Bounds for parallel machine scheduling with prede?ned parts of jobs and setup time

Abstract We examine a parallel machine scheduling problem with setup time in order to minimize the makespan. Each job consists of prede?ned parts, and the parts of a job can be processed concurrently in different machines. We ?rst provide worst-case bounds of the Longest Processing Time and list schedules for special cases. We also develop a heuristic algorithmforschedulingpartsofjobswithfamilysetuptimeandproposeitsworst-caseperformanceratio.TheapplicationistheIoT-basedsmartfactorywith3Dprintersasprocessing machines