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Asymptotically optimal linear time algorithms for two‐stage and three‐stage flexible flow shops

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  • Christos Koulamas
  • George J. Kyparisis

Abstract

We consider two‐stage and three‐stage flexible flow shops with parallel machines in each stage and the minimum makespan objective. We develop linear time algorithms for these problems with absolute worst‐case bounds either sharper or no worse than the currently available ones and we accomplish this with lower complexity algorithms. We also demonstrate the asymptotic optimality of a class of algorithms for multistage flexible flow shop problems (which includes the proposed algorithms) under certain probabilistic assumptions on the job processing times. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 259–268, 2000

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  • Christos Koulamas & George J. Kyparisis, 2000. "Asymptotically optimal linear time algorithms for two‐stage and three‐stage flexible flow shops," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(3), pages 259-268, April.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:3:p:259-268
    DOI: 10.1002/(SICI)1520-6750(200004)47:33.0.CO;2-K
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    References listed on IDEAS

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    1. Hoogeveen, J. A. & Lenstra, J. K. & Veltman, B., 1996. "Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard," European Journal of Operational Research, Elsevier, vol. 89(1), pages 172-175, February.
    2. Sergey Sevast'janov, 1995. "Vector Summation in Banach Space and Polynomial Algorithms for Flow Shops and Open Shops," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 90-103, February.
    3. E. G. Coffman & E. N. Gilbert, 1985. "On the Expected Relative Performance of List Scheduling," Operations Research, INFORMS, vol. 33(3), pages 548-561, June.
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