Size-reduction methods for the unrelated parallel machines problem and makespan criterion

In this work we study the unrelated parallel machines problem with the objective of the minimization of the maximum completion time or makespan (Cmax). We propose some metaheuristics based on a size-reduction of the original assignment problem. The idea is to consider only a few of the best possible machine assignments for the jobs and not all of them. We test the proposed simple algorithms with a large benchmark of instances and compare them with current state-of-the-art methods. In most cases, the proposed size-reduction algorithms produce results that are statistically better by a significant margin.