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A note on the generalized due dates scheduling problems

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  • C. Sriskandarajah

Abstract

We consider the problem of scheduling jobs on a single machine with generalized due dates. The due dates are given according to the position in which a job is completed, rather than the identity of that job. The computational complexity question of whether the total weighted tardiness problem can be solved in polynomial time or NP‐hard is posed as an open problem in [4]. We show that this problem is NP‐hard. We also establish NP‐hardness results for the scheduling problems with precedence constraints.

Suggested Citation

  • C. Sriskandarajah, 1990. "A note on the generalized due dates scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 587-597, August.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:4:p:587-597
    DOI: 10.1002/1520-6750(199008)37:43.0.CO;2-O
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    References listed on IDEAS

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    1. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "Complexity results for scheduling chains on a single machine," European Journal of Operational Research, Elsevier, vol. 4(4), pages 270-275, April.
    2. E. L. Lawler, 1973. "Optimal Sequencing of a Single Machine Subject to Precedence Constraints," Management Science, INFORMS, vol. 19(5), pages 544-546, January.
    3. K. R. Baker & E. L. Lawler & J. K. Lenstra & A. H. G. Rinnooy Kan, 1983. "Preemptive Scheduling of a Single Machine to Minimize Maximum Cost Subject to Release Dates and Precedence Constraints," Operations Research, INFORMS, vol. 31(2), pages 381-386, April.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Wang, Du-Juan & Yin, Yunqiang & Xu, Jianyou & Wu, Wen-Hsiang & Cheng, Shuenn-Ren & Wu, Chin-Chia, 2015. "Some due date determination scheduling problems with two agents on a single machine," International Journal of Production Economics, Elsevier, vol. 168(C), pages 81-90.
    6. Lin, B.M.T. & Liu, S.T., 2008. "Maximizing the reward in the relocation problem with generalized due dates," International Journal of Production Economics, Elsevier, vol. 115(1), pages 55-63, September.

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