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On the complexity of constructing a minmax regret solution for the two-machine flow shop problem under the interval uncertainty

Author

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  • Yakov Shafransky

    (United Institute of Informatics Problems, NAS of Belarus)

  • Viktor Shinkarevich

    (Belarusian State University)

Abstract

We prove the NP-hardness of constructing a minmax regret solution for the two-machine flow shop problem under the interval uncertainty of the job processing times. The problem complexity status has been an open question for over the past 20 years. We establish the NP-hardness of this problem using a so-called alternative scheme for proving the NP-hardness of optimization problems. Also, we show that the problem is non-approximable in polynomial time.

Suggested Citation

  • Yakov Shafransky & Viktor Shinkarevich, 2020. "On the complexity of constructing a minmax regret solution for the two-machine flow shop problem under the interval uncertainty," Journal of Scheduling, Springer, vol. 23(6), pages 745-749, December.
    • Handle: RePEc:spr:jsched:v:23:y:2020:i:6:d:10.1007_s10951-020-00663-6
    DOI: 10.1007/s10951-020-00663-6
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    References listed on IDEAS

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    1. Lin, Yixun & Wang, Xiumei, 2007. "Necessary and sufficient conditions of optimality for some classical scheduling problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 809-818, January.
    2. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    3. Cheng, T.C.E. & Shafransky, Y. & Ng, C.T., 2016. "An alternative approach for proving the NP-hardness of optimization problems," European Journal of Operational Research, Elsevier, vol. 248(1), pages 52-58.
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    Cited by:

    1. Levorato, Mario & Figueiredo, Rosa & Frota, Yuri, 2022. "Exact solutions for the two-machine robust flow shop with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 300(1), pages 46-57.

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