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A column generation-based approach for proportionate flexible two-stage no-wait job shop scheduling

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  • Zhi Pei
  • Xuefang Zhang
  • Li Zheng
  • Mingzhong Wan

Abstract

Job shop scheduling, as one of the classical scheduling problems, has been widely studied in literatures, and proved to be mostly NP-hard. Although it is extremely difficult to solve job shop scheduling with no-wait constraint to optimality, the two-machine no-wait job shop scheduling to minimise makespan could be solvable in polynomial time when each job has exactly two equal length operations (proportionate job shop). In the present paper, an extension is attempted by considering a proportionate flexible two-stage no-wait job shop scheduling problem with minimum makespan, and a set-covering formulation is put forward which contains a master problem and a pricing problem. To solve this problem, a column generation (CG)-based approach is implemented. In comparison, a mixed integer programming model is constructed and optimised by Cplex. A series of randomly generated numerical instances are calculated. And the testing result shows that the mixed integer model handled by Cplex can only solve small scale cases, while the proposed CG-based method can conquer larger size problems in acceptable time.

Suggested Citation

  • Zhi Pei & Xuefang Zhang & Li Zheng & Mingzhong Wan, 2020. "A column generation-based approach for proportionate flexible two-stage no-wait job shop scheduling," International Journal of Production Research, Taylor & Francis Journals, vol. 58(2), pages 487-508, January.
    • Handle: RePEc:taf:tprsxx:v:58:y:2020:i:2:p:487-508
    DOI: 10.1080/00207543.2019.1597291
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    Cited by:

    1. Omid Shahvari & Rasaratnam Logendran & Madjid Tavana, 2022. "An efficient model-based branch-and-price algorithm for unrelated-parallel machine batching and scheduling problems," Journal of Scheduling, Springer, vol. 25(5), pages 589-621, October.
    2. Shao, Kaining & Fan, Wenjuan & Lan, Shaowen & Kong, Min & Yang, Shanlin, 2023. "A column generation-based heuristic for brachytherapy patient scheduling with multiple treatment sessions considering radioactive source decay and time constraints," Omega, Elsevier, vol. 118(C).
    3. Dauzère-Pérès, Stéphane & Ding, Junwen & Shen, Liji & Tamssaouet, Karim, 2024. "The flexible job shop scheduling problem: A review," European Journal of Operational Research, Elsevier, vol. 314(2), pages 409-432.

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