A Reformulation for the Problem of Scheduling Unrelated Parallel Machines with Sequence and Machine Dependent Setup Times

In this paper we propose an improved formulation for an unrelated parallel machine problem with machine and job sequence-dependent setup times that outperforms the previously published formulations regarding size of instances and CPU time to reach optimal solutions. The main difference between the proposed formulation and previous ones is the way the makespan has been linearized. It provides improved dual bounds which speeds up the solution process when using a branch-and-bound commercial solver. Computational experiments show that, using this model, it is possible to solve instances four times larger than what was previously possible using other mixed integer programming formulations in the literature and obtain optimal solutions on instances of the same size up to three orders of magnitude faster.