A branchandpricealgorithmtominimizemakespanonasinglebatch processing machinewithnon-identicaljobsizes

In thispaper,weconsidertheschedulingproblemonasinglebatchprocessingmachinewithnon- identicaljobsizes;inwhichthemachinehasalimitedcapacityandcanprocessagroupofjobs simultaneouslyasabatch.Theprocessingtimeofabatchisthelongestprocessingtimeofalljobsinthe batch. Theobjectiveistominimizethemakespan.WeformulatetheproblemusingDantzig–Wolfe decompositionasasetpartitioningproblem.Basedonthesetpartitioningformulation,wepresenta tight lowerboundusingcolumngenerationmethod.Aheuristicalgorithmisalsodevelopedtogenerate the basicsolutioninthecolumngenerationmethod.Abranchandpricealgorithmwhichcombinesthe column generationtechniquewithbranchandboundmethodisthenpresentedtoobtaintheoptimal solution oftheproblem.Theefficiencyoftheproposedbranchandpricealgorithmisultimately comparedtothebranchandboundalgorithmfromtheliterature,basedonthegeneratedsample problems.