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1、TransportationResearchPartE44(2008)114–123www.elsevier.com/locate/treTosplitornottosplit:Thatisthequestionab,*aClaudiaArchetti,MartinW.P.Savelsbergh,M.GraziaSperanzaaDepartmentofQuantitativeMethods,UniversityofBrescia,ContradaS.Chiara50,25122Brescia,ItalybSchoolofIndustrialandS
2、ystemsEngineering,GeorgiaInstituteofTechnology,Atlanta,GA30332-0205,USAReceived16January2006;receivedinrevisedform22April2006;accepted27April2006AbstractIndistributionproblems,a?eetofvehiclesservesthedemandofasetofcustomers.Eachcustomeristypicallyservedbyasinglevehicle.However,
3、morecoste?ectivedistributionplansmayexistifsomecustomersareservedbymorethanonevehicle,i.e.,ifsomedeliveriesaresplit.Wecharacterizedistributionenvironmentsinwhichallowingsplitdeliveriesislikelytobebene?cial.Weshow,throughanempiricalstudy,thatthelargestbene?tsareobtainedwhenmeanc
4、ustomerdemandisalittleoverhalfthevehiclecapacityandcustomerdemandvarianceisrelativelysmall.ó2006ElsevierLtd.Allrightsreserved.Keywords:Vehiclerouting;Splitdeliveries1.IntroductionIntheclassicalvehicleroutingproblem(VRP)a?eetofcapacitatedvehiclesisavailabletoserveasetofcus-tomer
5、swithknowndemand.Eachcustomerisrequiredtobevisitedbyexactlyonevehicleandtheobjectiveistominimizethetotaldistancetraveled.Inthesplitdeliveryvehicleroutingproblem(SDVRP),introducedbyDrorandTrudeau(1989),therestrictionthateachcustomerhastobevisitedexactlyonceisremoved,i.e.,splitde
6、liveriesareallowed.Recently,therehasbeenaresurgenceininterestfortheSDVRP.Andrightfullyso.Itisachallengingvariantofthevehicleroutingproblemwithsigni?cantpotentialforpracticalimplications.Thelat-ter,i.e.,thepracticalimplicationsofsplitdeliveries,isthefocusofthispaper.Thereduction
7、indeliverycosts,i.e.,theupside,isacriticalfactorforcompaniesconsideringtomovetoadistributionsysteminwhichsplitdeliveriesareallowed.However,thereisadownsideaswell,e.g.,highercustomerinconvenienceandmorecom-plexadministrationandaccounting.Companiesneedtocarefullyevaluatethesetrad
8、e-o?s.Recently,Archettietal.(2006)haveshownthattheredu
