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A three-machine permutation flow-shop problem with minimum makespan on the second machine

Author

Listed:
  • S Yanai

    (Kobe University of Commerce)

  • T Fujie

    (University of Hyogo)

Abstract

In this paper, we consider a three-machine permutation flow-shop scheduling problem where the criterion is to minimize the total completion time without idle times subject to the minimum makespan on the second machine. This problem is NP-hard while each of the objective functions alone can be optimized in polynomial time. We develop a branch-and-bound algorithm with effective branching rules and dominance properties which help to reduce the search space. By our computational experiments, the branch-and-bound algorithm is comparable to a recent mixed integer programming solver and, for some kinds of problem instances, the branch-and-bound algorithm outperforms the solver. On the other hand, the computational result would indicate that the hierarchical scheduling problems are essentially hard in both theoretical and computational points of view.

Suggested Citation

  • S Yanai & T Fujie, 2006. "A three-machine permutation flow-shop problem with minimum makespan on the second machine," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 460-468, April.
    • Handle: RePEc:pal:jorsoc:v:57:y:2006:i:4:d:10.1057_palgrave.jors.2602014
    DOI: 10.1057/palgrave.jors.2602014
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    References listed on IDEAS

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    1. Jinliang Cheng & Hiroshi Kise & Hironori Matsumoto, 1997. "A branch-and-bound algorithm with fuzzy inference for a permutation flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 96(3), pages 578-590, February.
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    7. Potts, C. N., 1980. "An adaptive branching rule for the permutation flow-shop problem," European Journal of Operational Research, Elsevier, vol. 5(1), pages 19-25, July.
    8. Gupta, Jatinder N. D. & Neppalli, Venkata R. & Werner, Frank, 2001. "Minimizing total flow time in a two-machine flowshop problem with minimum makespan," International Journal of Production Economics, Elsevier, vol. 69(3), pages 323-338, February.
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    10. J M Framinan & J N D Gupta & R Leisten, 2004. "A review and classification of heuristics for permutation flow-shop scheduling with makespan objective," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1243-1255, December.
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