2000年度日本オペレーションズ・リサーチ学会 秋季研究発表会
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Minim12;lngtheExpectedTbtalVAlueofShortagesforaPopulationofItems SubjecttoPracticalRestrictionsontheReorderPoints Ilkyeong Moon DepartmentofIndustrialEngineering,PusanNationalUniversity,KOREA EdwardA.Silver FacultyofManagement,TheUniversityofCalgary,CANADA AbstractManagersareconcernedwiththee鮎ctiveuseoflimitedresources・Anexampleistheallocationof
aspecificbudgetamongthesafbtystocksofapopulationofitems,eaChofwhichiscontrolledbya continuousreview,Orderpoint,Orderquantitysystem.Onepossiblecriterionistheminimization ofanaggregatemeasureofdisservice,SuChastheexpectedtotalvalueofunitsshortperyear(ETVSPY).Thecasewherethereisnorestriction,Otherthanthebudgetconstraint,Onthe
choiceofsafetystocks(orreorderpoints)hasbeentreatedintheliterature・Infact,byvaryingthelevelsoftheavailablebudget,OneCantraCeOutaWholeexchangecurvewhichshowsthe
bestthatonecandoontheservicemeasureasthebudgetisvaried.However,theseresultshinge
uponcontinuouspossiblevaluesofthedecisionvariables(thereorderpointsor,equivalently,the
safetystocks);but,inpractice,managerSOftenprefertorestrictthedecisionvariablestoasetof
easilyunderstoodandimplementablediscretevalues,e・g・thereorderpoint,eXpreSSedasatimesupply,Whichisrestrictedtooneofthefo1lowlngValues:1week,2weeks,1month,2months,3
months,6monthsorlyear・Thispaperaddresseshowtodealwiththeaboveconstrainedprobleminapragmaticfashion・
Specificallywetreatthecasewherethereisasetoftimesupplies70neOfwhichmustbeusedfor
eachofapopulationofitems・Thereisaspecifiedupperlimitonthetotalvalueofsaf6tystockto
ー166− © 日本オペレーションズ・リサーチ学会. 無断複写・複製・転載を禁ず.beusedandwewishtochoosethetimesupplyreorderpointsofthepopulationofitems,Subject tothediscretesetofoptionsandtheaggregateconstraint,SOaStOminimizetheexpectedtotal Valuesoftheunitsshortperyear. Inthenextsectionweintroducethenotationandmathematicallyfbrmulatetheproblem,includ−