A bin packing reformulation and matheuristics for the unrelated parallel machines scheduling problem with resources

This short paper studies a parallel machines scheduling problem with the consideration of resources. Each job needs a number of resources at each machine for its completion. The objective studied is the minimization of the makespan. We model this problem by means of two integer linear programming problems. One of them is based on a model previously proposed in the literature, whereas the other exploits the resemblance of our problem with the well-known strip packing problems. Since none of these models is capable of solving to optimality mediumsized instances, we propose three matheuristic strategies. All algorithms proposed are run over randomly generated instances of small-medium size. Results show that matheuristics outperform the mathematical models by a large margin that widens with instance size.