In this paper, an unrelated parallel machine scheduling problem with sequence and machine-dependent setup times and makespan minimization is studied. A new makespan linearization and several mixed integer formulations are proposed for this problem. These formulations outperform the previously published formulations regarding size of instances and computational time to reach optimal solutions. Using these models, it is possible to solve instances six times larger than what was previously solved and to obtain optimal solutions on instances of the same size up to four orders of magnitude faster. A metaheuristic algorithm based on multi-start algorithm and variable neighbourhood descent metaheuristic is proposed. Composite movements were defined for the improvement phase of the proposed metaheuristic algorithm that considerably improved the performance of the algorithm providing small deviations from optimal solutions in medium-sized instances and outperforming the best known solutions for large instances.

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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.

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