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Two-Machine Flow-Shop Minimum-Length Scheduling With Interval Processing Times

Author

Listed:
  • C. T. NG

    (Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

  • NATALJA M. MATSVEICHUK

    (United Institute of Informatics Problems, National Academy of Sciences of Belarus, Surganova Street, 6, Minsk 220012, Belarus)

  • YURI N. SOTSKOV

    (United Institute of Informatics Problems, National Academy of Sciences of Belarus, Surganova Street, 6, Minsk 220012, Belarus)

  • T. C. EDWIN CHENG

    (Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

Abstract

The flow-shop minimum-length scheduling problem withnjobs processed on two machines is addressed where processing times are uncertain: only lower and upper bounds of the random processing times are given before scheduling, but their probability distributions are unknown. For such a problem, there may not exist a dominant schedule that remains optimal for all possible realizations of the processing times and so we look for a minimal set of schedules that are dominant. We obtain necessary and sufficient conditions for the case when it is possible to fix the order of two jobs in a minimal set of dominant schedules. The necessary and sufficient conditions are proven for the case when one schedule dominates all the others. We characterize also the case where there does not exist non-trivial schedule domination. All the conditions proven may be tested in polynomial time ofn.

Suggested Citation

  • C. T. Ng & Natalja M. Matsveichuk & Yuri N. Sotskov & T. C. Edwin Cheng, 2009. "Two-Machine Flow-Shop Minimum-Length Scheduling With Interval Processing Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(06), pages 715-734.
    • Handle: RePEc:wsi:apjorx:v:26:y:2009:i:06:n:s0217595909002432
    DOI: 10.1142/S0217595909002432
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    Citations

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    Cited by:

    1. Michał Ćwik & Jerzy Józefczyk, 2018. "Heuristic algorithms for the minmax regret flow-shop problem with interval processing times," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 215-238, March.
    2. Faicel Hnaien & Taha Arbaoui, 2023. "Minimizing the makespan for the two-machine flow shop scheduling problem with random breakdown," Annals of Operations Research, Springer, vol. 328(2), pages 1437-1460, September.
    3. Yuri N. Sotskov & Natalja M. Matsveichuk & Vadzim D. Hatsura, 2020. "Schedule Execution for Two-Machine Job-Shop to Minimize Makespan with Uncertain Processing Times," Mathematics, MDPI, vol. 8(8), pages 1-51, August.

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