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Exponential time algorithms for just-in-time scheduling problems with common due date and symmetric weights

Author

Listed:
  • Vincent T’kindt

    (University of Tours)

  • Lei Shang

    (University of Tours)

  • Federico Della Croce

    (DIGEP
    CNR, IEIIT)

Abstract

This paper focuses on the solution, by exact exponential-time algorithms, of just-in-time scheduling problems when jobs have symmetric earliness/tardiness weights and share a non restrictive common due date. For the single machine problem, a Sort & Search algorithm is proposed with worst-case time and space complexities in $$\mathcal {O}^*(1.4143^n)$$O∗(1.4143n). This algorithm relies on an original modeling of the problem. For the case of parallel machines, an algorithm integrating a dynamic programming algorithm across subsets and machines and the above Sort & Search algorithm is proposed with worst-case time and space complexities in $$\mathcal {O}^*(3^n)$$O∗(3n). To the best of our knowledge, these are the first worst-case complexity results obtained for non regular criteria in scheduling.

Suggested Citation

  • Vincent T’kindt & Lei Shang & Federico Della Croce, 2020. "Exponential time algorithms for just-in-time scheduling problems with common due date and symmetric weights," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 764-775, April.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:3:d:10.1007_s10878-019-00512-z
    DOI: 10.1007/s10878-019-00512-z
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    References listed on IDEAS

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    1. John J. Kanet, 1981. "Minimizing the average deviation of job completion times about a common due date," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 643-651, December.
    2. Nicholas G. Hall & Marc E. Posner, 1991. "Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 836-846, October.
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    Cited by:

    1. Lei Pan & Xinyu Sun & Ji-Bo Wang & Li-Han Zhang & Dan-Yang Lv, 2023. "Due date assignment single-machine scheduling with delivery times, position-dependent weights and deteriorating jobs," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-16, May.
    2. Vincent T’kindt & Federico Della Croce & Mathieu Liedloff, 2022. "Moderate exponential-time algorithms for scheduling problems," 4OR, Springer, vol. 20(4), pages 533-566, December.
    3. Klaus Heeger & Danny Hermelin & George B. Mertzios & Hendrik Molter & Rolf Niedermeier & Dvir Shabtay, 2023. "Equitable scheduling on a single machine," Journal of Scheduling, Springer, vol. 26(2), pages 209-225, April.

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