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An O(n2) algorithm for time-bound adjustments for the cumulative scheduling problem

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  • Carlier, J.
  • Pinson, E.
  • Sahli, A.
  • Jouglet, A.

Abstract

Energetic Reasoning (ER) is one of the most powerful methods for efficient cumulative scheduling. It computes destructive bounds and adjustments of task time intervals. ER is not commonly used in practice due to its time complexity, and its efficiency is highly dependent on the tightness of the time intervals. Here, we present a new algorithm with a better complexity than previous algorithms for speeding up time bound adjustments. More precisely, we show how to reduce the complexity of heads and tails adjustments from O(n2log n) to O(n2), which is an important theoretical advance.

Suggested Citation

  • Carlier, J. & Pinson, E. & Sahli, A. & Jouglet, A., 2020. "An O(n2) algorithm for time-bound adjustments for the cumulative scheduling problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 468-476.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:2:p:468-476
    DOI: 10.1016/j.ejor.2020.03.079
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    References listed on IDEAS

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    1. Carlier, Jacques, 1982. "The one-machine sequencing problem," European Journal of Operational Research, Elsevier, vol. 11(1), pages 42-47, September.
    2. Brucker, Peter & Knust, Sigrid, 2000. "A linear programming and constraint propagation-based lower bound for the RCPSP," European Journal of Operational Research, Elsevier, vol. 127(2), pages 355-362, December.
    3. Carlier, Jacques, 1987. "Scheduling jobs with release dates and tails on identical machines to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 29(3), pages 298-306, June.
    4. Ph. Baptiste & C. Le Pape & W. Nuijten, 1999. "Satisfiability tests and time‐bound adjustmentsfor cumulative scheduling problems," Annals of Operations Research, Springer, vol. 92(0), pages 305-333, January.
    5. Carlier, J. & Pinson, E., 1994. "Adjustment of heads and tails for the job-shop problem," European Journal of Operational Research, Elsevier, vol. 78(2), pages 146-161, October.
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