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

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.

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Acknowledgements

The authors are deeply grateful to an anonymous referee for the valuable comments and suggestions. The research of the first author has been partially supported by the BRFFR project \(\Phi \)15CO-043.

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Correspondence to Yakov Shafransky.

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Shafransky, Y., Shinkarevich, V. On the complexity of constructing a minmax regret solution for the two-machine flow shop problem under the interval uncertainty. J Sched 23, 745–749 (2020). https://doi.org/10.1007/s10951-020-00663-6

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  • DOI: https://doi.org/10.1007/s10951-020-00663-6

Keywords

  • Minmax regret
  • Interval uncertainty
  • Two-machine flow shop
  • NP-hardness