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Single machine scheduling with step-learning

Author

Listed:
  • Matan Atsmony

    (The Hebrew University)

  • Baruch Mor

    (Ariel University)

  • Gur Mosheiov

    (The Hebrew University
    Lev Academic Center)

Abstract

In this paper, we study scheduling with step-learning, i.e., a setting where the processing times of the jobs started after their job-dependent learning-dates are reduced. The goal is to minimize makespan on a single machine. We focus first on the case that idle times between consecutive jobs are not allowed. We prove that the problem is NP-hard, implying that no polynomial-time solution exists and, consequently, propose a pseudo-polynomial time dynamic programming algorithm. An extensive numerical study is provided to examine the running time of the algorithm with different learning-dates and job processing time ranges. The special case of a common learning-date for all the jobs is also studied, and a (more efficient) pseudo-polynomial dynamic programming is introduced and tested numerically. In the last part of the paper, the more complicated setting in which idle times are allowed is studied. An appropriate dynamic programming is introduced and tested as well.

Suggested Citation

  • Matan Atsmony & Baruch Mor & Gur Mosheiov, 2024. "Single machine scheduling with step-learning," Journal of Scheduling, Springer, vol. 27(3), pages 227-237, June.
    • Handle: RePEc:spr:jsched:v:27:y:2024:i:3:d:10.1007_s10951-022-00763-5
    DOI: 10.1007/s10951-022-00763-5
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    References listed on IDEAS

    as
    1. Baruch Mor & Gur Mosheiov & Dana Shapira, 2020. "Flowshop scheduling with learning effect and job rejection," Journal of Scheduling, Springer, vol. 23(6), pages 631-641, December.
    2. Chin-Chia Wu & Ameni Azzouz & I-Hong Chung & Win-Chin Lin & Lamjed Ben Said, 2019. "A two-stage three-machine assembly scheduling problem with deterioration effect," International Journal of Production Research, Taylor & Francis Journals, vol. 57(21), pages 6634-6647, November.
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    14. Xinyu Sun & Xin-Na Geng & Ji-Bo Wang & Feng Liu, 2019. "Convex resource allocation scheduling in the no-wait flowshop with common flow allowance and learning effect," International Journal of Production Research, Taylor & Francis Journals, vol. 57(6), pages 1873-1891, March.
    15. S. M. Mousavi & I. Mahdavi & J. Rezaeian & M. Zandieh, 2018. "An efficient bi-objective algorithm to solve re-entrant hybrid flow shop scheduling with learning effect and setup times," Operational Research, Springer, vol. 18(1), pages 123-158, April.
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