Resource-constrained project scheduling_ Notation, classific(12)

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14P.Bruckeretal./EuropeanJournalofOperationalResearch112(1999)3±41

andtheseries±parallelseries±parallelthenperformingcase.theThe``easy''calculationsfortaintionnodesfornetworksuccessivelytransformationidenti®esintocer-aparalleltransforms``duplication''.thenetwork``closer''Anysuchtoaduplica-amultiplicativeone,butincreasesthecomputationtimeseries±byandThisideaseemsfactor.

tobeduetoRobinson[164]DealsoethasbeenfurtherdevelopedbyBeinetal.[13],in¯uencedcameal.[45]upandElmaghraby[66].Thesameideaseachinreliabilityother,seetheoryandseemtohaveimplementationDemeulemeestermentduplication.twostrategiesofetthisal.[6].

[50]providethe®rstforapproach.®ndingtheTheynodesimple-foretofal.toduplications[13],whichThe®rstfollowsthetheoryofBeinrequired,resultsinwhiletheminimumthenumbertominimizethenumberofrealizationssecondthathavetriesmeulemeesterbeconsideredexperienceetal.[50]duringreportthealgorithm.De-withoutfornetworkswithupontocomputational45activitiestwoidentifyingaclearwinnerbetweentimeThestrategies.

worknetwork.[13]referintoaseries±Ittoprovidesitasthefrombeingforthe``distance''ofthegivennetworkadesignSuchnetworkofadistanceseries±parallel.

measureisimportantforthechasticproblemspolynomial-time(seealsoalgorithmsSection8.1foronmanyproachesscheduling),extendedforseries±parallelsincegraphscomputationalsto-canap-areseries±parallel,exponentialtoalgorithmsforarbitrarygraphsoftenthatberatheronlyinthanthein``distance''itsfrombeingtoringAnother[13],allwhichcomplexitymeasureforthisdistancesize.

isthefac-isbasedalsoonintroducedbyBeinetal.work.pathscomplexityBeinfrometal.the[13]sourceaspecialshowedtothewaysinkofofdescribingthenet-ductionprovidesanupperthatboundtheforfactoringthere-bothmeasurescomplexity.areinNaumannfactequal.

[137]showedthat4.3.Approximationalgorithms

time±costTheapproximationalyzedtradeo problembehaviorhasrecentlyofthebeendiscretean-caseHe®rstbySkutellapresents[177].

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