A two-stageflowshopschedulingproblemonabatchingmachineandadiscrete machine withblockingandsharedsetuptimes

Motivated byapplicationsinironandsteelindustry,weconsideratwo-stageflowshopscheduling problem wherethefirstmachineisabatchingmachinesubjecttotheblockingconstraintandthesecond machine isadiscretemachinewithsharedsetuptimes.WeshowthattheproblemisstronglyNP-hard when theobjectiveistominimizethemakespan.Whensolvedwithaheuristicpriorityrule,theworstcase ratio withtheminimummakespanis2.Foramoregeneralobjective,theminimizationofalinearcombi- nation ofthemakespanandthetotalblockingtime,aquadraticmixedintegerprogramispresentedfirst. Then wepinpointtwocaseswithpolynomialtimealgorithms:thecasewithoutblockingconstraintand the casewithagivenjobsequence.Alsoforthegeneralobjective,weanalyzeanapproximationalgorithm. Finally, weevaluatethealgorithms,givingexperimentalresultsonrandomlygeneratedtestproblems.