Heuristic algorithms for the unrelated parallel machine scheduling problem with one scarce additional resource

In this paper, we study the unrelated parallel machine scheduling problem with one scarce additional resource to minimise the maximum completion time of the jobs or makespan. Several heuristics are proposed following two strategies: the first one is based on the consideration of the resource constraint during the whole solution construction process. The second one starts from several assignment rules without considering the resource constraint, and repairs the non feasible assignments in order to obtain a feasible solution. Several computation experiments are carried out over an extensive benchmark. A comparative evaluation against previously proposed mathematical models and matheuristics (combination of mathematical models and heuristics) is carried out. From the results, we can conclude that our methods outperform the existing ones, and the second strategy performs better, especially for large instances.