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Inventorydecision-makingmodelsforaclosed-loopsupplychainsystemwithdifferentdecision-makingstructuresKaiFuYuana,b,c*,ShiHuaMaa,BoHedandYangGaoeaSchoolofManagement,HuazhongUniversityofScienceandTechnology,Wuhan,China;bSchoolofBusinessAdministration,GuizhouUniversityofFinanceandEconomics,Guiyang,China;cGuizhouKeyLabofEconomicSystemSimulation,Guiyang,China;dSchoolofEconomicsandBusinessAdministration,ChongqingUniversity,Chongqing,China;eSchoolofBusiness,CentralSouthUniversity,Changsha,China(Received29January2014;accepted10July2014)Aclosed-loopsupplychainsystemwithtwotypesofdecision-makingstructuresisinvestigated.Thesystemincludesaretailer,amanufacturer,asupplierandacollector,inwhichthedemandoftheretailerisfulfilledeitherbynewlymanu-facturedproductsorbyremanufacturedproductswhichareasgoodasthenewonesinfunctionandquality.WeextendtheworkofYuanandGao[2010.“InventoryDecision-makingModelsforaClosed-loopSupplyChainSystem.”Inter-nationalJournalofProductionResearch48(20),6155–6187.]tothepartlycentraliseddecision-making(PCD)structurewhichconsistsofAandBtypedecision-makingstructures.Thesystemprofit-maximisationmodelsarederivedandthesolutionproceduresarepresentedtodeterminetheoptimalsystempoliciesofAandBtypedecision-makingstructuresunderthe(1,R)and(P,1)policesbytheeliminationtheory.Throughthecomparativeanalysisoneightdecision-makingstructuresandsensitivityanalysisonthereturnrate,wegetthefollowingresults:(1)thevariationofdecision-makingstructuredoesn’tchangethechoiceofthemanufacturerpolicytypeonmanufacturingandremanufacturingoperationsforagivenreturnrate;(2)CDstructureandCCstructureinYuanandGao(2010)aretwoextremecasesofthePCDstructure,andthemaximumsystemprofitsofBtypedecision-makingstructurearegreaterthanthoseofAtypedecision-makingstructure;(3)CDsystemisnottheworstdecision-makingstructuretomaximisethesystemprofitforspecificmanufacturerpolicytype;(4)themaximumsystemprofitofCCsystemisalwaysgreaterthanthoseofotherdecision-makingstructures;(5)thecoordinationofdifferentmembersinthesystemhasvariouseffectonthesystemprofit;(6)Btypedecision-makingstructurehasmorestrikingeffectontheprofitsofthemanufacturerandtheretailerthanAtypedecision-makingstructure,thecoordinationofthemanufacturerandtheretaileristhekeytomaximisethesystemprofit;and(7)forgivendecision-makingstructuresandmanufacturerpolicytype,themaximumsystemprofitriseswiththeincreaseofthereturnrate.Keywords:inventorymanagement;closed-loopsupplychain;decision-makingstructures;remanufacturing;manufacturing1.IntroductionBeforetheemergenceofproducttake-backlaws,manyoriginalequipmentmanufacturershadbeenalreadyparticipatedinvoluntaryproductrecovery,suchasKodak,FujiFilm,Hewlett-Packard,IBMEurope,XeroxandDell(Galbreth,Boyaci,andVerter2012;Qiangetal.2013).Asarecoveryoption,remanufacturingistheprocessofrestoringend-of-lifeproducts(cores),components,modulesandpartstolikenewconditioninamanufacturingenvironment(ChenandChang2012),whichtendstoconsumelessmaterials,labourandenergy,andgeneratelesswastethanmanufacturingbrand-newproductsfromvirginmaterials.Forexample,thecostoftakingbackandremanufacturingacoreistypically40–60%lessthanthatofbrand-newproduction(GiuntiniandGaudette2003).Tobemoreimportant,remanufacturingisthefoundationofclosed-loopsupplychains(CSCs),becausethroughremanufacturingusedproductscanberestoredtolike-newqualitystandardsandreturnedtothemarket(Guide,Jayaraman,andLinton2003).TheCSCconsistsofaforwardsupplychainandareversesupplychain.Intheforwardsupplychain,rawmaterialsaremanufacturedintonewproducts,i.e.newlymanufacturedproductswhileinthereversesupplychain,usedproductsarereclaimedandremanu-facturedinto‘asnew’products,i.e.remanufacturedproducts.Generallyspeaking,tofulfilcustomers’request,aCSCsystemusuallyconsistsofallpartiesinvolveddirectlyorindirectly,includingnotonlymanufacturers,retailers,suppliersandcollectors,butalsotransporters,warehousesandevencustomersthemselves.Obviously,forsomespecificpartici-pant,todeterminehisoptimaldecision-making,hehastoconsiderotherparticipants’actions.What’smore,whendifferentparticipantscoordinatetheiractions,therewillbevariousdecision-makingstructures.Fordifferent*Correspondingauthor.Email:kaifuy@126.com©2014Taylor&FrancisInternationalJournalofProductionResearch,2015Vol.53,No.1,183–219,fitabilityanddecision-makingprocedureswillbevaried.Besidesdeci-sion-makingstructures,theCSCsystemprofitisalsoaffectedbythemanufacturerpolicyonmanufactureandremanu-facture.Allofthesemaketheinventorydecision-makingoftheCSCsystemmorecomplicated.Inthispaper,weinvestigatetheeffectofthedecision-makingstructurevariation(manufacturers,retailers,suppliersandcollectorsmakingtheirdecisionsjointlyorindependently)onthemanufacturerpoliciesonmanufactureandreman-ufacture,thesystempolicies,thememberprofitsandthesystemprofits.Wefocusoncasesinwhichusedproductsreturnedbycustomersareremanufacturedbythemanufacturerintoproductsoftheoriginalfunctionandquality.Weassumeperfectsubstitutionbetweennewlymanufacturedproductsandr