This work deals with the parallel machines scheduling problem which consists in the assignment of n jobs on m parallel machines. The most general variant of this problem is when the processing time depends on the machine to which each job is assigned to. This case is known as the unrelated parallel machines problem.Similarly to most of the literature, this paper deals with the minimization of the maximum completion time of the jobs, commonly referred to as makespan (C max ).Many algorithms and methods have been proposed for this hard combinatorial problem, including several highly sophisticated procedures. By contrast, in this paper we propose a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time. Extensive computational campaigns show that these solutions are, most of the time, better than the current state-of-the-art methodologies by a statistically significant margin.

In this paper we analyze a parallel machine scheduling problem in which the processing of jobs on the machines requires a number of units of a scarce resource. This number depends both on the job and on the machine. The availability of resources is limited and fixed throughout the production horizon. The objective considered is the minimization of the makespan. We model this problem by means of two integer linear programming problems. One of them is based on a model previously proposed in the literature. The other one, which is based on the resemblance to strip packing problems, is an original contribution of this paper. As the models presented are incapable of solving medium-sized instances to optimality, we propose three matheuristic strategies for each of these two models. The algorithms proposed are tested over an extensive computational experience. Results show that the matheuristic strategies significantly outperform the mathematical models.

Villa Juliá, MF.; Vallada Regalado, E.; Fanjul Peyró, L. (2018). Heuristic algorithms for the unrelated parallel machine scheduling problem with one scarce additional resource. Expert Systems with Applications. 93:28-38. https://doi. AbstractIn 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.