Logic-based Benders Decomposition for Alternative Resource Scheduling with Sequence Dependent Setups

We study an unrelated parallel machines scheduling problem with sequence and machine dependent setup times. A logic-based Benders decomposition approach is proposed to minimize the makespan. This approach is a hybrid model that makes use of a mixed integer programming master problem and a specialized solver for travelling salesman subproblems. The master problem is used to assign jobs to machines while the subproblems obtain optimal schedules on each machine given the master problem assignments. Computational results show that the Benders model is able to find optimal solutions up to six orders of magnitude faster as well as solving problems six times the size previously possible with a mixed integer programming model in the literature and twice the size that a branch-and-bound algorithm can solve for similar problems. We further relax the Benders decomposition to accept suboptimal schedules and demonstrate the ability to parameterize solution quality while outperforming state-of-the-art metaheuristics both in terms of solution quality and mean run-time.