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A note on the single machine scheduling to minimize the number of tardy jobs with deadlines

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  • He, Cheng
  • Lin, Yixun
  • Yuan, Jinjiang

Abstract

It is known that the single machine scheduling problem of minimizing the number of tardy jobs is polynomially solvable. However, it becomes NP-hard if each job has a deadline. Recently, Huo et al. solved some special cases by a backwards scheduling approach. In this note we present a dual approach--forwards greedy algorithms which may have better running time. For example, in the case that the due dates, deadlines, and processing times are agreeable, the running time of the backwards scheduling algorithm is O(n2), while that of the forwards algorithm is O(nlogn).

Suggested Citation

  • He, Cheng & Lin, Yixun & Yuan, Jinjiang, 2010. "A note on the single machine scheduling to minimize the number of tardy jobs with deadlines," European Journal of Operational Research, Elsevier, vol. 201(3), pages 966-970, March.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:3:p:966-970
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    References listed on IDEAS

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    1. Burkard, Rainer E., 2007. "Monge properties, discrete convexity and applications," European Journal of Operational Research, Elsevier, vol. 176(1), pages 1-14, January.
    2. Lin, Yixun & Wang, Xiumei, 2007. "Necessary and sufficient conditions of optimality for some classical scheduling problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 809-818, January.
    3. 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.
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    Cited by:

    1. Cheng He & Hao Lin, 2016. "Hierarchical optimization with double due dates on an unbounded parallel-batching machine to minimize maximum lateness," 4OR, Springer, vol. 14(2), pages 153-164, June.
    2. 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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