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Finding an Optimal Sequence by Dynamic Programming: An Extension to Precedence-Related Tasks

Author

Listed:
  • Kenneth R. Baker

    (Duke University, Durham, North Carolina)

  • Linus E. Schrage

    (University of Chicago, Chicago, Illinois)

Abstract

We discuss the dynamic programming approach to finding an optimal sequence of a set of tasks when the tasks are related by precedence restrictions. We describe how to use this approach in problems where no explicit precedence relations exist. Computer implementation considerations played an important role in its development. Computational results indicate that, when the curse of dimensionality can be dispelled, dynamic programming can be a useful procedure for large sequencing problems.

Suggested Citation

  • Kenneth R. Baker & Linus E. Schrage, 1978. "Finding an Optimal Sequence by Dynamic Programming: An Extension to Precedence-Related Tasks," Operations Research, INFORMS, vol. 26(1), pages 111-120, February.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:1:p:111-120
    DOI: 10.1287/opre.26.1.111
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    Cited by:

    1. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    2. John J. Kanet, 2014. "One-Machine Sequencing to Minimize Total Tardiness: A Fourth Theorem for Emmons," Operations Research, INFORMS, vol. 62(2), pages 345-347, April.
    3. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    4. Tanaka, Shunji & Sato, Shun, 2013. "An exact algorithm for the precedence-constrained single-machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 229(2), pages 345-352.
    5. Chengbin Chu, 1992. "A branch‐and‐bound algorithm to minimize total tardiness with different release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 265-283, March.
    6. Holsenback, J. E. & Russell, R. M. & Markland, R. E. & Philipoom, P. R., 1999. "An improved heuristic for the single-machine, weighted-tardiness problem," Omega, Elsevier, vol. 27(4), pages 485-495, August.

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