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Optimal Sequencing by Modular Decomposition: Polynomial Algorithms

Author

Listed:
  • Jeffrey B. Sidney

    (University of Ottawa, Ontario, Canada)

  • George Steiner

    (McMaster University, Hamilton, Ontario, Canada)

Abstract

We show that the combination of dynamic programming with partial-order decomposition algorithms enables us to solve sequencing problems in polynomial time for substantially larger classes of precedence constraints than previously realized. The algorithm's efficiency depends on the maximum number of jobs that are not related by the precedence constraints in certain subsets of the jobs. We also demonstrate how to modify this general algorithm lo take advantage of special problem characteristics.

Suggested Citation

  • Jeffrey B. Sidney & George Steiner, 1986. "Optimal Sequencing by Modular Decomposition: Polynomial Algorithms," Operations Research, INFORMS, vol. 34(4), pages 606-612, August.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:4:p:606-612
    DOI: 10.1287/opre.34.4.606
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    Cited by:

    1. Erel, Erdal & Gokcen, Hadi, 1999. "Shortest-route formulation of mixed-model assembly line balancing problem," European Journal of Operational Research, Elsevier, vol. 116(1), pages 194-204, July.
    2. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    3. Ecker, Klaus H., 1999. "Scheduling of resource tasks," European Journal of Operational Research, Elsevier, vol. 115(2), pages 314-327, June.
    4. De, Prabuddha & James Dunne, E. & Ghosh, Jay B. & Wells, Charles E., 1995. "The discrete time-cost tradeoff problem revisited," European Journal of Operational Research, Elsevier, vol. 81(2), pages 225-238, March.
    5. Demeulemeester, Erik L. & Herroelen, Willy S. & Elmaghraby, Salah E., 1996. "Optimal procedures for the discrete time/cost trade-off problem in project networks," European Journal of Operational Research, Elsevier, vol. 88(1), pages 50-68, January.

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