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A multivariate complexity analysis of the material consumption scheduling problem

Author

Listed:
  • Matthias Bentert

    (Technische Universität Berlin)

  • Robert Bredereck

    (Technische Universität Berlin
    Humboldt-Universität zu Berlin
    TU Clausthal)

  • Péter Györgyi

    (Eötvös Loránd Research Network)

  • Andrzej Kaczmarczyk

    (Technische Universität Berlin
    AGH University)

  • Rolf Niedermeier

    (Technische Universität Berlin)

Abstract

The NP-hard problem Material Consumption Scheduling and related problems have been thoroughly studied since the 1980’s. Roughly speaking, the problem deals with scheduling jobs that consume non-renewable resources—each job has individual resource demands. The goal is to minimize the makespan. We focus on the single-machine case without preemption: from time to time, the resources of the machine are (partially) replenished, thus allowing for meeting a necessary precondition for processing further jobs. We initiate a systematic exploration of the parameterized computational complexity landscape of Material Consumption Scheduling, providing parameterized tractability as well as intractability results. Doing so, we mainly investigate how parameters related to the resource supplies influence the problem’s computational complexity. This leads to a deepened understanding of this fundamental scheduling problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jsched:v:26:y:2023:i:4:d:10.1007_s10951-022-00771-5
    DOI: 10.1007/s10951-022-00771-5
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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. Hermelin, Danny & Pinedo, Michael & Shabtay, Dvir & Talmon, Nimrod, 2019. "On the parameterized tractability of single machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 273(1), pages 67-73.
    3. Edmund Burke & Michael Pinedo, 2019. "Journal of scheduling (2019)," Journal of Scheduling, Springer, vol. 22(1), pages 1-2, February.
    4. Alexander Grigoriev & Martijn Holthuijsen & Joris van de Klundert, 2005. "Basic scheduling problems with raw material constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 527-535, September.
    5. Slowinski, Roman, 1984. "Preemptive scheduling of independent jobs on parallel machines subject to financial constraints," European Journal of Operational Research, Elsevier, vol. 15(3), pages 366-373, March.
    6. 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.
    7. Györgyi, Péter & Kis, Tamás, 2017. "Approximation schemes for parallel machine scheduling with non-renewable resources," European Journal of Operational Research, Elsevier, vol. 258(1), pages 113-123.
    8. Danny Hermelin & Dvir Shabtay & Nimrod Talmon, 2019. "On the parameterized tractability of the just-in-time flow-shop scheduling problem," Journal of Scheduling, Springer, vol. 22(6), pages 663-676, December.
    9. Péter Györgyi & Tamás Kis, 2015. "Approximability of scheduling problems with resource consuming jobs," Annals of Operations Research, Springer, vol. 235(1), pages 319-336, December.
    10. Dušan Knop & Martin Koutecký, 2018. "Scheduling meets n-fold integer programming," Journal of Scheduling, Springer, vol. 21(5), pages 493-503, October.
    11. Davari, Morteza & Ranjbar, Mohammad & De Causmaecker, Patrick & Leus, Roel, 2020. "Minimizing makespan on a single machine with release dates and inventory constraints," European Journal of Operational Research, Elsevier, vol. 286(1), pages 115-128.
    12. Ravi Kannan, 1987. "Minkowski's Convex Body Theorem and Integer Programming," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 415-440, August.
    13. Péter Györgyi & Tamás Kis, 2019. "Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints," Journal of Scheduling, Springer, vol. 22(6), pages 623-634, December.
    14. Matthias Bentert & René Bevern & Rolf Niedermeier, 2019. "Inductive $$k$$ k -independent graphs and c-colorable subgraphs in scheduling: a review," Journal of Scheduling, Springer, vol. 22(1), pages 3-20, February.
    15. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    16. Herr, Oliver & Goel, Asvin, 2016. "Minimising total tardiness for a single machine scheduling problem with family setups and resource constraints," European Journal of Operational Research, Elsevier, vol. 248(1), pages 123-135.
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