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Mathematical Model and Evaluation Function for Conflict-Free Warranted Makespan Minimization of Mixed Blocking Constraint Job-Shop Problems

Author

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  • Christophe Sauvey

    (Université de Lorraine, LGIPM, F-57000 Metz, France)

  • Wajdi Trabelsi

    (ICN Business School, LGIPM, F-57000 Metz, France)

  • Nathalie Sauer

    (Université de Lorraine, LGIPM, F-57000 Metz, France)

Abstract

In this paper, we consider a job-shop scheduling problem with mixed blocking constraints. Contrary to most previous studies, where no blocking or only one type of blocking constraint was used among successive operations, we assume that, generally, we may address several different blocking constraints in the same scheduling problem depending on the intermediate storage among machines, the characteristics of the machines, the technical constraints, and even the jobs. Our objective was to schedule a set of jobs to minimize the makespan. Thus, we propose, for the first time, a mathematical model of the job-shop problem taking into account the general case of mixed blocking constraints, and the results were obtained using Mosel Xpress software. Then, after explaining why and how groups of jobs have to be processed, a blocking constraint conflict-free warranted evaluation function is proposed and tested with the particle swarm optimization and genetic algorithm methods. The results prove that we obtained a near-optimal solution to this problem in a very short time.

Suggested Citation

  • Christophe Sauvey & Wajdi Trabelsi & Nathalie Sauer, 2020. "Mathematical Model and Evaluation Function for Conflict-Free Warranted Makespan Minimization of Mixed Blocking Constraint Job-Shop Problems," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:121-:d:308291
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    References listed on IDEAS

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    Cited by:

    1. Anran Zhao & Peng Liu & Xiyu Gao & Guotai Huang & Xiuguang Yang & Yuan Ma & Zheyu Xie & Yunfeng Li, 2022. "Data-Mining-Based Real-Time Optimization of the Job Shop Scheduling Problem," Mathematics, MDPI, vol. 10(23), pages 1-30, December.
    2. M. Saqlain & S. Ali & J. Y. Lee, 2023. "A Monte-Carlo tree search algorithm for the flexible job-shop scheduling in manufacturing systems," Flexible Services and Manufacturing Journal, Springer, vol. 35(2), pages 548-571, June.

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