Scheduling unrelated parallel machines computational results

Abstract

Scheduling n independent jobs on m unrelated parallel machines without preemption belongs to the most difficult scheduling problems. Here, processing job i on machine j takes time pij, and the total time used by a machine is the sum of the processing times for the jobs assigned to it. The objective is to minimize makespan. In this paper we present an experimental study on the Unsplittable-Truemper algorithm. This purely combinatorial approach computes 2-approximate solutions in the best worst-case running time known so far. The goal of our simulations was to prove its efficiency in practice. We compare our technique with algorithms and heuristics used in practice, especially with those based on the two-step approach. The experiments show that for large and difficult instances the Unsplittable-Truemper algorithm has a clear advantage over methods based on linear programming. Moreover, it requires much less operational memory, and thus is more effective and easier to handle. © Springer-Verlag Berlin Heidelberg 2006.