Algorithms for the unspecified unrelated parallel machine scheduling problem with additional resources

In this paper we study the unspecified unrelated parallel machine scheduling problem with additional resources. Jobs can be processed at any machine, using a certain number of units of a scarce resource. The objective is to schedule jobs in parallel machines, so that the makespan is minimized, and the use of resources does not exceed a given limit, at any time. We propose an ILP program to solve this problem to optimality. Due to the complexity of the problem, this program explodes for medium-size instances. Therefore, we introduce a heuristic procedure. Both algorithms are tested over a computational experience.