物流专业外文期刊

SystemsEngineering—Theory&PracticeVolume29,Issue4,April2009OnlineEnglisheditionoftheChineselanguagejournalCitethisarticleas:SETP,2009,29(4):176–183OptimalModelandAlgorithmforMulti-CommodityLogisticsNetworkDesignConsideringStochasticDemandandInventoryControlQINJin12;¤,SHIFeng1,MIAOLi-xin2,TANGui-jun11.SchoolofTrafficandTransportationEngineering,CentralSouthUniversity,Changsha410075,China2.ResearchCenterforLogistics,GraduateSchoolatShenzhen,TsinghuaUniversity,Shenzhen518055,ChinaAbstract:Asimultaneousapproachthatincorporatesinventorycontroldecisionintofacilitylocationmodelisproposed,whichisusedtosolvethemulti-commoditylogisticsnetworkdesignproblem.Basedontheassumptionthatthestochasticdemandsoftheretailersarenormaldistributed,anon-linearmixedintegerprogrammingmodelthatsimultaneouslydescribedtheinventorydecisionandthefacilitylocationdecisionispresented,inwhichtheobjectiveistominimizethetotalcostthatincludinglocationcosts,inventorycosts,andtransportationcostsunderthecertainservicelevel.Thecombinedsimulatedannealing(CSA)algorithmisdevelopedtosolvetheproblem.Themodelandeffectivenessofthealgorithmareclarifiedbythecomputationalexperiments.Keywords:multi-commodity;logisticsnetworkdesign;stochasticdemand;optimizationmodel;simulatedannealingalgorithm1IntroductionInahighcompetitiveenvironment,themanufacturingcompaniesmustpaycloseattentiontotheirinventoryman-agement.Tooptimizetheirinventorysystem,thecompaniesshouldsolvetwocriticalproblems.First,theymustselecttheproperplacesthatthecommoditiessaving,namely,thesitesandthenumberofstockinglocationsorlogisticsnodes(LNs).Second,theymustdeterminetheamountofcom-moditiestomaintainineachLN.Sointhelogisticsnetworkdesignproblem,thefacilitylocationproblemandinventorydecisionproblemaretwokeysubproblemsandbothofthemarehighlyrelated.Butinmanyliteratures,theabovetwoproblemsalwayswerestudiedasthefacilitylocationprob-lem[1¡3]andtheinventorycontrolproblem[4¡5]separately.Thedecision-makingresultsinincompatibilityandinconfor-mityatdifferentlevels,whichcouldaffecttherationalityofthefinalstrategydecisions.Inaddition,thedemandsoftheretailersforthecom-moditiesarealwaysuncertainintherealworld,butintheresearchonthelogisticsnetworkdesignproblem,thede-mandswerealwaysconsideredasadeterministicvariablesinordertosimplifytheanalysisandmodeling.Furthermore,thecompaniesshouldmaintainacertainstocktosatisfythestochasticdemandsasfaraspossible.Theyarerequiredtocontroltheirinventorycostbecausetheinventorycostisin-creasingfollowingtheinventoryamount,sothecompaniesmustselectthescientificinventorypolicies.Basedontheassumptionthatthestochasticdemandoftheeachretailerisnormaldistributed,theproblemthatintegratedthefacilitylocationproblemandinventorycontrolproblemisstudiedinthisarticle,whichcouldincreasetherationalityandscien-tificityofthedecisions.Forthesinglecommoditylogisticsnetworkdesignproblemconsideringtheinventorycost,theliteratures[6-8]ignoredmanyfactorswhichhaveinfluenceontheinven-torycost,andonlyaddedthecostasthenon-linearfunctionofthecommodityquantitytotheobjectivefunction;thelit-erature[9]studiedthejointlocation-inventoryproblemun-dertwospecialcases:thevarianceofdemandwaspropor-tionaltothemeanandthedemandhadzerovariance,andrestructuredthemodelintoaset-coveringintegerprogram-mingmodel;theliterature[10]developedamoreefficiencyalgorithmforthespecialcasesintheliterature[9];thelit-erature[11]analyzedthetransportationcostconsideringthevehicleroutinginthelogisticsnetwork,buttheordernum-berwasconsideredasacontinuousvariableintheformula-tionderivation;theliterature[12]investigatedthetrade-offsproblembetweentheservicelevelandservicecostmakinguseoftheexistedmodelintheliteratures[9-10],andpro-posedaweightingmethodandaheuristicsolutionapproachbasedongeneticalgorithmstosolvetheproblem.Theliteraturesthatstudiedthelogisticsnetworkdesignproblemwithmulti-commodityarefewforthepresentathomeandabroad.Theliterature[13]simplifiedtheinven-torycostofthecommoditiesasintheliteratures[6-8]andproposedtheLagrangealgorithmtosolvetheproblem;theliteratures[14–15]regardedtheinventorycostasthelin-earfunctionofcommodityquantity;theliterature[16]de-velopedthemodelframeworkofmulti-commoditydynamiccapacitatedfacilitylocationandreportedontheircomputa-Receiveddate:November28,2007¤Correspondingauthor:Tel:[phone];E-mail:[e-mail]:SupportedbytheChinaPostdoctoralScienceFoundationfundedproject(No.20090450915);ChinaNationalNatureScienceFoundationfundedproject(No.70771116)Copyrightc°2009,SystemsEngineeringSocietyofChina.PublishedbyElsevierBV.Allrightsreserved.QINJin,etal./SystemsEngineering—Theory&Practice,2009,29(4):176–183tionalexperiencewithstandardmathematicalprogrammingsoftware,buttheinventorycostinthemodelwasalinearfunctionofdemandquantitytoo.2AssumptionsandnotationsToformulatethemodel,thefollowingnotationsareused:idenotesthecandidateLNsite,i=1;2;¢¢¢;N;jdenotestheretailer,j=1;2;¢¢¢;M;ldenotesthecom-modity,l=1;2;¢¢¢;L.FiisthefixedcostoflocatingatcandidateLNsitei;Videnotesthestoragecapacityofcan-didateLNi;RPliisthereorderpo