Optimal productionplanningforamulti-productclosedloopsystemwith uncertain demandandreturn

We studytheproductionplanningproblemforamulti-productclosedloopsystem,inwhichthe manufacturerhastwochannelsforsupplyingproducts:producingbrand-newproductsand remanufacturingreturnsintoas-newones.Intheremanufacturingprocess,usedproductsarebought back andremanufacturedintoas-newproductswhicharesoldtogetherwiththebrand-newones.The demandsforalltheproductsareuncertain,andtheirreturnsareuncertainandprice-sensitive.The problemistomaximizethemanufacturer’sexpectedprofitbyjointlydeterminingtheproduction quantitiesofbrand-newproducts,thequantitiesofremanufacturedproductsandtheacquisitionprices of theusedproducts,subjecttoacapacityconstraint.Amathematicalmodelispresentedtoformulate the problemandaLagrangianrelaxationbasedapproachisdevelopedtosolvetheproblem.Numerical examplesarepresentedtoillustratethemodelandtestthesolutionapproach.Computationalresults show thattheproposedapproachishighlypromisingforsolvingtheproblems.Thesensitivityanalysis is alsoconductedtogeneratemanagerialinsights.