Abstract
This paper considers the problem of scheduling a set of jobs on unrelated parallel machines subject to several constraints which are non-zero arbitrary release dates, limited additional resources, and non-anticipatory sequence-dependent setup times. The objective function is to minimize the maximum completion time. In order to find an optimal solution for this problem, a new mixed-integer linear programming model (MILP) is presented. Moreover, a two-stage hybrid metaheuristic based on variable neighborhood search hybrid and simulated annealing (TVNS_SA) is proposed. In the first stage, a developed heuristic is used to find an initial solution with good quality. At the second stage, the obtained initial solution is used as the first neighborhood structures in the proposed metaheuristic, for further progress different neighborhood structures and effective resolution schemes are also presented. The computational results indicate that the proposed metaheuristic is capable of obtaining optimal solutions for most of the instances when compared to the solution obtained by the developed mixed-integer linear programming model. In addition, the metaheuristic dominated the MILP with respect to computing time. The overall evaluation of the proposed algorithm shows its efficiency and effectiveness when compared with other algorithms. Finally, in order to obtain rigorous and fair conclusions, a paired t-test has been conducted to test the significant differences between the five variants of the TVNS_SA.
Highlights
Production scheduling problems are the most probably related problem to the industrial world since it is a question of reconciling, optimally, limited resources with activities in time
A Mixed Integer Linear Programming (MILP), tabu Search, and simulated annealing algorithms were presented in the study of Bektur and Saraç [44] to minimize the total weighted tardiness of a scheduling problem of unrelated parallel machine with a common server and sequence dependent setup times
This study presents a new MILP to minimize the maximum completion time
Summary
Production scheduling problems are the most probably related problem to the industrial world since it is a question of reconciling, optimally, limited resources with activities in time. This study considers a scheduling problem of unrelated parallel machines under several constraints with the objective of minimizing the maximum completion time. In this context, this study develops an exact methodology and metaheuristic to solve different size problems, which made the contribution of this paper different from the existing work as it will be shown in the literature reviewed and to the best of our knowledge. This work led to the development of solving methods for the scheduling problem in the type of workshop that is described previously. It is clear from the literature reviewed that just a few papers have been reported on the problem addressed in this paper.
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