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Scheduling two agents on a single machine: A parameterized analysis of NP-hard problems

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  • Hermelin, Danny
  • Kubitza, Judith-Madeleine
  • Shabtay, Dvir
  • Talmon, Nimrod
  • Woeginger, Gerhard J.

Abstract

Scheduling theory is a well-established area in combinatorial optimization, whereas the much younger area of parameterized complexity has only recently gained the attention of the scheduling community. Our aim is to bring these two fields closer together by studying the parameterized complexity of a class of two-agent single-machine scheduling problems. Our analysis focuses on the case where the number of jobs belonging to the second agent is considerably smaller than the number of jobs belonging to the first agent and thus can be considered as a fixed parameter k. We study a variety of combinations of scheduling criteria for the two agents and for each such combination we determine its parameterized complexity with respect to the parameter k. The scheduling criteria that we analyze include the total weighted completion time, the total weighted number of tardy jobs, and the total weighted number of just-in-time jobs. Our analysis determines the border between tractable and intractable variants of these problems.

Suggested Citation

  • Hermelin, Danny & Kubitza, Judith-Madeleine & Shabtay, Dvir & Talmon, Nimrod & Woeginger, Gerhard J., 2019. "Scheduling two agents on a single machine: A parameterized analysis of NP-hard problems," Omega, Elsevier, vol. 83(C), pages 275-286.
    • Handle: RePEc:eee:jomega:v:83:y:2019:i:c:p:275-286
    DOI: 10.1016/j.omega.2018.08.001
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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. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    3. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    4. Matthias Bentert & Robert Bredereck & Péter Györgyi & Andrzej Kaczmarczyk & Rolf Niedermeier, 2023. "A multivariate complexity analysis of the material consumption scheduling problem," Journal of Scheduling, Springer, vol. 26(4), pages 369-382, August.
    5. Oron, Daniel, 2021. "Two-agent scheduling problems under rejection budget constraints," Omega, Elsevier, vol. 102(C).
    6. Shi-Sheng Li & Ren-Xia Chen, 2023. "Competitive two-agent scheduling with release dates and preemption on a single machine," Journal of Scheduling, Springer, vol. 26(3), pages 227-249, June.
    7. 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.
    8. Ajay Singh, 2022. "Sustainable Waste Management Through Systems Engineering Models and Remote Sensing Approaches," Circular Economy and Sustainability, Springer, vol. 2(3), pages 1105-1126, September.

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