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Two-stage open-shop scheduling with a two-machine flow shop as a stage: approximation algorithms and empirical experiments

Author

Listed:
  • Jianming Dong

    (Zhejiang Sci-Tech University)

  • Joshua Chang

    (University of Alberta)

  • Bing Su

    (Xi’an Technological University)

  • Jueliang Hu

    (Zhejiang Sci-Tech University)

  • Guohui Lin

    (University of Alberta)

Abstract

We study a scheduling environment that finds many real-world manufacturing applications, in which there is a close connection between a hybrid multiprocessor open shop and multiple parallel identical flow shops. In this environment, there is an extended two-stage open shop, where in one stage we have a set of parallel identical machines, while in the other we have a two-machine flow shop. Our objective is to minimize the makespan, that is, the latest completion time of all jobs. We pursue approximation algorithms with provable performance, and we achieve a 2-approximation when the number of parallel identical machines is constant or is part of the input; we also design a 5/3-approximation for the special case where there is only one machine in the multiprocessor stage, which remains weakly NP-hard. Our empirical experiments show that both approximation algorithms perform much better in simulated instances; their average ratios over the proposed lower bound are around 1.5 and 1.2, respectively.

Suggested Citation

  • Jianming Dong & Joshua Chang & Bing Su & Jueliang Hu & Guohui Lin, 2020. "Two-stage open-shop scheduling with a two-machine flow shop as a stage: approximation algorithms and empirical experiments," Journal of Scheduling, Springer, vol. 23(5), pages 595-608, October.
    • Handle: RePEc:spr:jsched:v:23:y:2020:i:5:d:10.1007_s10951-019-00633-7
    DOI: 10.1007/s10951-019-00633-7
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    References listed on IDEAS

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    1. Hoogeveen, J. A. & Lenstra, J. K. & Veltman, B., 1996. "Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard," European Journal of Operational Research, Elsevier, vol. 89(1), pages 172-175, February.
    2. Ruiz, Rubén & Vázquez-Rodríguez, José Antonio, 2010. "The hybrid flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 205(1), pages 1-18, August.
    3. D. P. Williamson & L. A. Hall & J. A. Hoogeveen & C. A. J. Hurkens & J. K. Lenstra & S. V. Sevast'janov & D. B. Shmoys, 1997. "Short Shop Schedules," Operations Research, INFORMS, vol. 45(2), pages 288-294, April.
    4. Zhang, Xiandong & van de Velde, Steef, 2012. "Approximation algorithms for the parallel flow shop problem," European Journal of Operational Research, Elsevier, vol. 216(3), pages 544-552.
    5. Bo Chen & Celia A. Glass & Chris N. Potts & Vitaly A. Strusevich, 1996. "A New Heuristic for Three-Machine Flow Shop Scheduling," Operations Research, INFORMS, vol. 44(6), pages 891-898, December.
    6. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
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    Cited by:

    1. Zeynep Adak & Mahmure Övül Arıoğlu Akan & Serol Bulkan, 0. "Multiprocessor open shop problem: literature review and future directions," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    2. Zeynep Adak & Mahmure Övül Arıoğlu Akan & Serol Bulkan, 2020. "Multiprocessor open shop problem: literature review and future directions," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 547-569, August.

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