Optimize Unrelated Parallel Machines Scheduling Problems With Multiple Limited Additional Resources, Sequence-Dependent Setup Times and Release Date Constraints

• Published in: IEEE access Vol. 7; pp. 171533 - 171547
• Main Authors: Al-harkan, Ibrahim M., Qamhan, Ammar A.
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Completion time; Computing time; Heuristic methods; Integer programming; Job shop scheduling; Job shops; Linear programming; Mathematical model; Mixed integer; Mixed integer linear programming; Optimization; Parallel machines; Processor scheduling; renewable resources; Scheduling; Setup times; Simulated annealing; variable neighborhood search
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2019.2955975

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.