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An Optimization Problem of Distributed Permutation Flowshop Scheduling with an Order Acceptance Strategy in Heterogeneous Factories

Author

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  • Seung Jae Lee

    (Department of Industrial and Management Engineering, Incheon National University, 119, Academy-ro, Yeonsu-gu, Incheon 22012, Republic of Korea)

  • Byung Soo Kim

    (Department of Industrial and Management Engineering, Incheon National University, 119, Academy-ro, Yeonsu-gu, Incheon 22012, Republic of Korea)

Abstract

This paper addresses a distributed permutation flowshop scheduling problem with an order acceptance strategy in heterogeneous factories. Each order has a related revenue and due date, and several flowshop machines are operated in each factory, and they have a distinct sequence-dependent setup time. We select/reject production orders, assign the selected orders to the factories, and determine the permutation manufacturing sequence in each factory to maximize the total profit. To optimally solve the scheduling problem, we formulate the scheduling problem as a mixed integer linear programming model to find an optimal solution for small-sized experiments. Then, we propose two population-based algorithms, a genetic algorithm and particle swarm optimization for large-sized experiments. We proved that the proposed genetic algorithm effectively and efficiently solves the problem to guarantee a near optimal solution through computational experiments. Finally, we conduct a sensitivity analysis of the genetic algorithm to observe the relationship between order selection, revenue, and order tardiness cost.

Suggested Citation

  • Seung Jae Lee & Byung Soo Kim, 2025. "An Optimization Problem of Distributed Permutation Flowshop Scheduling with an Order Acceptance Strategy in Heterogeneous Factories," Mathematics, MDPI, vol. 13(5), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:877-:d:1606605
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    References listed on IDEAS

    as
    1. Deming Lei & Yue Yuan & Jingcao Cai & Danyu Bai, 2020. "An imperialist competitive algorithm with memory for distributed unrelated parallel machines scheduling," International Journal of Production Research, Taylor & Francis Journals, vol. 58(2), pages 597-614, January.
    2. Hao-Chin Chang & Tung-Kuan Liu, 2017. "Optimisation of distributed manufacturing flexible job shop scheduling by using hybrid genetic algorithms," Journal of Intelligent Manufacturing, Springer, vol. 28(8), pages 1973-1986, December.
    3. Ruiz, Ruben & Stutzle, Thomas, 2008. "An Iterated Greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1143-1159, June.
    4. De Giovanni, L. & Pezzella, F., 2010. "An Improved Genetic Algorithm for the Distributed and Flexible Job-shop Scheduling problem," European Journal of Operational Research, Elsevier, vol. 200(2), pages 395-408, January.
    5. J. Behnamian & S. M. T. Fatemi Ghomi, 2016. "A survey of multi-factory scheduling," Journal of Intelligent Manufacturing, Springer, vol. 27(1), pages 231-249, February.
    6. Shengluo Yang & Zhigang Xu, 2021. "The distributed assembly permutation flowshop scheduling problem with flexible assembly and batch delivery," International Journal of Production Research, Taylor & Francis Journals, vol. 59(13), pages 4053-4071, July.
    7. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    8. Ankit Khare & Sunil Agrawal, 2021. "Effective heuristics and metaheuristics to minimise total tardiness for the distributed permutation flowshop scheduling problem," International Journal of Production Research, Taylor & Francis Journals, vol. 59(23), pages 7266-7282, December.
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