Resource-constrained project scheduling_ Notation, classific(13)

时间:2025-07-08

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P.Bruckeretal./EuropeanJournalofOperationalResearch112(1999)3±4115

gorithmgproducesarealizationpwith p T andgorithmmax p TisdO jopt j3 elog.Thej runningtimeoftheal-makespanTheNP-completenessj .

showsof2canberealizedofdecidingwithwhetheraimprovedthattheperformanceratioofagivenbudgetcannotbetionalForprojects(unlesswithP NPp).

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theofthenonrenewableresourcejconsumesk.Ingeneral,rjkmWeparametersnondecreasingassumethemodesareassumedtobetobeinteger-valued.pprocessinglabeledtimes,withrespectthattois,mjmTpjYm 1forallactivitiesjP andmodesmakespan-minimalPf1YFFFYjMjjÀ1gconstraintsschedule.TheobjectiveSisto®ndaand formulatedjpre bylimitedimposedjgresourcebytheavailabilities.precedencethatmeetsSimilarrelationsthetomaxingeneralalsow optimizationmathematicallyintermsjpre ofajgbinarymaxisvariablesmodexmodelwhichmakesuseofbinaryjmt 1,ifshortness,minperiodt(0,activityotherwise).jisForcompletedinfeasibleIfjRmwedonotpresentaformalmodelthesakehere.ofever,solutionjP2andisjNP-completeMjjP2YjP (cf.Ythen[109]).®ndingariodupperavailabilitypresumingfeasibilityoftherenewableandaconstantper-pe-How-bytimes.theboundontheminimummakespanresources, isgivenanprecedenceGivensumofantheuppermaximumboundactivity weprocessingprocessingrelationstervalstimesandthemodesofcantheshortestusetheplained inigtoderivetimewindows,i.e.in-SectionjYvgj similar3.towhathasbeenex-5.1.Exactalgorithms

w Optimalinjpre jgproceduresforsolvingmaxgeneralizeproceduresdescribed jSectionpre jg3.1forsolvingthespecialcaseimprovedThePrecedencemax.WeTree:summarizeSprecherthreeandalgorithms.Drexl[186]ducedboundingbyPattersontheprecedenceetal.[155]treebyalgorithmintro-and-boundcriteria.quently,EachamodetreeanHere,onlevelgofincludingthebranch-newmeligibleactivityjgand,subse-jgrelatedcombinationofofanthiseligibleactivityactivityareselected.andacurrentmodenodeincorrespondsthebranch-and-boundtoadescendanttree.

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