Resource-constrained project scheduling_ Notation, classific(20)

项目进度管理

22P.Bruckeretal./EuropeanJournalofOperationalResearch112(1999)3±41

beenPriority-rulemethodsfor jtempjgmaxhaveandandZhandevised[140],andBrinkmanntestedbyZhan[201],NeumanncontainsFranckandNeumann[70]and(theNeumannlastreference[26],approachesthesequentialhavemostturnedrecentoutresults).toTwodi erentoneordirectmethodschedulesbeexpedient.theactivitiesThestructuresafteranothertractionofthenetworkwithoutconsideringseparately.ThethecycleTheorem.methodminedFirst,againafeasibleexploitstheDecompositioncon-structureforeachcyclestructure.subscheduleSecond,eachisdeter-cyclerespectively,isreplaceddependent)withappropriatebyasinglenodeoractivity,schedulewithoutforresourcetheusage.durationThird,aandfeasible(time-schedulecyclesisresultingcomputed.``contracted''Fourth,anetworkfeasibleusingthetheforschedulestheoriginalforthecontractednetworkisdeterminedwork,Toindividualathe®ndcontractedafeasiblecyclestructures.

networkandnetwork,scheduleor(foracyclethewholestructure),net-haveserialprioritybeenandbest.rules,developed.aparallelschedulegenerationschemetheLSTAmongrulehasaturnedlargenumberofalwaysThatis,theactivitytobescheduledouttobewithscheduled)respectan``eligible''activity(allofitspredecessorsnextisTogenerationtakemaximumwithtostrictsmallestordertimelatest0havealreadybeenlagsstartintoaccount,time(cf.[70]).bothprocessfeasiblewhichschemesexceedsstarttimeisasoffollows:containabackwardschedulingtheactivityIfthejearliesttoresource-someactivitymaximumthelatestpossibletimelagstartdmax

time,theofbestartjinducedscheduledtimeby

ofscheduled)i(andhasofsomeadditionalij

activitiesalreadyuponAnresources120experimentaltobeenlargedappropriately.

instancesperformanceanalysisbasedprovidedeach(generatedwith500byactivitiesProGen/max)and®vehasThetruncatedpriority-rulethefollowingmethodsmainareresultsmuch(cf.[142,174]):the2thes,directbranch-and-boundfasterthantherespectively,andcontractionprocedures.Whereasofcomputingmethodstimeperrequireinstance1andcompositionaverage(usingaPCPentium200),thede-onalmost1m.methodThedecompositionasslowestheuristicandcontraction

requiresmethods,rem,(6%)providewhichfeasibleexploit(optimal)theDecompositionschedulesforTheo-instances,and98%thewhere(4%),therespectively,ofallsolvable100%boundprojectdurationcomputedaveragerelativefromthedeviationbestlowerofsolvemethodmuchisaroundlessinstances5%.Thetoremainingheuristicsmality(theonly®ltered53%),beambutsearchmorefeasibilityinstances(thetechniquetodirect62%).opti-7.Nonregularobjectivefunctions

gTheobjectivecreasingdiscussedtheintheinfunctioncompletionSection6ofisproblem jtempjmaxtimesregular,ofactivitiesi.e.nonde-tion,casetiveminimumfunctionswedealofawithminimizationproblem).Inthissec-(inwheretwowekindsagainofnonregularobjec-given.representsIftheandmaximumstart±startassumetimethatlagsgeneralaresourcesomeobjectivemeasurefunctionofthetovariationbeminimizedproblemutilization,jectivetheprojectfunction.Inthewespeakofaresourcelevelingofre-whichrepresentsnetpresentvalueproblem,theob-istobemaximized.thenetpresentvalueof7.1.Model

In jtempadditiontothetemporalconstraints(5)ofproject jPjg max ,,weexplicitlyrequirethat 0 0YjPZproblemInthedurationandPthereZisaprescribedmaximumP0withPd0Yn 1.cost objectivejtempfunctionj

oftheresourcelevelingkf rk Yt bestatedperunitofresourcek.Thisproblem, kb0canisthenthemin

asfollows:

kf rk Yt 9 kPR

sXtX jÀ iPdij iYj PiY

0 0Y

n 1Td

"Y 10

jPZP0jP Yrk Yt T kYkPRY

t 0Y1YFFFYd

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