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Ideal schedules in parallel machine settings

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ARTICLEINPRESSJID:EOR[m5G;September4,2020;12:9]EuropeanJournalofOperationalResearchxxx(xxxx)xxxContentslistsavailableatScienceDirectEuropeanJournalofOperationalResearchjournalhomepage:www.elsevier.com/locate/ejorDiscreteOptimizationIdealschedulesinparallelmachinesettings�XiaojuanJianga,KangbokLeea,∗,MichaelL.PinedobaDepartmentofIndustrialandManagementEngineering,PohangUniversityofScienceandTechnology,77Cheongam-Ro,Nam-Gu,Pohang37673,SouthKoreabDepartmentofInformation,OperationsandManagementScience,SternSchoolofBusiness,NewYorkUniversity,44West4thStreet,NewYork,NY10012,USAarticleinfoArticlehistory:Received31January2020Accepted5August2020AvailableonlinexxxKeywords:SchedulingMakespanTotalcompletiontimePrecedenceEligibilityabstractAnidealscheduleisaschedulethatsimultaneouslyminimizesthetwomostpopularschedulingobjec-tives,namelythemakespanandthetotalcompletiontime.Ifaschedulingproblemalwayshasanidealschedule,thentheproblemiscalledanidealproblem.Wesummarizeidealproblemresultsofvariousschedulingproblemsindifferentmachineenvironmentsandwithjobcharacteristicsthatincludeprece-denceconstraints,releasedates,processingtimes,eligibilityconstraintsandpreemptions.Wepresentacomprehensiveoverviewofidealschedulesincludingournewfindings.©2020ElsevierB.V.Allrightsreserved.1.IntroductionIntheschedulingliterature,anobjectiveistypicallydefinedasafunctionofthecompletiontimesofthejobstobescheduled.Mostobjectivesareofoneoftwotypes.Theyareeitherofthemin-maxtypeorofthemin-sumtype.Amin-maxobjectiveisanobje

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