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Approximating the 2-machine flow shop problem with exact delays taking two values

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Abstract

In the 2-Machine Flow Shop problem with exact delays the operations of each job are separated by a given time lag (delay). Leung et al. (Int J Found Comput Sci 18:341–359, 2007) established that the problem is strongly NP-hard when the delays may have at most two different values. We present further results for this case: we prove that the existence of \((1.25-\varepsilon )\)-approximation implies \(\hbox {P}=\hbox {NP}\) and develop a 2-approximation algorithm.

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Acknowledgements

The author would like to thank the anonymous referees for many helpful comments and suggestions.

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  1. Sobolev Institute of Mathematics, Koptyuga Avenue, 4, Novosibirsk, Russia

    Alexander Ageev

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  1. Alexander Ageev
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Correspondence to Alexander Ageev.

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This research was supported by the Russian Science Foundation, Grant 17-11-01021.

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Ageev, A. Approximating the 2-machine flow shop problem with exact delays taking two values. J Glob Optim 76, 491–497 (2020). https://doi.org/10.1007/s10898-019-00775-0

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  • DOI: https://doi.org/10.1007/s10898-019-00775-0

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