Resource-constrained project scheduling_ Notation, classific(17)

项目进度管理

P.Bruckeretal./EuropeanJournalofOperationalResearch112(1999)3±4119

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activities.[149]onHartmann'stheProGenset

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Hartmannproducedmorethanthoseofthe[84]twoisheuristicsnearlyby0.8%.theHence,theaveragefourgeneticfromtimesalgorithmtheliterature.lowerthanof6.Minimumandmaximumtimelags

Thissectionisconcernedwiththetweenjtempditionthejstartgproblemmax,ofthatdi erentis,maximumactivitiestimelagsbe-oftentominimumones.Maximumtimeoccurlagsinad-neousneededinpractice,forexample,ifsimulta-arerequired,ornondelayactivitiesdeadlinesexecutionsourcesareprescribed,forsubprojectsofseveralactivitiesistimewindowsorindividualforre-orderproductionaregiven,orinschedulingofmake-to- Sectionboundjtemp6.1deals(cf.[138,139]).

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0Y 1YFFFY n 1 ,A Yt fjP j jTt` j pjg

is(orthespectively)insettimeofactivitiesand

interval tinYtprogress 1 orperiodattimett P1,ZPre-0r

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5

rk Yt T kYkPRYt 0Y1YFFFY À1Y 6

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iP max piYmax iYj PischedulesItisondij isanupperwelltheknownminimumthatprojectduration.

actlypositiveifthe(whichsatisfytheEq.set(5))STisofnonemptytime-feasibleex-scheduleslengthnetwork(see[12]).doesnotThecontainsetSofacyclefeasibleoferallyconvexdisconnected(whichsatisfyandEqs.represents(5)andthe(6))unionisgen-oftiallywhetherinpolyhedrawhosenumbergrowsexponen-[12,144]).

ornnot.Moreover,S YisstronglythedecisionNP-completeproblem(cf.Z SometimesjP areaddedtheconstraintstoEq.(5). We0 deleted0andthese

jP