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Scheduling problems on parallel machines with machine-dependent generalized due-dates

Author

Listed:
  • Baruch Mor

    (Ariel University)

  • Gur Mosheiov

    (The Hebrew University
    Lev Academic Center)

  • Dvir Shabtay

    (Ben-Gurion University of the Negev)

Abstract

In scheduling problems with generalized due-dates, the due-dates are position-dependent (and not job-dependent as in classical scheduling). In this paper, we study scheduling problems on parallel machines, and the underlying assumption is that the generalized due-dates are machine-dependent. The following scheduling measures are considered: total tardiness, maximum tardiness, number of tardy jobs, and total late work. We show that all the problems are NP-hard even if all generalized due-dates are identical. We complement this hardness result by showing that all problems are solvable in pseudo-polynomial time and that minimizing total late work is fixed parametrized tractable with respect to the number of different generalized due-dates and processing times in the instance. We also tested the pseudo-polynomial time algorithms, showing they can easily solve instances containing up to 200 jobs.

Suggested Citation

  • Baruch Mor & Gur Mosheiov & Dvir Shabtay, 2025. "Scheduling problems on parallel machines with machine-dependent generalized due-dates," Annals of Operations Research, Springer, vol. 347(3), pages 1455-1471, April.
    • Handle: RePEc:spr:annopr:v:347:y:2025:i:3:d:10.1007_s10479-025-06468-0
    DOI: 10.1007/s10479-025-06468-0
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    References listed on IDEAS

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    1. Myoung-Ju Park & Byung-Cheon Choi & Yunhong Min & Kyung Min Kim, 2020. "Two-Machine Ordered Flow Shop Scheduling with Generalized Due Dates," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-16, January.
    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. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    4. Hall, Nicholas G. & Sethi, Suresh P. & Sriskandarajah, Chelliah, 1991. "On the complexity of generalized due date scheduling problems," European Journal of Operational Research, Elsevier, vol. 51(1), pages 100-109, March.
    5. Baruch Mor & Gur Mosheiov & Dvir Shabtay, 2021. "Minimizing the total tardiness and job rejection cost in a proportionate flow shop with generalized due dates," Journal of Scheduling, Springer, vol. 24(6), pages 553-567, December.
    6. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    7. Gur Mosheiov & Daniel Oron & Dvir Shabtay, 2022. "On the tractability of hard scheduling problems with generalized due-dates with respect to the number of different due-dates," Journal of Scheduling, Springer, vol. 25(5), pages 577-587, October.
    8. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
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