A Logic-Based Benders Approach to Scheduling with Alternative Resources and Setup Times

We study an unrelated parallel machines scheduling problem with sequence and machine dependent setup times. A logicbased Benders decomposition approach is proposed to minimize the makespan. The decomposition approach is a hybrid model that makes use of a mixed integer programming master problem and a travelling salesman problem subproblem. The master problem is a relaxation of the problem and is used to create assignments of jobs to machines, while the subproblem obtains optimal schedules based on the master problem assignments. Computational results comparing the Benders decomposition and mixed integer program formulation show that the Benders model is able to find optimal solutions to problems up to five orders of magnitude faster as well as solving problems four times the size possible previously.