Optimal and heuristic solution methods for a multiprocessor machine scheduling problem

This paper deals with the scheduling of operations on a multiprocessor machine in the context of shoe manufacturing. Multiprocessor machines are composed of several parallel processors. Unlike parallel machines, the entire machine needs to be stopped whenever a single processor needs a setup. Our industrial partner, one of the major winter-shoe manufacturers in Canada, offers a relatively large variety of models. For each of these models, all the sizes proposed by this manufacturer must be produced in various quantities. Our objective is to schedule the production of the required sizes on the machine's different processors in order to minimize the global makespan, which includes both the production time and the set up time. We first present a mathematical formulation of the problem. Then, we introduce a decomposition procedure based on the mathematical model, and we demonstrate that this procedure is very efficient for small- and medium-size instances. We also propose two construction heuristics and two improvement heuristics for larger problems, and we report the results of our extensive computational experiments to demonstrate the quality of the proposed heuristics in terms of reducing production time and computational effort.