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1、AppliedMathematicalModelling35(2011)637–649ContentslistsavailableatScienceDirectAppliedMathematicalModellingjournalhomepage:www.elsevier.com/locate/apmArobustoptimizationapproachtoclosed-loopsupplychainnetworkdesignunderuncertaintyMirSamanPishvaee,MasoudRabbani*,SeyedAliTorabiDepartmentofIndustrialE
2、ngineering,CollegeofEngineering,UniversityofTehran,Tehran,IranarticleinfoabstractArticlehistory:Theconcernaboutsignificantchangesinthebusinessenvironment(suchascustomerReceived3March2009demandsandtransportationcosts)hasspurredaninterestindesigningscalableandrobustReceivedinrevisedform3July2010supplyc
3、hains.ThispaperproposesarobustoptimizationmodelforhandlingtheinherentAccepted7July2010uncertaintyofinputdatainaclosed-loopsupplychainnetworkdesignproblem.First,aAvailableonline13July2010deterministicmixed-integerlinearprogrammingmodelisdevelopedfordesigningaclosed-loopsupplychainnetwork.Then,therobu
4、stcounterpartoftheproposedmixed-Keywords:integerlinearprogrammingmodelispresentedbyusingtherecentextensionsinrobustClosed-loopsupplychainnetworkoptimizationtheory.Finally,toassesstherobustnessofthesolutionsobtainedbythenovelReverselogisticsRobustoptimizationrobustoptimizationmodel,theyarecomparedtot
5、hosegeneratedbythedeterministicmixed-integerlinearprogrammingmodelinanumberofrealizationsunderdifferenttestproblems.Ó2010ElsevierInc.Allrightsreserved.1.IntroductionAneffective,efficientandrobustsupplychainisasustainablecompetitiveadvantageforcountriesandfirmsandhelpsthemtocopewithincreasingenvironmen
6、talturbulencesandmoreintensecompetitivepressures.Asupplychainisanet-workofsupplier,production,distributioncentersandchannelsbetweenthemorganizedtoacquirerawmaterials,convertthemtofinishedproducts,anddistributefinalproductsinanefficientwaytocustomers.Supplychainnetworkdesignisoneofthemostimportantstrate
7、gicdecisionsinsupplychainmanagement.Ingeneral,networkdesigndecisionsincludedeter-miningthenumbers,locationsandcapacitiesoffacilitiesandthequantityofflowbetweenthem[1].Inrecentdecades,manycompaniessucha
