一个基于两个产品的按订单组装系统

@[e-mail]ssemble-to-ordersystemconsistingofamanufacturerandthreesupplierswasconsidered.Themanufacturerproducestwodifferenttypesofcorrelatedendproducts,eachproductneedsadifferentmixofacommonsetofcomponentparts,whichbelongtotwotypes,onetypeisspecificcomponentsandtheotheriscommoncomponents.Howtomanageinventoriesofcomponentsinsuchasystemisofmanagerialinterest.Weformulatetheinventorymanagementproblemforthesystemasatwo-stagestochasticnonlinearintegerprogram.Weprovethedecompositionoftotalexpectedprofitfunctionandgivetwoalgorithms.Wesolvethefirststageoftheproblemtodeterminetheoptimalstocklevelsofthecomponentsbyalgorithm2andsolvethesecondstageproblembyalgorithm1,wherethecomponentallocationdecisionsaremade.Atlast,wegiveanumericalexample.Keywords:Assemble-to-order,inventory(stock)management,optimalstocklevels.1IntroductionOverthepastdecade,theassemble-to-order(ATO)systemhasbecomeawidelyacceptedbusinessmodelinelectronicindustry.Manyhigh-techfirms,whichfaceheighteningcustomerexpectations,shrinkingproductlifecycles,increasingdemandforproductvarieties,andrapidtechnologybreakthroughs,havesuccessfullyusedATOtobroadentheircustomizedproductofferings,tolowerinventorycost,andtoreducetime-to-market.IncontrasttothetraditionalMake-to-Stocksystem,whichkeepsinventoryattheendproductlevel,ATOkeepsinventoryatthecomponentlevel.Componentsareacquiredinadvance.Whenacustomerorderarrives,requiredcomponentsarepulledfrominventoryandtheendproductisassembledanddeliveredtothecustomer.ATOpostponesthepointofcommitmentofcomponentstospecificproductsandincreasestheprobabilityofmeetingcustomizeddemandontime.Similarstrategieshavebeentermeddelayedcustomization''andpostponement(AvivandFedergruen(2001a,b),Brown,Lee,andPetrakin(2000),JohnsonandAnderson(2000),VanHoek(2001)).Inthispaper,weconsiderasingleperiodATOsystemconsistingofamanufacturerandthreesuppliers.Themanufacturerproducestwodifferenttypesofcorrelatedendproducts(suchas,printer,computer,TVset,ect.),oneistheinnovationoftheother.Usingacommonsetofinputs(e.g.,componentparts)fromthesuppliers.Eachendproductneedsadifferentmixofthesecomponentparts.Thesecomponentpartsbelongtotwotypes,onetypeweshallcallspecificcomponentsandtheotherweshallcallcommoncomponents.Productdemandsareinteger-valued,possiblycorrelated,randomvariables.Atthebeginningoftheperiod(thatisthefirststage),themanufacturermakestheorderquantitiesof1SupportbytheNationalNaturalScienceFoundationofChina(GrantNo.60474062).1(1980)andGraves(1982).LuandSong(2003)formulateacustomer-orderlevelcost-minimizationmodeltodeterminethejointoptimalbase-stocklevelsinthemulti-productATOsystemandcompareitwiththesingle-itemcostminimizationmodel.Lu,SongandYao(2003)treattheATOsystemasasetofqueuesdrivenbyacommon,multiclassbatchPoissoninput.BernsteinandDeCroix(2004)studytheissueofmodularassemblyinamulti-tierassemblysystem.WerefertoSongandZipkin(2003)forarecentsurveypaperinthisresearchareas.Otherrelatedworkincludesthestudyofcomponentcommonality.RelevantresearchoncomponentcommonalityincludesCollier(1982),Bakeretal.(1986),Gerchaketal.(2004)andGerchakandHenig(1989).Differfromallexistingpapers,wemodeltheinventory(stock)managementproblemfortwoend-productATOsystemasatwo-stagestochasticnonlinearintegerprogram.Inthispaper,wedemonstratethedecompositionoftotalexpectedprofitfunction,andgivetwoalgorithms.Wesolvethesecondstageproblembyalgorithm1,wherethecomponentallocationdecisionsaremade.Wesolvethefirststageoftheproblemtodeterminetheoptimalstocklevelsofthecomponentsbyalgorithm2.Therestofthepaperisorganizedasfollows.Section2introducesthemodel,notation,anddemonstratesthepropertiesofoptimalorderquantities,thedecompositionoftotalexpectedprofitfunction,andgivestwoalgorithms.Insection3,wegiveanumericalexample.Finally,section4providessomeconcludingremarks.2ModelandnotationConsiderasingleperiodATOsystemconsistingofamanufacturerandthreesuppliers.Themanufacturerproducestwocorrelatedendproducts(labeled1and2)usingthreecomponents(labeledA,Band).Product1consistsofoneuniteachofcomponentAandCB,whileproduct2consistsofoneuniteachofcomponentsBandC.(Moregeneralcomponentquantityrequirementscanbereducedtothiscasebyre-scalingtheproblemparameters.)Product1istheinnovationtypeofproduct2.WesaycomponentAandCarededicatedtoproducts1and2respectively,andcallthemspecificcomponents.WecallcomponentBiscommoncomponent.ComponentA,BandareproducedbysuppliersA,BandCrespectively.Demandforendproductduringasinglesellingseason,denotedby,isastochasticinteger-valuedvariab