A hybridizationofmathematicalprogramminganddominance-driven enumerationforsolvingshift-selectionandtask-sequencingproblems

A commonprobleminproductionplanningistosequenceaseriesoftaskssoastomeetdemandwhile satisfyingoperationalconstraints.Thisproblemcanbechallengingtosolveinitsownright.Itbecomes even morechallengingwhenhigher-leveldecisionsarealsotakenintoaccount.Forexample, determining whichshiftstooperateclearlyimpactshowtasksarethenscheduled;additionally, reducing thenumberofshiftsthatmustbeoperatedcanhavegreatcostbenefits.Integratingtheshift- selectionandtask-sequencingdecisionscangreatlyimpacttractability,however,traditional mathematicalprogrammingapproachesoftenfailingtoconvergeinreasonableruntimes.Instead, we developanapproachthatembedsmathematicalprogramming,asamechanismforsolvingsimpler feasibilityproblems,withinalargersearch-basedalgorithmthatleveragesdominancetoachieve substantialpruning.Inthispaper,weintroducetheShift-SelectionandTaskSequencingproblem(SS- TS), developtheTest-and-Prunealgorithm(T&P),andpresentcomputationalexperimentsbasedona real-worldproblemin automotivestamping to demonstrateitseffectiveness.Inparticular,weareableto solve toprovableoptimality,inveryshortruntimes,anumberofprobleminstancesthatcouldnotbe solvedthroughtraditionalintegerprogrammingmethods.