In this paper, an unrelated parallel machine scheduling problem with sequence and machine-dependent setup times and makespan minimization is studied. A new makespan linearization and several mixed integer formulations are proposed for this problem. These formulations outperform the previously published formulations regarding size of instances and computational time to reach optimal solutions. Using these models, it is possible to solve instances six times larger than what was previously solved and to obtain optimal solutions on instances of the same size up to four orders of magnitude faster. A metaheuristic algorithm based on multi-start algorithm and variable neighbourhood descent metaheuristic is proposed. Composite movements were defined for the improvement phase of the proposed metaheuristic algorithm that considerably improved the performance of the algorithm providing small deviations from optimal solutions in medium-sized instances and outperforming the best known solutions for large instances.

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In this study, we introduce a routing problem with multiple uses of a single vehicle and service time in demand points, minimizing the sum of clients' waiting time to receive service. This problem is relevant in the distribution of aid in disaster-stricken communities, in the recollection and/or delivery of perishable goods and personnel transportation, among other situations, where reaching clients to perform service, fast and fair, is a priority. We consider vehicle capacity and travel distance constraints, forcing multiple use of the vehicle during the planning horizon. This paper presents two mixed integer formulations for this problem, based on a multi-level network, as well as a metaheuristic algorithm. The proposed models can solve to optimality instances with up to 30 clients. The proposed metaheuristic algorithm obtains high-quality solutions in short computational times.