Reformulations and an exact algorithm for unrelated parallel machine scheduling problems with setup times

Parallel machine scheduling problems have many practical and industrial applications. In this paper we study a generalization which is the unrelated parallel machine scheduling problem with machine and job sequence setup times (UPMS) with makespan minimization criterion. We propose new mixed integer linear programs and a mathematical programming based algorithm. These new models and algorithms are tested and compared with the existing ones in an extensive and comprehensive computational campaign. The performance of two popular commercial solvers (CPLEX and Gurobi) is also compared in the experiments. Results show that the proposed methods significantly improve on existing methods and are able to obtain solutions for extremely large instances of up to 1000 jobs and eight machines with relative deviations from lower bounds below 0.8%. (C) 2018 Elsevier Ltd. All rights reserved.