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Unary NP-hardness of minimizing the number of tardy jobs with deadlines

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  • Jinjiang Yuan

    (Zhengzhou University)

Abstract

For single machine scheduling to minimize the number of tardy jobs with deadlines, Lawler showed in 1983 that the problem is binary NP-hard. But the exact complexity (unary NP-hard or pseudo-polynomial-time solvability) is a long- standing open problem. We show in this paper that the problem is unary NP-hard. Our research also implies that the scheduling problem for finding an optimal schedule to minimize the number of tardy jobs that also satisfies the restriction of deadlines is unary NP-hard. As a consequence, some multi-agent scheduling problems related to minimizing the number of tardy jobs and maximum lateness are unary NP-hard.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jsched:v:20:y:2017:i:2:d:10.1007_s10951-016-0479-8
    DOI: 10.1007/s10951-016-0479-8
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    References listed on IDEAS

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    1. A. M. A. Hariri & C. N. Potts, 1994. "Single Machine Scheduling with Deadlines to Minimize the Weighted Number of Tardy Jobs," Management Science, INFORMS, vol. 40(12), pages 1712-1719, December.
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    3. J. Michael Moore, 1968. "An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs," Management Science, INFORMS, vol. 15(1), pages 102-109, September.
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    5. Huo, Yumei & Leung, Joseph Y.-T. & Zhao, Hairong, 2007. "Bi-criteria scheduling problems: Number of tardy jobs and maximum weighted tardiness," European Journal of Operational Research, Elsevier, vol. 177(1), pages 116-134, February.
    6. Lu, L.F. & Yuan, J.J., 2007. "The single machine batching problem with identical family setup times to minimize maximum lateness is strongly NP-hard," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1302-1309, March.
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    Cited by:

    1. Rubing Chen & Jinjiang Yuan & C.T. Ng & T.C.E. Cheng, 2019. "Single‐machine scheduling with deadlines to minimize the total weighted late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 582-595, October.
    2. Rubing Chen & Jinjiang Yuan, 2020. "Single-machine scheduling of proportional-linearly deteriorating jobs with positional due indices," 4OR, Springer, vol. 18(2), pages 177-196, June.
    3. Yuan Gao & Jinjiang Yuan & C. T. Ng & T. C. E. Cheng, 2022. "Pareto-scheduling with family jobs or ND-agent on a parallel-batch machine to minimize the makespan and maximum cost," 4OR, Springer, vol. 20(2), pages 273-287, June.
    4. Shuen Guo & Hao Lang & Hanxiang Zhang, 2023. "Scheduling of Jobs with Multiple Weights on a Single Machine for Minimizing the Total Weighted Number of Tardy Jobs," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
    5. 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.
    6. Jin Qian & Yu Zhan, 2021. "The Due Date Assignment Scheduling Problem with Delivery Times and Truncated Sum-of-Processing-Times-Based Learning Effect," Mathematics, MDPI, vol. 9(23), pages 1-14, November.
    7. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.

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