An exact approach for the identical parallel machine scheduling problem with sequence-dependent setup times and the job splitting property

Parallel machine scheduling problems have long been studied due to their importance in manufacturing and planning. We consider the identical parallel machine scheduling problem with sequence-dependent setup times and the job splitting property. Jobs can divided into sections which can be assigned to different machines simultaneously. A setup time is required between any two job sections. The aim is to minimize the makespan. We propose an exact approach based on Benders decomposition that is able to solve to optimality the instances considered in the literature. The problem is decomposed in two parts. The master problem assigns the job sections to machine while partially considering the setup times. The subproblems sequence the jobs to assess the makespan on each machine using a Traveling Salesman Problem (TSP) exact algorithm. The master problem is updated by adding Benders cuts after solving the subproblems. The computational results are presented and discussed.