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Mathematical Modeling and A Novel Heuristic Method for Flexible Job-Shop Batch Scheduling Problem with Incompatible Jobs

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  • Bin Ji

    (School of Traffic & Transportation Engineering, Central South University, Changsha 410075, China)

  • Shujing Zhang

    (School of Traffic & Transportation Engineering, Central South University, Changsha 410075, China)

  • Samson S. Yu

    (School of Engineering, Deakin University, Geelong, VIC 3216, Australia)

  • Binqiao Zhang

    (Hubei Provincial Key Laboratory for Operation and Control of Cascaded Hydropower Station, China Three Gorges University, Yichang 443002, China
    College of Electrical Engineering and New Energy, China Three Gorges University, Yichang 443002, China)

Abstract

This paper investigates a novel flexible job-shop scheduling problem, where the machines have batch-processing capacity, but incompatible jobs cannot be processed in a batch (FJSPBI) simultaneously. This problem has wide applications in discrete manufacturing, especially in chemical and steel casting industries. For the first time, in this study, a 3-indexed mixed-integer linear programming (MILP) model is proposed, which can be efficiently and optimally solved by commercial solvers for small-scale problems. In addition, an improved large neighborhood search (LNS) algorithmic framework with an optimal insertion and tabu-based components (LNSIT) is proposed, which can achieve high-quality solutions for a large-scale FJSPBI in a reasonable time. A perturbation strategy and an optimal insertion strategy are then additionally embedded to improve the exploitation and exploration ability of the algorithm. The proposed model and algorithm are tested on numerous existing benchmark instances without the incompatibility characteristics, and on newly generated instances of the FJSPBI. The experimental results indicate the effectiveness of the proposed MILP model and the algorithm, including the proposed strategies, and the optimal insertion strategy can significantly reduce the computational burden of the LNS algorithm. The comparison results further verify that the proposed LNSIT can directly solve the specific flexible job-shop batch scheduling problem without incompatibility, with better results than existing methods, especially for large-scale instances. Additionally, the impacts of a wide range of characteristics, including batch capacity, incompatibility rate, instance scale, and machine processing rate, on the performance of the LNSIT and the scheduling results are analyzed and presented.

Suggested Citation

  • Bin Ji & Shujing Zhang & Samson S. Yu & Binqiao Zhang, 2023. "Mathematical Modeling and A Novel Heuristic Method for Flexible Job-Shop Batch Scheduling Problem with Incompatible Jobs," Sustainability, MDPI, vol. 15(3), pages 1-26, January.
  • Handle: RePEc:gam:jsusta:v:15:y:2023:i:3:p:1954-:d:1041665
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    References listed on IDEAS

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    1. João M. R. C. Fernandes & Seyed Mahdi Homayouni & Dalila B. M. M. Fontes, 2022. "Energy-Efficient Scheduling in Job Shop Manufacturing Systems: A Literature Review," Sustainability, MDPI, vol. 14(10), pages 1-34, May.
    2. Stefan Ropke & David Pisinger, 2006. "An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 40(4), pages 455-472, November.
    3. Abdelhakim AitZai & Brahim Benmedjdoub & Mourad Boudhar, 2016. "Branch-and-bound and PSO algorithms for no-wait job shop scheduling," Journal of Intelligent Manufacturing, Springer, vol. 27(3), pages 679-688, June.
    4. Raaymakers, W. H. M. & Hoogeveen, J. A., 2000. "Scheduling multipurpose batch process industries with no-wait restrictions by simulated annealing," European Journal of Operational Research, Elsevier, vol. 126(1), pages 131-151, October.
    5. Christian Gahm & Stefan Wahl & Axel Tuma, 2022. "Scheduling parallel serial-batch processing machines with incompatible job families, sequence-dependent setup times and arbitrary sizes," International Journal of Production Research, Taylor & Francis Journals, vol. 60(17), pages 5131-5154, September.
    6. J. Carlier & E. Pinson, 1989. "An Algorithm for Solving the Job-Shop Problem," Management Science, INFORMS, vol. 35(2), pages 164-176, February.
    7. Peter J. M. van Laarhoven & Emile H. L. Aarts & Jan Karel Lenstra, 1992. "Job Shop Scheduling by Simulated Annealing," Operations Research, INFORMS, vol. 40(1), pages 113-125, February.
    8. Jia, Zhao-hong & Leung, Joseph Y.-T., 2015. "A meta-heuristic to minimize makespan for parallel batch machines with arbitrary job sizes," European Journal of Operational Research, Elsevier, vol. 240(3), pages 649-665.
    9. Ansis Ozolins, 2020. "Bounded dynamic programming algorithm for the job shop problem with sequence dependent setup times," Operational Research, Springer, vol. 20(3), pages 1701-1728, September.
    10. Haicao Song & Pan Liu, 2022. "A Study on the Optimal Flexible Job-Shop Scheduling with Sequence-Dependent Setup Time Based on a Hybrid Algorithm of Improved Quantum Cat Swarm Optimization," Sustainability, MDPI, vol. 14(15), pages 1-16, August.
    11. Stéphane Dauzère-Pérès & Jan Paulli, 1997. "An integrated approach for modeling and solving the general multiprocessor job-shop scheduling problem using tabu search," Annals of Operations Research, Springer, vol. 70(0), pages 281-306, April.
    12. Shoujing Zhang & Tiantian Hou & Qing Qu & Adam Glowacz & Samar M. Alqhtani & Muhammad Irfan & Grzegorz Królczyk & Zhixiong Li, 2022. "An Improved Mayfly Method to Solve Distributed Flexible Job Shop Scheduling Problem under Dual Resource Constraints," Sustainability, MDPI, vol. 14(19), pages 1-19, September.
    13. Muter, İbrahim, 2020. "Exact algorithms to minimize makespan on single and parallel batch processing machines," European Journal of Operational Research, Elsevier, vol. 285(2), pages 470-483.
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