Resource-constrained project scheduling_ Notation, classific(5)

项目进度管理

P.Bruckeretal./EuropeanJournalofOperationalResearch112(1999)3±417

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problemthebasic resource-constrainedjpre jgmaxsettivity f0Y1YAssumeFFFYnYnthattheprojectconsistswillofbea(termination)j 0(j 1gofactivitieswhereac-beactivity. n 1)Theisa®ctitiousbeginningnetworkacyclicanddepictedbynetworkanactivity-on-nodeisassumedtocedencewithThererelations.nodesPreemptionasactivitiesandisnotarcsaspre-assumedare®ndconstraintsamakespan-minimaltoscarcebeinteger-valued.renewableresources.Allallowed.dataarescheduleThethatobjectivemeetsisthetoandimposedbytheprecedencerelationsprojectGivenbylimitedresourceavailabilities.

tionsdurationanupperwecanbounduse theontheminimum latestigYvgtoderivetimewindows,precedencei.e.intervalsrela-jj ,withearliestcompletiontimeigjanddencecompletionbyfeasiblecompletiontimevgjtimes,containingofactivitytheprece-jP ,theforwardandbackwardrecursion.Analogously,aboveinterval i jYv j boundedfrombelowandtimebytheearlieststarttimei jandlateststartthe programjprecedencev j,respectively,pre jgfeasiblecanstartbecalculatedtimes.Intogeneral,re¯ectmaxisformulatedasactivitywhichmakesuseofvariablesa0-1xintegerjt Alternatively,jiscompleted1,ifsenteditinperiodt(0,otherwise). notjtempinjgSectionisstated6.1forsimilarthetomorewhatgeneralispre-max.ForthesakeapproachesSectionpresentofshortness,wedo3.1aformalmodelhere.

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