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1、Chapter9MaintenanceandReplacementTheproblemofdeterminingthehfetimeofanassetoranactivitysi?multaneouslywithitsmanagementduringthatlifetimeisanimportantprobleminpractice.Themosttypicalexampleistheproblemofopti?malmaintenanceandreplacementofamachine;seeRapp(1974)andP
2、ierskallaandVoelker(1976).Otherexamplesoccm'inforestmanage?mentsuchasinNaslimd(1969),Clark(1976),andHeaps(1984),andinadvertisingcopymanagementasinPekelmanandSethi(1978).Thefirstmajorworkdealingwithmachinereplacementproblemsap?pearedin1949asaMAPI(MachineryandApplie
3、dProductsInstitute)studybyTerborgh(1949).Forthemostpart,thisstudywasconfinedtothoseproblemswheretheoptimizationwascarriedoutonlywithrespecttothereplacementUvesofthemachinesunderconsideration.Boiteux(1955)andMasse(1962)extendedthesinglemachinereplacementprob?lemtoi
4、ncludetheoptimaltimingofapartialreplacementofthemachinebeforeitsactualretirement.Naslund(1966)wasthefirsttosolveagen?eralizedversionoftheBoiteuxproblembyusingthemaximumprinciple.Heconsideredoptimalpreventivemaintenanceappliedcontinuouslyovertheentireperiodinsteado
5、fasingleoptimalpartialreplacementbeforethemachineisretired.Thompson(1968)presentedamodificationofNaslimd'smodelwhichisdescribedinthefollowingsection.2429.MaintenanceandReplacement9.1ASimpleMaintenanceandReplacementModelConsiderasinglemachinewhoseresalevaluegradual
6、lydeclinesovertime.Itsoutputisassimiedtobeproportionaltoitsresalevalue.Byapplyingpreventivemaintenance,itispossibletoslowdowntherateofdeclineoftheresalevalue.Thecontrolproblemconsistsofsimultane?ouslydeterminingtheoptimalrateofpreventivemaintenanceandthesaledateof
7、themachine.Clearlythisisanoptimalcontrolproblemwithunspecifiedterminaltime;seeSection3.1andExample3.5.9.1.1TheModelInordertodefineThompson'smodel,weusethefollowingnotation:T=thesaledateofthemachinetobedetermined,p=theconstantdiscountrate,x(t)=theresalevalueofmachi
8、neindollarsattimet;letx{0)=xo,u{t)=thepreventivemaintenancerateattimet(mainte?nanceheremeansmoneyspendoverandabovetheminimumrequiredfornecessaryrepairs)
