Unrelated Machines Scheduling With Machine Eligibility Restrictions

Abstract

In this paper we present a new heuristic algorithm to minimize the makespan for scheduling jobs on unrelated parallel machines with machine eligibility restrictions ( R^ I M .1 C^^). To the best of our knowledge, the problem has not been addressed previously in the literature. The multi-phase heuristic algorithm incorporates new concepts from the multi-depot vehicle routing in the constructive heuristic. A computational study includes problems with two or four machines, up to 105 jobs, and three levels of a machine selection parameter. The heuristic algorithm solution values are compared to optimal solution values. The results show that the heuristic algorithm can yield solutions within a few percent of the optimal solutions with performance improving as the number of jobs to be scheduled increases.