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

Yakov Shafransky () and Viktor Shinkarevich ()
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Yakov Shafransky: United Institute of Informatics Problems, NAS of Belarus
Viktor Shinkarevich: Belarusian State University

Journal of Scheduling, 2020, vol. 23, issue 6, No 10, 745-749

Abstract: 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.

Keywords: Minmax regret; Interval uncertainty; Two-machine flow shop; NP-hardness (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10951-020-00663-6

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