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Minimizing the Expected Total Value of Shortages for a Population of Items Subject to Practical Restrictions on the Reorder Points)

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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 Abstract

Managersareconcernedwiththee鮎ctiveuseoflimitedresources・Anexampleistheallocationof

aspecificbudgetamongthesafbtystocksofapopulationofitems,eaChofwhichiscontrolledbya continuousreview,Orderpoint,Orderquantitysystem.Onepossiblecriterionistheminimization ofanaggregatemeasureofdisservice,SuChastheexpectedtotalvalueofunitsshortperyear

(ETVSPY).Thecasewherethereisnorestriction,Otherthanthebudgetconstraint,Onthe

choiceofsafetystocks(orreorderpoints)hasbeentreatedintheliterature・Infact,byvarying

thelevelsoftheavailablebudget,OneCantraCeOutaWholeexchangecurvewhichshowsthe

bestthatonecandoontheservicemeasureasthebudgetisvaried.However,theseresultshinge

uponcontinuouspossiblevaluesofthedecisionvariables(thereorderpointsor,equivalently,the

safetystocks);but,inpractice,managerSOftenprefertorestrictthedecisionvariablestoasetof

easilyunderstoodandimplementablediscretevalues,e・g・thereorderpoint,eXpreSSedasatime

supply,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.

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beusedandwewishtochoosethetimesupplyreorderpointsofthepopulationofitems,Subject tothediscretesetofoptionsandtheaggregateconstraint,SOaStOminimizetheexpectedtotal Valuesoftheunitsshortperyear. Inthenextsectionweintroducethenotationandmathematicallyfbrmulatetheproblem,includ−

1ngObtainlngauSefu1lowerbound・Thisisfo1lowedbythespecificationofanoptimalsolution

procedureuslngabranchandboundalgorithm・Theassociatedcomputationale鮎rtrequired

increasessubstantiallywiththenumberofitems・Perhapsmoreimportant,branchandboundis averydifBcultconcepttoexplaintopractitioners・Therefore,WeSubsequentlypresentaheuristic

approachthatovercomesbothofthesedrawbacks・Moreover,WepreSentreSultsofcomputational

experimentsthatshowthatverylittledegradationintheobjectivefunctionvalueresultsfrom usingtheheuristicinsteadoftheoptimalsolution・However,theperformanceoftheoptimal SOlutionismarkedlya鮎ctedbythediscretechoiceofthetimesupplies,particularlyifthesetis fairlysparseaswouldlikelybetheca5einpractice. Keywords:inventory,Safetystock,lowerbound,branchandbound,heuristic ThispaperwillbeappearedinIntemationalJoumalqfProductionEconomics. Com5POndence‥Dr・Ⅰ・Moon,DepartmentofIndustrialEngineering,PusanNationalUniversity, Pusan609−735,KOREA Email:ikmoon@hyowon.pusan.ac.kr Tbl:+82−51−510−2451 Fhx:+82−51−512−7603 ー167− © 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.

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