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:100725429(2007)0520037206:2006208225;:2006210225:(70572088);(20050145022);(2004401015):(19802),,,,1,2,3,4(1.,100041;2.,10027;3.,110004;4.,110136):,,,,,:;;;:F224:ADynamicOperationModelsforaClassofClosed2loopSupplyChainwithProductRemanufacturingYANNi2na1,2,HUANGXiao2yuan3,XUJia2wang4(1.ShougangIron&SteelCo.,Beijing100041,China;2.BusinessSchool,RenminUniversity,Beijing100027,China;3.SchoolofBusinessAdministration,NortheasternUniversity,Shenyang110004,China;4.ManagementDepartment,ShenyangAeronauticalEngineeringInstitute,Shenyang110136,China)Abstract:Underthesyntheticallyconsideringthere2distribution,remanufacturingandre2use,adynamicoperationmodelforclosed2loopsupplychainisestablished.Thesupplychainiscomposedofonemanufacturerandonesupplier,inwhichthemanufacturerisinchargeofrecy2clingandre2disposaltheusedproducts.Usingdiscreteprobabilitydistributiontodescribethedis2useprobabilityofultimateproducts,theoperationsofclosed2loopsupplychainaredynamicandmeetmulti2objectivessuchascoordinationbetweenmembers,maximumprofitsofeachmemberetc.Anumericalexampleisdesignedtovalidatethemodel,andtheimpactoftherecyclingrateonoperationperformanceofthesupplychainisanalyzed.Theresultsindicatethatthewholeper2formanceoftheclosed2loopsupplychainwouldincreasewiththerecyclingrate.Keywords:operationmanagement;closed2loopsupplychain;productremanufacturing;dy2namicprogramming1,,[1,2],73IndustrialEngineeringandManagementNo.5,200720075,,:Savas2kanVanWassenhove(2000)[3]GroeneveltMajumder(2001),OEM[4]Savaskan(2004),,[5];Savaskan(2006),,,[6]Dobos(2003),[7],,,[2],22.1,,,,,,,,,,112.21::();,;,;2:,t3:jNj,tfjt,t1tNjfjt=0,Njt=1fjt=1,Pj;jt1t;1jt2jt3jt,1jt+2jt+3jt1;jt1jt2jt3jt,1jt2jt3jt,83,:wjt4:,,j(j=1,...,J);i(i=1,...,I);t(t=1,...,T);h(h=1,...,H)vjtjt;zjtjt;zLjtjt;yLitit;bitti;litti;xitti;xLittipjttj;qitti;czjj;hzjj;hyii;kjj;Kmax;zLj0j;ozjj;zLmax;syijjiBOM;yLi0i;oyii;yLmax;rhtth;cxii;srhiihBOM;hxii;gii;Gmax;xLi0i;oxii;xLmax;shtth;djttj3,,,,,,1,(a),,,:bit=litPi,t(1)(b),:maxCP=Tt=1Jj=1(pjtvjt-czjzjt-hzjzLjt)-Ii=1(qitbit+hyiyLit)+Tt=1Jj=1wjtt-k=(jkfjkvj,t-k3jk)Hh=1Ii=1(syijsrhi)-Tt=1Jj=1t-k=[jkfjkvj,t-k(jk+1jk1jk+2jk2jk+3jk3jk)](2),(2)2,3(c),maxCS=Tt=1Ii=1(qitlit-hxixLit-[cxi+(Hh=1rhtsrhi)]xit)-Tt=1Jj=1wjtt-k=(jkfjkvj,t-k3jk)Hh=1Ii=1(syijsrhi)(3)93IndustrialEngineeringandManagementNo.5,200720075,,1minPTTt=1Ii=1(d-it+d+it)+PPd-P+PSd-S,PTPPPS(a)(b)(c),,,,1,,PTsPPsPSd-itd+itti;d-P;d-S(a):-bit+lit+d-it-d+it=0Pi,t(4)(b):CP+d-P-d+P=MP(5)CP+Tt=1Jj=1(-pjtvjt+czjzjt+hzjzLjt)+Ii=1(qitbit+hyiyLit)-Tt=1Jj=1wjtt-k=(jkfjkvj,t-k3jk)Hh=1Ii=1(syijsrhi)+Tt=1Jj=1t-k=[jkfjkvj,t-k(jk+1jk1jk+2jk2jk+3jk3jk)]0(6),MP,;d-Pd+P;CP(c):CS+d-S-d+S=MS(7)CS+Tt=1Ii=1(-qitlit+hxixLit+[cxi+Hh=1rhtsrhi)]xit+Tt=1Jj=1wjtt-k=(jkfjkvj,t-k3jk)Hh=1Ii=1(syijsrhi)0(8),MS,;d-Sd+S;CS:Jj=1kjzjtKmaxPt(9):zLjt=zLj,t-1+zjt-vjt+t-k=(1jkjkfjkvj,t-k)Pj,t(10)zLj0=zLj0Pj(11)Jj=1ozjzLjtzLmaxPt(12):yLit=yLi,t-1+bit+Jj=1syij-zjt+t-k=(2jkjkfjkvj,t-k)Pi,t(13)yLi0=yLi0Pi(14)Ii=1oyiyLityLmaxPt(15):vjtdjtPj,t(16):Ii=1gixitGmaxPt(17):xLit=xLi,t-1+xit-litPi,t(18)xLi0=xLi0Pi(19)Ii=1oxixLitxLmaxPt(20):Ii=1srhixit-Jj=1syijt-k=(3jkjkfjkvj,t-k)shtPh,t(21)04,::bit,zjt,zLjt,yLit,lit,xLit,d-it,d+it,d-P,d+P,d-S,d+S,CP,CS,vjt,xit0Pi,j,t,,4,1J=1()I=1()H=1()T=4():Kmax=400,Gmax=500,zLmax=50,yLmax=50,xLmax=50,zL’0=0,yL’0=0,xL’0=0,cx=10,cz=15,q=75hx=1,hy=2,hz=3,g=1,k=1,sr=1,sy=1,ox=1,oy=1,oz=1,:PTPPPS1000010010,MPMS106111234(kg)350398367386(kg)387376397357(/kg)100105110100(/kg)40454540=1,N=3,{0.1,0.3,0.6},60%,1t=20%2t=30%3t=40%(t=1,2,3,4)t=8,1t=32t=83t=20,wt=30,t=1,2,3,4,Matlab7.0Linprog,22(:31642.59)(kg)(kg)(kg)(kg)(kg)(:26092.97)(kg)(kg)(kg)1350.00350.0000350.00350.00387.00372393.80398.0000387.50387.50350.5003349.62367.0000323.56323.56323.5604342.07386.0000276.17276.17276.1702,,;,,1,,,,,,,50%55%60%65%70%75%80%,,33,,,,,,,,,,,,,,,14IndustrialEngineeringandManagementNo.5,2007200753(:)(%)033674.0020670.0054344.005027385.4729813.8257199.305526739.2230728.2157467.436026092.9731642.5957735.566525446.7232556.9758003.697024800.4633471.3558271.827524154.2134385.7458539.958023507.9635300.1258808.085,,,,,:[1]FleichmannRDM,InderfurthK,WassenhoveLNV.Reverselogistics:Quantitativemodelsforclosed2loopsupplychains[M].Berlin:SpringerVerlag,2004.[2]GuideVDR,HarrisonTP,WassenhoveLNV.Thechallengeofclosed2loopsupplychain[J].Interface,2003,33(6):326.[3]SavaskanVW.Strategicdecentralizationofreversechannelsandpricediscriminationthroughbuybackpayments[R].MathCenterWorkingPaperSeries.KelloggSchoolofManagement,NorthwesternUniversity,Evanston,IL2000.[4]GroeneveltH,MajumderP.Competitioninremanufacturing[J].ProductionandOperationsManagement,2001,10(2):1252141.[5]SavaskanRC,BhattacharyaS,WassenhoveLNV.Closed2loopsupplychainmodelswithproductremanufacturing[J].Manage2mentScience,2004,50(2):2392252.[6]SavaskanRC,WassenhoveVLN.Reversechanneldesign:Thecaseofcompetingretailers[J].ManagementScience,2006,52(1):1214.[7]DobosI.Optimalproduction2inventorystrategiesforaHMMS2typereverselogisticssystems[J].InternationalJournalofPro2ductionEconomics,2003,81282(1):3512360.(26)CP