varey of reasons rangng from unexpeced delays n shppng, ransporaon, and recevng mes o varable seup, processng, and nspecon mes. In nvenory wh uncerany, leadme can be reduced a an added cos. By reducng he leadme, cusomer servce and responsveness o produconschedule changes can be mproved and reducon n safey socks can be acheved. Manufacurers also end o reduce he oal operaon cos whle ryng o sasfy objecves n leadme and delvery prompness, so ha more prof can be aaned. Our model negraes uncerany n forms of marke demand probably nformaon wh sraegc and operaonal decsons n a sngle framework. The model wll be able o capure he coss of accal and/ or operaonal funcons of he supply chan under uncerany. Opmal leadme decsons beween buyers and orgnal equpmen manufacurers (OEMs ha mnmze he oal amoun of ems ou of sock and nvenory holdng coss by addng he possbly o reduce hem, whch s refleced n he leadme crashng cos, ogeher wh opmal procuremen, economc order quany (EOQ, and parner decsons under demand uncerany are also negraed n our mul-echelon nvenory model. Our purpose s o develop procuremen decson regardng sraegc parner selecon and opmal order quany wh he negraon of leadme operaonal decsons. Takng no consderaon he drec mpac of demand uncerany o buyers, subsequenly o he amoun of nvenory of OEMs as he decouplng pon n our SC sysem, we focus on smulaneous procedures n achevng an opmal soluon. Three enes n SC neworks (supplers, subassembly manufacurers (OEMs, and buyers are negraed no one objecve funcon, maxmzng oal SC prof, whch conrass leadme crashng cos versus nvenory cos n he oal operaonal cos. Prevous sudes relaed o he ssues of suppler selecon n he suppler-buyer relaonshp and unceranes n erms of demand and leadme n SCM are dscussed n Secon 2. In Secon 3, we sae he problem o be addressed whch selecs approprae SC parner by consderng demand uncerany and lead me decson and conrasng nvenory versus crashng coss. In Secon 4, we formulae a mxedneger lnear programmng model for negraed sraegc parner selecon and operaonal leadme decson by consderng demand uncerany. We hen presen and dscuss some compuaonal resuls and analyss n Secon 5. Fnally, Secon 6 hghlghs he resuls of he sudy and dscusses he drecon for fuure work. 2. Leraure Revew There are a sgnfcan number of documened sudes n he area of operaons research and managemen scence n SC ha address some of hese ssues relaed o parner selecon and uncerany. In a suppler-buyer relaonshp, he parner selecon process becomes an mporan sraegc decson. Focusng on a sngle elemen (buyer only or suppler only n he SC canno assure he effecveness of he nework (Croom, 200. In parner selecon, here has been pleny of research snce he semnal work by Dckson (966. lso, Chan e al. (2004 provde a comprehensve revew and classfcaon of prcng and nvenory coordnaon problems dscussed n he leraure of SC. Weber and Curren (993 dscussed a mul-crera analyss for vendor selecon. They developed a model for mnmzng
Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 3 oal cos, lae delveres, and supply rejecon due o boh nfrasrucure consrans and consrans mposed by he company s polcy. Chaudhary e al. (993 developed a lnear programmng model for vendor selecon wh prce breaks. Degraeve e al. (2000 revewed and evaluaed a number of vendor selecon models, by usng he oal cos of ownershp as a bass for comparson. They obaned he relave effcency of he models and showed ha mahemacal programmng models ouperform rang models by solvng all he models for a sngle real-lfe daase of a purchasng problem. Curren and Weber (994 exended he exensve leraure n facly locaon problems o he soluon of vendor selecon problems. de Boer e al. (200 provded a comprehensve revew of publshed decson mehods for vendor selecon and classfed hem under a framework ha akes no accoun he dversy of purchasng scenaros and covers all phases of he vendor selecon process. Mos of he research menoned above only consdered he accal or sraegc level n hese decsons. Few consdered he operaonal level n hs sraegc decson. Wh regards o uncerany, Snyder (2006 concluded hs research by denfyng four research avenues applcable whn oday s operaon research echnology. One of he avenues s he mul echelon model. In hs avenue, Snyder (2006 saed ha here s a need for models ha capure he coss of accal and/or operaonal funcons of he supply chan under uncerany. Demand uncerany s he mos obvous and sgnfcan source of uncerany for mos sysems (rda and Henne, 2006. Therefore, managng uncerany s nevable for a componen ha requres sophscaed echnology and he manufacurer guaranees ha he damage probably of hs componen s very low for he lfe of he produc. The manufacurer produces only a lmed number of componens based only on order, and reorder usually s no allowed. Sabr and Beamon (2000 saed n her research ha uncerany (e.g. cusomer demands, exchanges raes, ravel mes, amoun of reurns n reverse logscs, supply leadme, ransporaon coss, and holdng coss s one of he mos challengng bu mporan problems n supply chan managemen. If a probablsc behavor s assocaed wh unceran parameers (eher by usng probably dsrbuons or by consderng a se of dscree scenaros each of whch wh some subjecvy probably of occurrence, hen a sochasc model may be he mos approprae for hs suaon (Melo e al., 2009. noher modelng possbly arses when some parameers predcably change over me (e.g. demand levels and coss. Under uncerany, an oversock produc canno be used n he fuure because of s lfe cycle, and s funcon, model and echnology are oudaed (Hdaya e al., 2009. In hs research, hey found ha by consderng demand uncerany, he buyer wll become more responsve o he marke, hus affecng he expeced leadme delvery delay and more able o reduce he rsk of under-sock and over sock condons ha mpac he expeced oal cos. Demand uncerany wh regards o nvenory problems also encourages us n negrang hs ssue n a sraegc parner selecon decson. Hller (2002 developed a model for consderng purchasng, orderng, nvenory, and shorage coss where componens are replenshed ndependenly accordng o lo sze and reorder pon polcy. Ma e al. (2002 developed a mul-perod and mulsage assembly nework model wh mulple producs and sochasc demands, and proposed a scheme o express he desred base-sock level a each sockng pon as a funcon of he correspondng acheved fll rae. Ln e al. (2006 analyzed he quanave relaonshp beween leadme and he nvenory level of common componens and found effcen ways o deermne cusomzaon level, opmze nvenory managemen, and lower coss n a mul-perod model of componen commonaly wh leadme. Mohebb and Choobneh (2005 suded he mpac of nroducng componen commonaly no an assemble-o-order envronmen when demand s subjec o random varaons and componen procuremen orders experence random delays. By usng smulaed daa, hey showed ha componen commonaly sgnfcanly neracs wh demand and SC unceranes, and he benefs of componen commonaly are mos pronounced when boh unceranes exs. Nonas (2007 consdered he problem of fndng he opmal nvenory level for componens n an
4 Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 assembly sysem where mulple producs share common componens n he presence of random demand. The nvenory problem he consdered s modeled as a wo-sage sochasc recourse problem where he frs sage s o se he nvenory levels o maxmze expeced prof, whle he second sage s o allocae componens o producs afer observng demand. Regardng he ssue of leadme uncerany n assembly sysems, several sudes ook he dualsourcng echnque no consderaon when he supplers leadmes are sochasc, bu much less research was concerned wh he coordnaon problem n supply leadme uncerany. Yano (987 consdered he coordnaon problem when he supply leadmes are sochasc for dfferen componens n an assembly sysem. Hopp and Spearman (993 consdered he problem of seng opmal leadmes n an assembly sysem where all componens are purchased and he only manufacurng operaon s he fnal assembly. They descrbed wo formulaons of he problem: ( mnmzng oal nvenory-carryng and ardness coss and (2 mnmzng nvenory-carryng coss subjec o a servce consran. Hegedus and Hopp (2000 descrbed a praccal mehod for seng safey leadmes for purchased componens n assembly sysems wh uncerany n he supply process. Tang and Grubbsroom (2003 suded a dealed coordnaon problem n a wo-level assembly sysem wh sochasc leadmes for lower-level ems and deermnsc demand for he fnshed em. They found ha he opmal safey leadme s he dfference beween planned and expeced leadmes. In hs research, we enhanced her research n solvng he opmal planned leadmes o mnmze he oal amoun of ou-of-sock ems/componens and nvenory holdng coss by addng he possbly o reduce hem, whch s refleced n he leadme crashng cos, ogeher wh opmal procuremen, EOQ, and parner decsons under demand uncerany. ccordng o our leraure sudes regardng suppler selecon, mos of he research menoned above only consdered a accal or sraegc level n her decsons. Few researchers consdered he operaonal level n hs sraegc decson. L and O Bren (999 developed a model of he supplerbuyer relaonshp n a herarchcal way of boh sraegc and operaonal levels, bu n a sequenal flow. In her research, afer he parner selecon process, hen a he operaonal level, manufacurng and logscs acves were opmzed under gven arges. We enhanced hs sequenal flow wh a smulaneous one and by addng new facor, demand uncerany and leadme decsons. Regardng leadme as an operaonal decson, he prevous research only consdered leadme decsons as me un measuremen decsons o acheve on-me delvery performance. They dd no negrae leadme delvery decsons wh he oal SC cos or prof. We negraed hese decsons wh he expeced oal SC cos; whch fnally affecs he oal SC prof as he negraed objecve funcon. 3. Problem Saemen We assume an SC whch comprses a number of componen supplers, sub-assembly manufacurers facles (OEM facles, and buyers n dfferen geographcal locaons and neracng hrough global markeplaces. We assume a global markeplace for componens hrough whch componen supplers sell a varey of componens o a sub-assembly manufacurer (OEM. The OEM uses hese componens n he producon of a varey of sub-assembles n s manufacurng facles. These sub-assembles are hen sold o buyers hrough sub-assembles markeplaces. The buyers can be defned as mulnaonal-sales companes of OEMs or ndependen dsrbuors. Our SC confguraon s shown n Fgure. Demand uncerany as a new facor n hs proposed model s affeced by cusomer buyng behavor, whch s refleced by poenal benefs of demand forecasng and s probably o reduce he rsk of oversockng or shorage. There are hree condons (wo non-deal and one deal ha mgh exs, ( real demand s more han procuremen quany (under-sock condon exss (2 real demand s less han procuremen quany (oversock condon exss, and (3 real demand s he same as procuremen quany (no oversock and undersock. For achevng a wn-wn soluon among hese hree condons, we should fnd he opmal quoed procuremen quany per year and quoed EOQ per order ha maxmzes prof by consderng demand uncerany n forms of probably. One of hese hree
Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 5 Fgure. Supply chan confguraon Decson varables Economc order quany (Q* Opmum procuremen lo sze quany(k* Bnary varables ha show supply from OEMs j o buyer and supply from suppler k o OEMs j Planned producon leadme (L Canddaes of Componen Supplers ( k Canddaes of ssembly Manufacurer (OEM s( j Canddaes of Buyers ( S B Parameers: ( D, P ( D, C s, Pr, C u S2 Demand unceranes S3 2 B2 physcal flows of componen and produc Parameers Un maeral, ransporaon, producon, carryng, orderng coss Mnmum producon hroughpu me Normal produconleadme un of componen ~ un of produc condons s faced by buyers because of he drec effec of demand uncerany from he marke. To ancpae leadme uncerany among supplers and conngen orders from buyers, OEMs should ac as a produc decouplng pon. The effor n reducng he leadme wll nduce an ncrease n he crashng cos, bu he decrease n leadme can reduce he safey sock of OEMs. The deermnaon of he opmum leadme leads o he deermnaon of demand durng leadme and he opmum order quany. The opmum order quany wll nduce he orderng cos, so he change n leadme leads o a change n nvenory and opmum order quany, and furhermore o he orderng cos. Our research also negraes he leadme operaonal decson ha wll mpac nvenory and crashng coss, and fnally wll be mposed on he oal operaonal cos and he sraegc parner selecon decson. The basc dea o add hs consderaon s o ge some rade-offs wh he followng hree OEM condon, ( longer leadme o he buyer bu a a lower cos for he suppler, so he buyer has o add crashng cos o reduce he leadme; (2 less leadme o he buyer bu a a hgher cos for he suppler; (3 shorer leadme o he buyer by addng crashng cos o reduce he nvenory cos. ccordng o he above suaon, we classfy wo ypes of sock pons ha are necessary beween OEMs and buyers n our SC srucure. Before a produc s sold o a buyer, consderng he leadme beween OEMs and buyers, OEMs should have some nvenory o ancpae conngen orders (couneraced by he demand safey facor from buyers and some delay from supplers. Therefore, he safey sock level of OEMs s a funcon of leadme. Excess nvenores of OEMs for boh producs and componens can be sored and used for he nex perods. The holdng cos of an OEM produc before s sold o buyers s calculaed usng Eq. (9. We assume ha he leadme of he suppler o he OEM s zero for componens. The holdng cos of an OEM componen s calculaed usng Eq. (20. On he oher hand, afer he fnshed produc s sold o buyers, becomes he nvenory of hese
6 Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 buyers. Ths nvenory of buyers s smlar o he newsboy nvenory problem, where excess nvenores are salvaged. There are only oversock and undersock coss, calculaed usng Eqs. ( o (. Ths s due o he fac ha a hgh-echnology conen produc as defned n Hdaya e al. (2009, such as auomobles producs, has a dsncve lfe cycle paern. Under uncerany, an oversock produc canno be used n he fuure because of s lfe cycle and because s funcon, model and echnology are oudaed (Hdaya e al., 2009. Ths prncpal s used by buyers n deermnng he opmal demand lo sze by consderng he probably of demand, under-sock, and oversock coss. fer decdng he opmal lo szes, buyers send he order nformaon o he OEMs and laer, he OEMs send he nformaon o he supplers. Ths flow of nformaon means ha buyers do no have nvenory sock. Moreover, excess nvenores of buyers are salvaged. However, for OEMs and supplers, excess produc and componen nvenores can be sored and used for he nex perods. The number of nvenores n OEMs s also nduced by he leadme beween buyers and OEMs. In bref, buyers own he oversock and under-sock coss, whle OEMs own he nvenory holdng cos. Regardng crashng cos, he OEMs nform he buyers of her mnmum producon hroughpu me (days and normal producon leadme (days for a produc. To avod oversock and under-sock condons, and also consderng demand uncerany (demand probably from he marke, buyers also consder he possbly of shorenng he delvery leadme o fulfl marke demand by payng crashng cos. These flows are closed-loop flows. ccordng o he flow of nformaon, he relaed coss of supplers, OEMs, and buyers ha fnally nduce he oal supply chan prof are developed n our model. 4. Model Developmen We developed a model for supply chan plannng ha harnesses he nformaon whn global markeplaces. Specfcally, we deermne he opmal procuremen quanes whn he seleced parner n he downsream and upsream markeplaces and selec he SC confguraon whn markeplaces ha wll allow us o mee he demand. Ths decson s based upon he produc demand n he downsream markeplaces n he SC afer he members of downsream markeplace consder demand uncerany and leadme facors from he marke and supply of maerals n he upsream markeplaces of he SC. In parcular, hs research wll nevably play an mporan role n hs SC n he conex of he global SC for componens and sub-assembly producs. Model ssumpons The followng assumpons were used n developng our model:. The leadme L s deermnsc, and he demand s sochasc. 2. Demand of a produc s derved from he marke by sochasc condons wh he nformaon of s probably of even. 3. Producs and componens wll be ordered a he begnnng of each plannng perod n one plannng horzon. Producs decrease a a consan speed, whereas componens decrease a a lo sze consumed by her suppored producs. 4. Consderng he leadme beween OEMs and buyers, he OEMs should have safey sock o ancpae flucuan and unceran demand. In hs case, leadme affecs safey sock and fnally he nvenory cos of he OEMs. 5. fer deermnng he opmal leadme and opmal order quany, buyers release orders o OEMs, who n urn release orders o her supplers. The release orders from he buyers are fxed and conan only he quany of componens and producs ha wll be suppled from he OEMs o he buyers and from he supplers o he OEMs. There s some leadme beween OEMs and buyers and zero leadme beween OEMs and her supplers. The exsence of leadme resuls n he need of produc safey socks n OEMs. 6. lo-for-lo (L4L polcy s used o deermne he szes of componen procuremen orders ha wll be aached o producs. Ths polcy s negraed usng he concep of a mul- echelon deermnsc nvenory sysem. 7. The orderng lo sze s fxed for every order. 8. The ordered pars wll be suppled a he me of order bu wll be consumed lo-per-lo. 9. The prce of componens does no depend on he order lo sze (no dscouned prce. 0. There are no producon capacy or sorage consrans.
Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 7 Model Noaons By referrng o he supply chan srucure n Fgure, ogeher wh he model assumpons, we developed a ls of parameers and varables n he developed model, as lsed n Table. 4. Objecve Funcon Table. Index Parameers Noaons and defnons of parameers, varables, and decson varables Buyer s ndex (=,2,...,n j ssembly componen manufacurer s (OEM s ndex (J=,2,...,o k Componen suppler s ndex (k=,2,..., u j lernaves of demand lo szes(=,2,...,z, z s maxmum demand lo szes durng plannng horzon. l Number of crashng componen (l=,2,..., w s D P(D P r C m C p C r C u C s C r H m H f m f PL mn PL normal Varables ETC LCC HCM HCF EF(K EM EF F(K D r DL Safey facor of demand Forecased marke demand (un/year Probably of demand D Fnshed produc sellng prce ($/un Componen purchasng cos ($/un Fxed producon cos ($/un Transporaon cos ($/un Buyer s under-sock cos ($/un Buyer s oversock cos ($/un Un coss reducng producon leadme of componen ($/day Un sock carryng cos of componen ($/me un Un sock carryng cos of fnshed produc ($/me un Un orderng cos of componen from OEMs o suppler ($/order Un orderng cos of fnshed produc from buyer o OEMs ($/order Mnmum producon hroughpu me (days Normal producon leadme (days Expeced oal cos ($/year Expeced leadme crashng cos ($/year Toal socks carryng cos of componen ($/year Toal socks carryng cos of fnshed produc ($/year Expeced prof of buyer when buyer procures K un Toal orderng cos of componen ($/year Toal orderng cos of fnshed produc ($/year Prof pay off f buyer procures K un of componen, when real demand s D uns Reorder pon Expeced demand durng leadme Varables sσ L Safey sock level * Opmal lo szes when demand un s equal o procuremen un (deal condon, no shorage or oversock. In hs case, demand un equals procuremen un. Oherwse, f <*, hen oversock condon exss, and *<<z, hen under-sock condon exss. Decson Varables b j Bnary varable ha shows supply from OEMs j o buyer b kj Bnary varable ha shows supply from suppler k o OEMs j L Planned producon leadme (me un K* Opmal procuremen quany (un/year Q* Economc order quany (un/order The expeced oal prof s consdered n our model as an negrave objecve funcon o oban opmal decson varables. Ths negraed objecve funcon akes no accoun he expeced oal operaonal coss by radng-off nvenory and leadme crashng cos ogeher wh he under-sock and oversock coss faced by buyers. Demand uncerany, as a new facor n hs proposed model, s affeced by cusomer buyng behavor ha s refleced by poenal benefs of demand forecasng and s probably n order o reduce he rsk of oversockng or shorage. In hs case, poenal demand and s probably, coss for maeral (C m fxed producon (C p ransporaon (C r, under-sock condon (C u, oversock cos condon (C s, carred maerals (HCM, carred fnshed producs (HCP, ordered maerals (EM, ordered fnshed producs (EF, and leadme crashng cos (LCC ogeher wh produc prce (P r are consdered o deermne he oal expeced prof as, shown n Eq. (. Equaon ( shows he relaonshp beween oal expeced prof, expeced prof f he buyer procures K uns of a componen when he real demand s D uns, and he probably of demand along he plannng perod. Subsequenly, Eq. ( s mpaced by he operaonal cos of he SC sysem. Ths relaonshp wll nerconnec he nfluence of demand uncerany and he decson of parner selecon. The ndexes, j, k, ndcae ha all prces and coss depend on where o produce and from whch supplers he componen s suppled. The decsons ha show where o produce and from
8 Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 where o procure are ndcaed n he bnary decson varables n Eq. (32, whch are relaed o he sraegc parner selecon decson. EF * + * ( K EF ( K < 0; for (6 Objecve Funcon: Maxmze ( There are wo non-deal condons ha mgh exs, ( real demand s more han he procuremen quany (under-sock condon exss (2 real demand s less han he procuremen quany (oversock condon exss. Buyers need o fnd he opmal quoed procuremen quany per year and quoed EOQ per order ha maxmze he oal supply chan prof by consderng demand probably. Furhermore, we would lke o se he mahemacal relaonshps relaed o demand uncerany and relaed varables. Equaons (2 o ( are relaed o he deermnaon of opmal quany o be procured o maxmze prof of SC sysems. In a non-deal condon, wheher demand quany s more or less han he procuremen quany, he excess or shorage of producs wll affec he expeced prof n each combnaon of suaons. (2 (3 If we consder under-sock cos as (D -K C and oversock cos as (K -D C, hen a buyer can esmae he opmal quany o be procured by comparng he expeced oal prof ha can be ganed f he/she decdes o procure ha quany, as shown n Eq. (4. Ths buyer s decson nduces he physcal and nformaon flow along he SC. EF + n EF( K = F F = = uj o n * ( K = [ {( Pr Cs D ( ETC Cs K } P( D ] uj o n z [ {( Pr ETC K ( D K Cu} P( D ] k= j= = = * z k = j= = = ([ K D] P( D uj o * n ([ K D] = [ {( Pr ETC D } {( ETC Cs K }]; f D < K F k= j= = = uj o n z ([ K D] = [ {( Pr ETC K } {( D K Cu }]; f D K k= j= = = * (4 z ( ETC Cs ( Pr + Cu Cs P( D < 0; for, j k z P = * + EF, = * + ( D ( ETC Cs <, ( Pr + Cu Cs * * ( K F( K < 0; for ; for, j k z ( ETC Cs ( Pr + Cu Cs P( D < 0; for, j, k = * z ( ETC Cs ( P D = * <, ( Pr + Cu Cs ; for, j k Equaons (7 and (9 lead us o he fnal concluson of he probably of he opmal procuremen un by consderng relaed varables, as expressed n Eqs. (0 and (. Henceforh, he probably value for each alernave of a supplerbuyer combnaon wll be used as he demand uncerany facor, (P * and negraed no he maeral npu and produc oupu processes. z P( D = * P ( ETC Cs ( + Cu Cs ( D ; for, j k > > P, Pr = * + * ( z K ( ETC Cs ( Pr + Cu Cs z * + ( z K ; for, j k > > P, (7 (8 (9 (0 ( 4.3.2 Dealed Explanaon of Cos Componens n Deermnng Toal Expeced Prof The expeced oal cos s he sum of he maeral cos, fxed producon and ransporaon coss, componens and producs holdng cos, componens and producs orderng cos, and leadme crashng cos for he enre SC. The oal relevan cos s denoed by ETC (Q j, Q j, L j, as shown n Eq. (2. EF + uj o n * ( K = ( Pr D P( D ( CsD P( D ( ETC K P( D + ( CsK P( D uj o n z ( Pr K P( D ( ETC K P( D + ( CuD P( D ( CuK P( D k= j= = = * k j = = = = (5 ETC Q ( j, Q, Lj, Q Qj D Cm + D Cr + h + hj + sjσ uj o n z 2 2 = k = j= = = D w + cr l l r Q jl ( jl j l = l= D D L + j + j Q Qj l l w ( Lj Lj + c ( PLnormalj PL mn j (2
Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 9 4.3.2. Varable coss relaed o me-based measuremen The oal cos componens n Eq. (2 consss of wo ypes of cos caegores, fxed cos (maeral, producon, and ransporaon coss and varable cos (nvenory, orderng, and leadme crashng coss ha are relaed o me-based measuremen (leadme decson. In hs subsecon, we explan n more deal he varable coss ha are affeced by leadme decson. Consderng ha leadme has l componens for each OEM manufacurng facly. The l h componen for each possble buyer and OEM j combnaon has a mnmum producon hroughpu me PL mn l, normal producon leadme PL normal l, and a crashng cos per un me c rj l. The leadme componens are crashed one a a me sarng wh he componen of leas c r. The ner-dependence among he leadme componens may requre crashng of more han one componen a a me. In many realsc cases, he leadme componens are ndependen. We assume ha here s no nerdependence among leadme componens. Le L j l be he lengh of he leadme wh componens,2,3,... w, whch s crashed o her mnmum, and hen we oban Eqs. (3 and (4. w Lj = PL mn Lj PLnormal = Lj ;, j mn l= jl w l = w Lj = Lj PLnormalj PL mn j ;, j max l l l = (3 (4 The leadme crashng cos LCC(L j for a gven s L < L j L gven by Eq. (5. LCC j l j l - (5 The reorder pon s gven by Eq. (6, whch s relaed o leadme decson. D L j n Eq. (6 s he expeced opmal demand of buyer durng he leadme consumed by OEM j o delver producs o buyer, and s j σ L j n Eq. (6 s he produc safey socks for buyer jl max w ( L = c ( L L + c ( PLnormal PL mn j rjl j ( l jl l= rjl j l j l Where s j s known safey facor of OEM j for ancpang conngen order from buyer. In deermnng he opmal safey facor, we use he echelon holdng cos concep, shown as Eq. (7. s j = ( h h j j h (7 To ancpae leadme and demand uncerany and avod producon delay, he OEMs n he SC sysem need some produc safey socks. On he oher hand, he leadme beween he OEMs and supplers s zero. In hs case, he OEMs and supplers do no necessary provde safey sock for componens. Subsequenly, he nvenory consumpon paern of he produc from OEMs o buyers and he nvenory consumpon paern of he componen from supplers o OEMs are dfferen. For OEMs, he nvenory-carryng cos per year s h j I j (Q j, r j, where I j (Q j, r j, s he average on-hand nvenory ha can be approxmaed by he average ne nvenory f he back-order durng a replenshmen cycle s small or even zero compared wh he cycle lengh. The expeced ne nvenory mmedaely before and afer he recep of an order of sze Q j s * * r j - D and Q j + r j - D L j, respecvely. If we assume a lnear de crease over he cycle, hen we oban Eq. (8. I Q ( Q, j j r + r D L = + s σ L ;, j j j j j j j j, 2 Q (8 In developng he nvenory cos, we use he concep of a mul-echelon seral nvenory sysem. ccordng o hs concep, we assume ha one produc s produced from one un of componens, whch, n urn, s obaned from a suppler. When delverng a bach, all he componens are delvered a he same me bu consumed per lo. No backorders are allowed. The produc wll be delvered a he same me based on he order from he buyers and he number of he produc wll consanly decrease. The above explanaons brng us o Eqs. (9 o (23. 2 rj = D Lj + sjσ Lj ;, j, r j = expeced demand durng lead me + produc safey sock (SS j SS j = ss j x (sandard devaon of lead me demand; (6 Toal socks carryngcos of HCF = = o n o j= = z j = = = n h j ( I ( Q, r j j Qj h j + sjσ 2 j producs(by OEM = o n z Qj h j + r j D L j= = = 2 L j j (9
0 Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 Toalsockscarryng cos of componens (by OEM = HCM = j Q u o h k= j= 2 u o z j Toalorderngcos of componens (OEM D Q k = j= = o j n z D j Q = = = j suppler = EM = Toal orderng cos of producs (buyer OEM = EF = (20 (2 (22 (4 Opmal Q j, Q, L j, and wll be he values for whch he oal expeced cos s mnmum. 4.3.3 Consrans The frs consran n Eq. (27 s relaed o he opmal leadme decson ha should occur beween he cumulave mnmum and maxmum duraon mes. Ths condon guaranees ha here s no delay on he SC sysem. L j l < L j L j l (27 Expeced crashng cos (buyer o n z j = = = ETC w D c Qj l = rjl = LCC ( Lj = ( Lj w Lj + cr ( PLnormal PL mn l j j l l l l = ( Q,, j Q L hj D w D c ( L L + c ( PLnormal PLmn = 0 Qj = 2 j 2 2 r l Qj Qj j ( l j l rl l = j l jl (23 b j = 0 or K * j M ( b j (28 (29 Noce ha n Eq. (2, for fxed L ETC(Q j,q,l j s convex n Q j dan Q (see Eqs. (24 and (25. However, for fxed Q j, ETC (Q j,q,l j s concave n L j n he nerval (L j, L j ] see Eq. (26. Therefore, l- for fxed, he mnmum leadme occurs a he end pons of he nerval. 2D c rl Qj = w 2 ( Lj L + ( mn ( j cr l PLnormalj PL l l l j l ( 2 [ + ( ] l= D j LCC Lj 2 hj = hj (24 Equaons (30 and (3 show ha f here s * acvy n varable K, hen he value of b would be. Oherwse, bnary varable ha shows componen supply from suppler k o OEM j o buyer (b would be zero. M ndcaes a very large number. b K = 0 or ( * M b (30 (3 ETC ( Q, Q, L j Q 2D Q = h (, Q, L ETC Qj Lj = 0 D = hj sjσ L 2 cr l = 0 2 Q (25 (26 Fnally, Eq. (32 shows ha every sage n he SC can only be suppled from one vendor from he prevous sage. n o = j= o uj j= k = b j + b = (32 ccordng o hese facs, we developed he followng procedure for fndng opmal Q, Q j, and L. ( For each break pon L j n Eq. (4, compue n Eq. (24. (2 Compue Q by usng he concep of a seral mul-echelon nvenory sysem n Eq. (25. (3 Compue he correspondng expeced oal cos n Eq. (2. 5. Numercal Expermens 5. Man Numercal nalyss To show he effecveness of he proposed model, we llusrae he above soluon procedure usng he followng example. The problem s solved usng he LINGO 8.0 program. The parameer daa for operaonal and sraegc decsons are npued no he program. I s caegorzed as mxed-neger lnear programmng. We used he daa lsed n Tables 2 and 3 for he numercal expermen. Table 2
Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 Table 2. Daa relaed o demand uncerany Buyers ( 2 Demand Lo Sze σ P(D P(z D = 400 4 0.3 =2 500 5 0.2 0.7 =3 600 6 0.2 0.5 =4 700 7 0.5 0.3 =5 800 8 0. 0.5 =6 900 9 0.05 0.05 = 400 4 0.3 =2 500 5 0.2 0.7 =3 600 6 0.2 0.5 =4 700 7 0.5 0.3 =5 800 8 0. 0.5 =6 900 9 0.05 0.05 P r = $50/un C u = $30/un C s = $50/un P r = $52/un C u = $40/un C s = $45/un Parameer relaed o oversock and under-sock Condons Table 3. Daa for operaonal and sraegc decsons Parameers Leadme Componen from o B Leadme Componen from o B Buyer (B Normal Duraon (day Normal Duraon (day Buyer 2 (B2 Mnmum Duraon (day Mnmum Duraon (day OEM Facly ( Un Crashng Cos ($/day Un Crashng Cos ($/day OEM Facly 2 (2 Leadme Componen from o B 2 Leadme Componen from o B 2 Suppler (S Normal Duraon (day Normal Duraon (day Suppler 2 (S2 Mnmum Duraon (day Mnmum Duraon (day Suppler 3 (S3 P r ($/un 50 52 - - - - - Cu ($/un 30 40 - - - - - Cs ($/un 50 45 - - - - - ($/order - - 50 (B 00 (B 50 ( 20 ( 60 ( - - 40 (B 2 80 (B 2 40 ( 2 00 ( 2 90 ( 2 h ($/un 50 ( 40 ( - - 20 ( 20 ( 20 ( 60 ( 2 80 ( 2 - - 40 ( 2 40 ( 2 40 ( 2 Cm ($/un - - - - 5 0 5 Cr ($/un - - 2 (B 3 (B 2 ( 2.5 ( 2.5 ( - - 4 (B 2 5 (B 2 2 ( 2 3 ( 2 4 ( 2 Un Crashng Cash (S/day 6 2 0.4 5 0.5 2 6 2.2 2 2 5 0.9 3 0 3 5 3 0 3 6 Un Crashng Cash (S/day 24 0 5 0.2 2 6 2.2 2 4 3 3 9 2 3.5 3 9 2 5 The resuls from our developed model are lsed n Table 4 and n Fgs. 2 o 4. represens he daa relaed o he marke and o demand uncerany. Table 3 represens he daa relaed o operaonal and sraegc decsons among SC members. ccordng o he numercal resuls lsed n Table 4, he bes buyer-oem-suppler combnaons ha maxmze he oal SC prof are B - 2 -S 2 and B 2 - - S 3. Ths s a global and negraed decson afer
2 Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 Table 4. Numercal resuls consderng demand uncerany, under-sock and oversock condons of buyers n response o marke demand, and also nvenory coss versus leadme crashng cos. For B - 2 -S 2, even hough he S 2 has a hgher cos (from he hgh fxed cos of hs combnaon, reducng he leadme from seven o hree weeks has sgnfcanly reduced nvenory cos of producs, compared wh addng a small crashng cos. Ths combnaon s a ypcal decson n choosng OEMs wh less leadme o buyers bu a a hgher cos for he suppler. Fgure 2. Invenory paerns of producs and componens Fgure 2(a. Produc nvenory paerns n OEMs For B 2 - -S 3, reducng he leadme from fve o wo weeks has reduced nvenory cos of producs, whch s balanced by he crashng cos. The lower fxed cos of hs combnaon mosly conrbued o he prof. Ths combnaon s a ypcal decson n choosng OEM wh shorer leadme o buyers by addng crashng cos o reduce he nvenory cos of OEM. These wo combnaons resuls n a prof of $4,02.95 per year o he SC sysem Fg. 2 shows he nvenory paerns of producs by buyer and componens by OEMs. OEMs have some amoun of safey socks of producs ha depend on he leadme decson (see Fg. 2(a, where OEMs only have carryng cos for her componens, whch s no affeced by he leadme decson (see Fg. 2 (b. From Fgs. 3 and 4, we can see he proporon and conrbuon of fxed and varable coss. By reducng he leadme for varable coss, he nvenory cos of a produc decreases by addng crashng cos. Overall, by consderng he opmal leadme decson, he oal varable coss are reduced for every combnaon of buyer-oem-buyer. The effecveness of our model n erms of reducng varable cos s shown n Fgure 4 (d. Q* Componen Consumpon Paern Fgure 2(b. veragenvenory = ½ Q* Componen nvenory paerns (black lne and componen consumpon paerns (grey lne n OEMs 5.2 Sensvy nalyss ccordng o Table 2 n sub-secon 5.2, we choose small numbers (% of demand devaons o gve some nsghs on he sgnfcan effecs of small demand devaon no opmal leadme and safey sock decsons of OEMs. Whle deermnng he opmal procuremen lo sze of buyers, however, he demand devaon does no affec more han he probably of demand evens. lso, our parameer seng and some key parameer values have shown a sgnfcan dfference
Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 3 Fgure 3. Conrbuon of fxed coss Fgure 4. Conrbuon of varable coss Fgure 4(a. Conrbuon of varable coss before consderng leadme decson Fgure 4(b. Conrbuon of varable coss afer consderng leadme decson
4 Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 Fgure 4(c. Recapulaon of oal varable cos mprovemen before and afer consderng leadme decson Fgure 4(d. Model effecveness (mproved on average by 3.% on average of operaonal process producvy for all parner combnaons beween before and afer consderng leadme and demand unceranes. In hs sub-secon, we explore a more flucuang sandard devaon of demand o show a more sgnfcan benef. The resuls were obaned from a larger sandard devaon of mean demand up o 30%. These sensvy analyss resuls are shown n Fg. 5, and he deals are aached n he ppendx. Fgures 5(a and 5(b show ha he greaer he demand devaes, he componen orderng cos ncreases nsgnfcanly, whle he produc orderng cos, and he componen and produc nvenory coss decrease sgnfcanly. sgnfcan decreases n OEM produc-nvenory cos needs o occur reduce leadme and he laer ncrease n crashng cos. fer demand devaes more han 0% from he mean demand, opmum leadme decsons are changed and he leadme should be mnmzed. The crashng cos only conrbues 2%-9% of he oal varable coss. s he demand devaon ncreases, he conrbuon of crashng cos o varable cos decreases. For he B 2 - -S 3 combnaon, he conrbuon of crashng cos sars o decrease afer 3% of demand devaon. Ths ndcaes ha B 2 - -S 3 s a ypcal decson n choosng shorer OEM leadme by addng he crashng cos o reduce OEM nvenory cos. From he composon of varable and fxed coss and he proporon of crashng cos o he oal varable cos, B - 2 -S 2 s a ypcal decson n choosng he leas amoun of leadme of OEMs bu a a hgher cos for he supplers. noher fndng s ha B - 2 -S 2 and B 2 - -S 3 are always he bes combnaons for maxmzng oal prof o he SC sysem. Ths means ha our model always acheves a global opmum soluon.
Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 5 Fgure 5. Conrbuon of varable coss Fg. 5(a Impac of demand devaon on componen cos and oal SC prof for B 2 - -S 3 combnaon condon by consderng he uncerany of order arrval, as shown n Fg. 6. To Observe he sensvy of some parameers n he model, we change some of he demand uncerany values (ndcaed as P(z > D and safey facor ha mpacs he leadme of componens and producs. Ths analyss s used for sudyng he approprae producon sraegy o be appled n several demand uncerany suaons. ccordng o xsaer (2000, he safey facor s srongly affeced by he value of j and. h j - h h j If, we should use he same bach sze for h j - h h boh producs and componens, and consequenly, each me we produce a bach of componens, should be mmedaely used for produc producon. Ths mples ha we do no need any sock of componens and ha our wo-sage sysem of suppler-oem and OEM-buyer can be replaced by a sngle-sage sysem. Ths condon s also suffcen n he case of me-varyng demand of a produc and wll become mporan n he leadme decson. In hs analyss, we wan o synergze our fndngs wh a praccal suaon n each sage or pon of even where unceranes occur. We dscuss hs qualavely (see Fg. 6 n he followng paragraphs. Fg. 5(b Impac of demand devaon on componen cos and oal SC prof for B - 2 -S 2 combnaon Fgure 6. Sensvy analyss pon of vew 5.3 Manageral Insghs For sensvy analyss, we nvesgaed he mpac of changng demand uncerany values ogeher wh changng safey facor values. We assume ha he safey facor value s a posve neger ha shows he replenshmen of sock beween producs and componens relaed o he sngle seral mulnvenory sysem; whle he demand uncerany value s he probably relaed o he supply of fnshed-produc socks o fulfll he marke s demand (uncerany oubound SC. We se up hree sensvy-analyss scenaros o deermne he effecs of safey facor and demand probably parameers. The sensvy analyss daa are summarzed n Table 5. For he concep of leadme n Fg. 2, he analyss of resuls wll be analyzed based on he approprae sraegy appled by manufacurng facles for each
6 Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 Based on Fg. 6, whch s relaed o he common manufacurng sraegy characerscs, when he order has a hgh probably of arrvng before he procuremen (maeral supply process, he bes manufacurng sraegy s make-o-order (MTO. In our model, hs condon also srenghens he procuremen probably of componens. When he order has a hgh probably of arrvng beween he procuremen (maeral supply and producon (produc manufacurng processes, he bes manufacurng sraegy s assembled-oorder (TO. Subsequenly, when he order has a hgh probably of arrvng beween producon (produc manufacurng and shpmen (produc oupu processes, he bes manufacurng sraegy s makeo-sock (MTS. In our model, hs condon srenghens he procuremen probably of producs. We deermned he expeced prof of each benef or loss by usng one of hese sraeges n he begnnng of our model by akng no accoun demand uncerany. Furhermore, we would lke o observe he mpacs of leadme o he oal performance crera ha are drecly affeced by demand uncerany and safey facor values on he approprae manufacurng sraegy for all alernaves of parner combnaons. The resuls are shown n Fgs.7 o 9. ccordng o Table 5, we choose and vary he demand uncerany values, procuremen probably of componens and procuremen probably of producs o nvesgae her mpac on he chosen sraegy (MTO, TO, or MTS. We use all model equaons o evaluae he approprae sraegy. When one of he values s fxed, he oher wo are vared. ccordng o he numercal resuls, he cos componens mosly mpaced by hese parameerrangng values are he nvenory coss of componen and producs. Subsequenly, hese cos componens sgnfcanly conrbue o oal SC prof performance. Based on he resuls of he frs scenaro (see Fg. 7, when he safey facor s a a lower level, OEM manufacurng facles should apply he MTS sraegy. Ths s shown by he slghly hgher produc nvenory cos compared o maeral nvenory cos. In conras, when he safey facor s a a hgher level, OEM manufacurng facles should apply he MTO sraegy. From he supply delay pon of vew, hs MTO sraegy wll reduce any wase n sock coss a a longer leadme. consanly ncreasng convex shape from he leadme and nvenory cos curves for boh componen and producs show ha along wh he ncreasng values of demand unceranes and safey facor, manufacurers end o change her sraegy from MTS o MTO. In he second scenaro, we appled dfferen values of and j for deermnng he safey h h j - h facor. When he value of s lower han he h value of j (see Fg. 8, OEM manufacurng h j - h facles should apply he TO sraegy. Ths s shown as a slghly dfferen rsk conrbuon of Table 5. Sensvy analyss daa Demand probably value (Scenaro I, II, III Scenaro I Scenaro II Scenaro III Toal safey facor wh equal j value of and. h h j - h h j h h j - h j h j - h 0.05 0.2 0.70 0.97 0.95 0.80 0.5 0.6 0.50 0.92 0.85 0.50 0.30.0 0.30 0.85 0.55 0.40 0.50.4 0.5 0.75 0.35 0.5 0.70 2.0 0.05 0.50 0.5 0.05
Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 7 Fgure 7. Resuls of Scenaro I nvenory coss of boh componens and producs, nsead of ncreasng leadme. However, when demand uncerany (P(z > D s hgh, MTS s he bes sraegy. Ths s due o a sharp ncrease n he nvenory cos of producs compared wh ha of componens. consanly ncreasng convex shape from he curve for componens and producs shows ha along wh ncreasng demand uncerany values and decreasng safey facors (where he value of s h lower han he value of j, OEM facles end o h j - h change her sraegy from TO o MTS. In he hrd scenaro, when he value of s h hgher han he value of j (see Fg. 9, he MTO h j - h sraegy s beer han MTS for OEM manufacurng facles. Ths s due o he fac ha he ncrease n makes he maeral socks n he manufacurer h neffecve. Therefore, non-sock sraeges wh an accepable leadme may be beer han he MTS sraegy. The MTS sraegy wll perform beer performance han MTO n suaons of hgher demand uncerany of producs ha wll affec he hgher leadme. The pure concave shapes from he componens and producs curves show ha along wh ncreasng demand uncerany values and decreasng safey facors n hs suaon (where he value of s hgher han he value of j, h h j - h manufacurers end o change her sraegy drascally from MTO o MTS. From hese hree scenaros, he expeced oal nvenory coss for boh componens and producs Fgure 8. Resuls of Scenaro II Fgure 9. Resuls of Scenaro III
8 Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 and he lengh of leadme wll generally be srongly affeced whle demand uncerany (P( z > D s a a hgh level. Ths general fndng of hs research s summarzed n Fg. 0. s a resul, he ncrease n leadme and hgher nvenory condons makes he suggesed sraegy superor under a gven condon Fgure 0. Resuls summary a a hgher cos for he suppler, whle B 2 - -S 3 s a ypcal decson n choosng a shorer leadme of OEMs by addng crashng cos o reduce he nvenory cos of OEMs. These wo combnaons gve a oal prof $4,02.95 per year o SC sysems. In praccal suaons, sraegy analyses are used n sensvy analyss, whch gves manageral nsghs no OEM operaon sraegy whle facng leadme and order arrval unceranes. Fuure research can be exended by consderng supply uncerany n forms of procuremen probably, whch s he probably relaed o he supply of maeral componens from supplers o OEMs and fnshed producs from OEMs o buyers (uncerany nbound SC and dynamc prcng beween SC members. References 6. Conclusons and Fuure Works We proposed a mahemacal model for consderng demand uncerany, under-sock and oversock condons of buyers n response o marke demand, nvenory coss versus leadme crashng cos no one negraed and smulaneous parner, opmal procuremen quany, and leadme decsons n a mul-echelon nvenory SC sysem. To ancpae demand and leadme uncerany and avod delay, OEMs, as decouplng pons n our SC model need some amoun of produc safey socks. The nvenory paern of producs and he consumpon paern of componens have dfferen paerns. The numercal resul showed ha leadme decson affecs he OEM s produc safey sock. Ths safey sock leads o an EOQ decson ha mpacs nvenory and orderng coss. By radng-off nvenory and leadme crashng coss, he bes possble combnaons of parners n fulfllng demand from he marke are B - 2 -S 2 and B 2 - -S 3. We analyzed he rade-off characerscs of each combnaon. B - 2 -S 2 s a ypcal decson n choosng he leas amoun of leadme of OEMs bu rda, Y. and Henne, J-C. (2006. Invenory conrol n a mulsuppler sysem. In. J. Producon Economcs, 04 (2, pp. 249-259. xsaer, S. (2000. Invenory Conrol: Inernaonal Seres n Operaons Research and Managemen Scence, Kluwer cademc Publshers, Boson/Dordrech/London, pp. 5-69. de Boer, L., Labro, E. and Morlacc, P. (200. revew of mehods supporng suppler selecon. Purchasng and Supply Managemen, 7, pp. 75-89. Chan, L. M.., Shen, Z. J. M., Smch-Lev, D. and Swann, J. (2004. Handbook of Quanave Supply Chan nalyss: Modellng n he e-nusness era (eds D. Smch-Lev, SD Wu, Z.J.M. Shen, M: Kluwer cademc, Boson Coordnaon of prcng and nvenory decsons: a survey and classfcaon, pp. 335-392. Chaudhry, S. S., Fros, F. G. and Zydak, J. L. (993. Vendor selecon wh prce break. European J. Operaons Research, 70, pp. 52-66. Croom, S. (200. Resrucurng supply chans hrough nformaon channel nnovaon. In. J. Operaons and Producon Managemen, pp. 504 527. Curren, J. R. and Weber, C.. (994. pplcaon of facly locaon modelng consrucs o vendor selecon problems. European J. Operaons Research, 76, pp. 387-392. Degraeve, Z., Labro, E., and Roodhoof, F. (2000. n evaluaon of vendor selecon mehods from a oal cos of ownershp perspecve. European J. Operaons Research, 25, pp. 34-58. Dckson, G. W. (966. n analyss of vendor selecon sysems and decsons. Journal of Purchasng, 2 (, pp. 5 7.
Hdaya e al. : Parner Selecon n Suppler-Buyer Relaonshp Operaons & Supply Chan Managemen 4 ( pp -20 20 9 Hegedus M. G. and Hopp W. J. (200. Seng procuremen safey leadmes for assembly sysems. Inernaonal Journal of Producon Research, 39(5, pp. 3459-3478(20. Hdaya, Y.., Takahash, K., Dawa, L., and Cakravasa,. (2009. Supply chan sraegy for hgh echnologyconen produc and s consequences o echnology ransfer mechansm. In. J. Inellgen Sysems Technologes and pplcaons, 6 (3/4, pp. 296-308. Hller, M. S. (2002. The coss and benefs of commonaly n assemble-o-order sysem wh a (Q. r-polcy for componen replenshmen. European Journal of Operaonal Research, 4, pp. 570-586. Hopp W. J. and Spearman, M. L. (993. Seng leadmes for purchased componens n assembly sysems. IIE Transacons, 25, pp. 2-. L, D. and O Bren, C. (999. Inegraed decson modelng of supply chan effcency. In. J. Producon Economcs, 59, pp. 47-57. Ln, Y., Ma, S., and Lu, L. (2006. mul-perod nvenory model of componen commonaly wh leadme. IEEE Inernaonal Conference on Servce Operaons and Informacs (SOLI, IEEE, pp. 352-357. Ma, S. H., Wang, W., and Lu, L. M. (2002. Commonaly and Posponemen n Mulsage ssembly Sysems. European Journal of Operaonal Research, 42, pp. 523-538. Melo, M. T., Nckel, S., and Saldanha-da-Gama, F. (2009. Inved Revew: Facly locaon and supply chan managemen - revew. European J. Operaonal Research, 96, pp. 40-42. Mohebb, E., and Choobneh, F. (2005. The mpac of componen commonaly n an assemble-o-order envronmen under supply and demand uncerany. Omega, The Inernaonal Journal of Managemen Scence, 33, pp. 472-482. Nonas, S. L. (2007. Fndng and denfyng opmal nvenory levels for sysems wh common componens, European Journal of Operaonal Research, p. Do: 0. 06/ j.ejor. 2007. 008. 045. Sabr, E. H. and Beamon, B. M. (2000. mul-objecve approach o smulaneous sraegc and operaonal plannng n supply chan desgn. Omega, 28 (5, pp. 58-598. Snyder, L. V. (2006. Facly locaon under uncerany: a revew. IEE Transacons, 38, pp. 537 554. Smch-Lev, D., Kamnsky, P., and Smch-Lev, E. (2000. Desgnng and Managng he Supply Chan: Conceps, Sraeges and Case Sudes. Irwn Mc-Graw Hll, Boson, M. Tang, O. and Grubbsroom, R. W. (2003. The dealed coordnaon problem n a wo-level assembly sysem wh sochasc leadmes. Inernaonal Journal of Producon Economcs, 8 82, pp. 45 429. Weber C.. and Curren J. R. (993. mulobjecve approach o vendor selecon. European J. Operaons Research, 68, pp. 73-84. Yano, C.. (987. Sochasc leadmes n wo-level assembly sysems. IIE Transacons, 9 (4, pp. 37-378. Yos. Hdaya s a faculy member of he Deparmen of Indusral Engneerng, Faculy of Indusral Technology, InsuTeknolog Bandung, Indonesa. She receved hs Docoral degree from Hroshma Unversy.Her research neress nclude echnology ransfer and supply sraegy n supply chan managemen. Her emal address s <yos@mal..b.ac.d> Kasuhko Takahash s a Professor a he Deparmen of rfcal Complex Sysems Engneerng, Graduae School of Engneerng, Hroshma Unversy. He receved hs Docoral degree from Waseda Unversy. Hs research neress nclude producon sysem and supply chan managemen. Hs emal address s <akahas@hroshma-u.ac.jp> Kasum Morkawa s an ssocae Professor a he Deparmen of rfcal Complex Sysems Engneerng, Graduae School of Engneerng, Hroshma Unversy. He receved hs Docoral degree from Hroshma Unversy. Hs research neress nclude producon plannng, schedulng, and human-compuer neracve sysems. Hs emal address s <mkasum@hroshma-u.ac.jp> Kunhro Hamada s an ssocae Professor a he Deparmen of Socal and Envronmenal Sysems Engneerng, Graduae School of Engneerng, Hroshma Unversy. He receved hs Docoral degree from he Unversy of Tokyo. Hs research neress nclude sysem engneerng, shp engneerng, and marne engneerng. Hs emal address s <hamada@naoe.hroshma-u.ac.jp>