Resource-constrained project scheduling_ Notation, classific(15)

项目进度管理

P.Bruckeretal./EuropeanJournalofOperationalResearch112(1999)3±4117

uatedimalpartialschedulewithcutsetg ,max- m®nishtimefmax andleftovercapacitiesbek ofthenonrenewableresourcesk.LetPSextendedthecurrenttimebyschedulingpartialschedulesomeactivityconsideredjtobe Ifwehaveg PS withg startj.kjPPRfmaxm

,

m,then PSand mk PS T k forallityImmediateformablejnomodeselection:needsConsidernotbecompleted.

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opera-awmotherConsiderthereadermutation,isreferredselectiontoHartmannisgiven[84]).(forandtwoafather.individualsThenselectedtworandomforcrossoverintegers,new1andw2with1Tw1Yw2Tducedindividuals,adaughternareanddrawn.ason,Nowarepro-twofollows:fromdaughter,Inthefromthetheparents.positionssequenceThedaughteri of1YFactivitiesisde®nedasFFYwofthe1tionstheHowever,i wmother.Theactivitysequenceareoftakenposi-1 1YFFFYnistakenfromthefather.kenThisfromthethemotheractivitiesmaythatnothavebealreadybeenta-inObservethede®nitionparents'ensuresactivitythatsequencestheconsideredrelativeagain.arepositionsprecedencethatthe®nedpositionsfeasible.theresultingi 1YFTheFFYwmodesactivityofthesequencepreserved.activitiesonis2modesbyinthedaughterarede-imode wofthetheremainingmother'sactivitiesmodeassignment.onthepositionsThe2 1YFFHowever,assignment.FYnaretivitythepositionsThederivedson1YFFisFYcomputedfromthefather'swsimilarly.1oftheson'sremainingsequenceAnalogously,positionsaretakenaredeterminedfromthefatherandac-themodethe®rstpartuptopositionbythewmother.2ofthethermother.whileassignmentthesecondofthepartsonistakenfromthefa-assignmentGivenscheduleforanisderivedfromtheallactivitysequenceandamodechildThemutationisconstructed.

activitiesanearlieststartisappliedtoeachnewlyindividualindividualrandomsofandtheiscurrentde®nedasfollows:generatedGivenan1tivityTqintegersqandqpopulation,thentwo12with1Tq1`nand2Tnaredrawn.q1isjs

ifsequencetheresultbyisexchangingusedtoanactivityactivitiesmodifysequencejthesac-q1which

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