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A note: maximizing the weighted number of Just-in-Time jobs for a given job sequence

Author

Listed:
  • Enrique Gerstl

    (The Hebrew University)

  • Gur Mosheiov

    (The Hebrew University
    Jerusalem College of Technology, Lev Academic Center)

Abstract

We study a single machine scheduling problem to maximize the weighted number of Just-in-Time jobs, i.e., jobs which are completed exactly at their due-dates. We focus on the case that the job sequence is given. A pseudo-polynomial solution algorithm has been published for this problem, and we introduce here an efficient polynomial time dynamic programming algorithm. The new algorithm is tested numerically, and the results are compared to those obtained by the old algorithm. While the running times required by both algorithms for solving large instances are extremely small, it appears that the new algorithm performs better in two aspects: (1) The resulting running time is independent of the actual density of the due-dates, (2) The required memory is significantly reduced. An extension to a two-machine flowshop is provided, and this case is shown to remain polynomially solvable.

Suggested Citation

  • Enrique Gerstl & Gur Mosheiov, 2023. "A note: maximizing the weighted number of Just-in-Time jobs for a given job sequence," Journal of Scheduling, Springer, vol. 26(4), pages 403-409, August.
    • Handle: RePEc:spr:jsched:v:26:y:2023:i:4:d:10.1007_s10951-022-00772-4
    DOI: 10.1007/s10951-022-00772-4
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    References listed on IDEAS

    as
    1. Yunqiang Yin & T. C. E. Cheng & Du-Juan Wang & Chin-Chia Wu, 2017. "Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs," Journal of Scheduling, Springer, vol. 20(4), pages 313-335, August.
    2. Enrique Gerstl & Gur Mosheiov, 2020. "Single machine scheduling to maximize the number of on-time jobs with generalized due-dates," Journal of Scheduling, Springer, vol. 23(3), pages 289-299, June.
    3. Yin, Yunqiang & Cheng, Shuenn-Ren & Cheng, T.C.E. & Wang, Du-Juan & Wu, Chin-Chia, 2016. "Just-in-time scheduling with two competing agents on unrelated parallel machines," Omega, Elsevier, vol. 63(C), pages 41-47.
    4. Shabtay, Dvir, 2012. "The just-in-time scheduling problem in a flow-shop scheduling system," European Journal of Operational Research, Elsevier, vol. 216(3), pages 521-532.
    5. Y.M. Shafransky & V.A. Strusevich, 1998. "The open shop scheduling problem with a given sequence of jobs on one machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(7), pages 705-731, October.
    6. Shabtay, Dvir & Bensoussan, Yaron & Kaspi, Moshe, 2012. "A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 67-74.
    Full references (including those not matched with items on IDEAS)

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