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

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  • Alexander Ageev

    (Sobolev Institute of Mathematics)

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 $$(1.25-\varepsilon )$$(1.25-ε)-approximation implies $$\hbox {P}=\hbox {NP}$$P=NP and develop a 2-approximation algorithm.

Suggested Citation

  • Alexander Ageev, 2020. "Approximating the 2-machine flow shop problem with exact delays taking two values," Journal of Global Optimization, Springer, vol. 76(3), pages 491-497, March.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:3:d:10.1007_s10898-019-00775-0
    DOI: 10.1007/s10898-019-00775-0
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    References listed on IDEAS

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    1. Moustafa Elshafei & Hanif D. Sherali & J. Cole Smith, 2004. "Radar pulse interleaving for multi‐target tracking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(1), pages 72-94, February.
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