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New algorithms for minimizing the weighted number of tardy jobs on a single machine

Author

Listed:
  • Danny Hermelin

    (Ben-Gurion University)

  • Shlomo Karhi

    (Bar-Ilan University)

  • Michael Pinedo

    (New York University)

  • Dvir Shabtay

    (Ben-Gurion University)

Abstract

In this paper we study the classical single machine scheduling problem where the objective is to minimize the weighted number of tardy jobs. Our analysis focuses on the case where one or more of three natural parameters is either constant or is taken as a parameter in the sense of parameterized complexity. These three parameters are the number of different due dates, processing times, and weights in our set of input jobs. We show that the problem belongs to the class of fixed parameter tractable (FPT) problems when combining any two of these three parameters. We also show that the problem is polynomial-time solvable when either one of the latter two parameters are constant, complementing Karp’s result who showed that the problem is NP-hard already for a single due date.

Suggested Citation

  • Danny Hermelin & Shlomo Karhi & Michael Pinedo & Dvir Shabtay, 2021. "New algorithms for minimizing the weighted number of tardy jobs on a single machine," Annals of Operations Research, Springer, vol. 298(1), pages 271-287, March.
    • Handle: RePEc:spr:annopr:v:298:y:2021:i:1:d:10.1007_s10479-018-2852-9
    DOI: 10.1007/s10479-018-2852-9
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    References listed on IDEAS

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    1. René Bevern & Rolf Niedermeier & Ondřej Suchý, 2017. "A parameterized complexity view on non-preemptively scheduling interval-constrained jobs: few machines, small looseness, and small slack," Journal of Scheduling, Springer, vol. 20(3), pages 255-265, June.
    2. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    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.
    4. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    5. Dušan Knop & Martin Koutecký, 2018. "Scheduling meets n-fold integer programming," Journal of Scheduling, Springer, vol. 21(5), pages 493-503, October.
    6. M'Hallah, Rym & Bulfin, R. L., 2003. "Minimizing the weighted number of tardy jobs on a single machine," European Journal of Operational Research, Elsevier, vol. 145(1), pages 45-56, February.
    7. Renhua Li & Leonie U Hempel & Tingbo Jiang, 2015. "A Non-Parametric Peak Calling Algorithm for DamID-Seq," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-12, March.
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    Citations

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    Cited by:

    1. Danny Hermelin & Dvir Shabtay & Chen Zelig & Michael Pinedo, 2022. "A general scheme for solving a large set of scheduling problems with rejection in FPT time," Journal of Scheduling, Springer, vol. 25(2), pages 229-255, April.
    2. 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.
    3. Chen, Ke & Cheng, T.C.E. & Huang, Hailiang & Ji, Min & Yao, Danli, 2023. "Single-machine scheduling with autonomous and induced learning to minimize total weighted number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 309(1), pages 24-34.
    4. Vincent T’kindt & Federico Della Croce & Mathieu Liedloff, 2022. "Moderate exponential-time algorithms for scheduling problems," 4OR, Springer, vol. 20(4), pages 533-566, December.
    5. Dvir Shabtay, 2023. "A new perspective on single-machine scheduling problems with late work related criteria," Annals of Operations Research, Springer, vol. 322(2), pages 947-966, March.

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