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1、ACuttingPlaneApproachfortheSingle-ProductAssemblySystemDesignProblembyRaduGadidovEmeryWorldwideAirlines,Vandalia,Ohio45377and1WilbertWilhelmTexasA&MUniversity,CollegeStation77843-31311CommunicatingAuthor;e-mail:wilhelm@tamu.eduApril24,1999Abstract.Thispaperevaluatesanewbranch-an
2、d-cutapproach,establishingacomputationalbenchmarkforthesingle-product,assemblysystemdesign(SPASD)problem.Ourapproach,whichincludesaheuristic,preprocessing,andtwocut-generatingmethods,outperformedOSLinsolvingasetof102instancesoftheSPASDproblem.Theapproachisrobust;testproblemsshow
3、thatitcanbeappliedtovariationsofthegenericSPASDproblemthatweencounteredinindustry.1.IntroductionThetraditional(TypeI)assemblylinebalancing(ALB)problemistoassignasetoftaskstostations,minimizingthenumberofstationsrequiredwhileobservingtaskprecedencerelationshipsandacycletimerequir
4、ement.ThispaperdealswithanextensionoftheALBproblem,thesingle-productassemblysystemdesign(SPASD)problem.TheobjectiveofthegenericSPASDproblemistominimizethetotalcostofsystemdesign;ingeneral,thisconsistsofthefixedcostsofactivatingstationsandpurchasingmachinesandthevariablecostofass
5、emblyovertheplanninghorizon.Weassumethatallofthesecostsaredeterministicandknowninadvance.Wealsoassumethatthesetofimmediatepredecessorsforeachtaskisknown.Therequirementsarethateachtaskmustbeassignedtosomestationandthatassignmentsobservetaskprecedences.Eachtaskcanbeperformedonanyo
6、neofasetofalternativemachines,andweassumethattheprocessingtimeoneachalternativemachineisdeterministicandalsoknowninadvance.Finally,weassumethatallstationshavethesamecycletimec,whichisalsodeterministicandknown.Inaddition,thispaperdealswithtwoactualSPASDproblemsweencounteredinindu
7、stry.Thefirstallowsparallel,identicalmachinestobelocatedateachstation.Thisconfigurationallows“l(fā)ong”jobs(i.e.,withprocessingtimeslargerthanthecycletime)tobehandled.Italsoincreases1stationavailability,helpingtoaccommodateprecedencerelationships.Thesecondimposespositionalrequiremen
8、tssothattasksthatrequireprocessingfromthefronts
