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Unary NP-hardness of single-machine scheduling to minimize the total tardiness with deadlines

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Listed:
  • Rubing Chen

    (Zhengzhou University)

  • Jinjiang Yuan

    (Zhengzhou University)

Abstract

We revisit the classical single-machine scheduling problem to minimize total tardiness with deadlines. The problem is binary NP-hard even without the deadline restrictions. It was reported early in Koulamas and Kyparisis (Eur J Oper Res 133:447–453, 2001) that the exact complexity (unary NP-hardness or pseudo-polynomial-time solvability) of the problem is still open. We show that this problem is unary NP-hard.

Suggested Citation

  • Rubing Chen & Jinjiang Yuan, 2019. "Unary NP-hardness of single-machine scheduling to minimize the total tardiness with deadlines," Journal of Scheduling, Springer, vol. 22(5), pages 595-601, October.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:5:d:10.1007_s10951-019-00615-9
    DOI: 10.1007/s10951-019-00615-9
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    References listed on IDEAS

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    1. Jianzhong Du & Joseph Y.-T. Leung, 1990. "Minimizing Total Tardiness on One Machine is NP-Hard," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 483-495, August.
    2. Koulamas, Christos & Kyparisis, George J., 2001. "Single machine scheduling with release times, deadlines and tardiness objectives," European Journal of Operational Research, Elsevier, vol. 133(2), pages 447-453, January.
    3. Hamilton Emmons, 1969. "One-Machine Sequencing to Minimize Certain Functions of Job Tardiness," Operations Research, INFORMS, vol. 17(4), pages 701-715, August.
    4. Jinjiang Yuan, 2017. "Unary NP-hardness of minimizing the number of tardy jobs with deadlines," Journal of Scheduling, Springer, vol. 20(2), pages 211-218, April.
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    Cited by:

    1. Christos Koulamas & George Steiner, 2021. "New results for scheduling to minimize tardiness on one machine with rejection and related problems," Journal of Scheduling, Springer, vol. 24(1), pages 27-34, February.

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