Modelling andasegmenteddynamicprogramming-basedheuristicapproachforthe slab stackshufflingproblem

This paperstudiestheslabstackshuffling(SSS)problemintheslabyard,whichisakeylogisticsproblem between thecontinuouscastingstageandthehotrollingmillinthesteelindustry.Theproblemisto choose appropriateslabsforasequenceofrollingitems,fromtheirrespectivecandidateslabsets(families) with aviewtoreducingtheresultingshufflingworkload.AlthoughtheSSSproblemhasbeeninvestigated by afewresearchers,theproblemunderconsiderationhasseveralnewfeatures.Oneofthemisthatthe shuffled slabwillnotreturntheoriginalstackbutremainatthenewposition.Anotherrequiresthatevery selected slabbetakenoutintime,whichwillresultinbalancingthecraneworkloadsamongthestorage areas oftheslabyardtoadegree.Inaddition,thelocalsimilarityofslabfamiliesisalsoconsidered,the closer theitemsintherollingsequence,themorethecommonslabsbetweenthecorrespondingfamilies. For theproblem,anintegerprogrammingmodelisproposedbyconsideringtheabovefeaturesandre- quirements. Forsmall-scaledproblem,adynamicprogrammingapproachisfirstconstructedtoobtainits optimal solution.Forthepracticalscale,duetoitsintractability,weproposeasegmenteddynamicpro- gramming (SDP)-basedheuristic,whichpartitionsthesequenceofitemsintoaseriesofsegments,each of whichcorrespondstoasubproblem.Thesubproblemsaresolvedsequentiallyusingthedynamicpro- gramming. Andthereassignmentstrategyofcommonslabsandtheexchangestrategyofcandidateslabs are designedtoimprovetheheuristic.Twointerestingpropertiesoftheproblemarealsoderivedtospeed up theSDP-basedheuristicapproach.Theexperimentresultsshowthattheheuristicisveryclosetothe optimum inaveragesolutionqualityforthesmall-scaledproblem,obviouslybetterthantheCPOptimizer for themediumscale,andcanreducethecraneworkloadby10.76%onaverageforthepracticalscale.