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The permutation flow shop problem with sum‐of‐completion times performance criterion

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  • Selcuk Karabati
  • Panagiotis Kouvelis

Abstract

In this article we address the non‐preemptive flow shop scheduling problem for minimization of the sum of the completion times. We present a new modeling framework and give a novel game‐theoretic interpretation of the scheduling problem. A lower‐bound generation scheme is developed by solving appropriately defined linear assignment problems. This scheme can also be used as a heuristic approach for the solution of the problem with satisfactory results. Its main use, however, is as a bounding scheme within a branch‐and‐bound procedure. Our branch‐and‐bound procedure improves significantly upon the best available enu‐merative procedures in the current literature. Extensive computational results are used to qualify the above statements. © 1993 John Wiley & Sons, Inc.

Suggested Citation

  • Selcuk Karabati & Panagiotis Kouvelis, 1993. "The permutation flow shop problem with sum‐of‐completion times performance criterion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(6), pages 843-862, October.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:6:p:843-862
    DOI: 10.1002/1520-6750(199310)40:63.0.CO;2-A
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    References listed on IDEAS

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    1. Wlodzimierz Szwarc, 1978. "Permutation flow‐shop theory revisited," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 25(3), pages 557-570, September.
    2. Edward Ignall & Linus Schrage, 1965. "Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems," Operations Research, INFORMS, vol. 13(3), pages 400-412, June.
    3. B. J. Lageweg & J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "A General Bounding Scheme for the Permutation Flow-Shop Problem," Operations Research, INFORMS, vol. 26(1), pages 53-67, February.
    4. Ahmadi, Reza H. & Bagchi, Uttarayan, 1990. "Improved lower bounds for minimizing the sum of completion times of n jobs over m machines in a flow shop," European Journal of Operational Research, Elsevier, vol. 44(3), pages 331-336, February.
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    Cited by:

    1. Allahverdi, Ali & Aldowaisan, Tariq, 2002. "New heuristics to minimize total completion time in m-machine flowshops," International Journal of Production Economics, Elsevier, vol. 77(1), pages 71-83, May.

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