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A general scheme for solving a large set of scheduling problems with rejection in FPT time

Author

Listed:
  • Danny Hermelin

    (Ben-Gurion University of the Negev)

  • Dvir Shabtay

    (Ben-Gurion University of the Negev)

  • Chen Zelig

    (Ben-Gurion University of the Negev)

  • Michael Pinedo

    (New York University)

Abstract

Mnich and Wiese (Math Program 154:533–562, 2015) proved that the $$\mathcal {NP}$$ NP -hard single-machine scheduling problem with rejection and the total weighted completion time plus total rejection cost as objective is fixed parameter tractable with respect to the number of different processing times and weights in the instance. This result is obtained by reducing the problem to an integer convex programming problem where the number of variables depends solely on the parameter (number of different processing times and weights). We show that this method can be incorporated into a more general scheme for solving a large set of scheduling problems with rejection which share common properties. These problems include various different machine environments, namely single machine, identical machines in parallel, and flow-shops.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jsched:v:25:y:2022:i:2:d:10.1007_s10951-022-00731-z
    DOI: 10.1007/s10951-022-00731-z
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    References listed on IDEAS

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    1. 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.
    2. Edmund Burke & Michael Pinedo, 2019. "Journal of scheduling (2019)," Journal of Scheduling, Springer, vol. 22(1), pages 1-2, February.
    3. 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.
    4. S. S. Panwalkar & M. L. Smith & A. Seidmann, 1982. "Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem," Operations Research, INFORMS, vol. 30(2), pages 391-399, April.
    5. 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.
    6. Dušan Knop & Martin Koutecký, 2018. "Scheduling meets n-fold integer programming," Journal of Scheduling, Springer, vol. 21(5), pages 493-503, October.
    7. de Weerdt, Mathijs & Baart, Robert & He, Lei, 2021. "Single-machine scheduling with release times, deadlines, setup times, and rejection," European Journal of Operational Research, Elsevier, vol. 291(2), pages 629-639.
    8. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    9. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    10. 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.
    11. Dvir Shabtay & Daniel Oron, 2016. "Proportionate flow-shop scheduling with rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(5), pages 752-769, May.
    12. Dvir Shabtay & Nufar Gaspar & Liron Yedidsion, 2012. "A bicriteria approach to scheduling a single machine with job rejection and positional penalties," Journal of Combinatorial Optimization, Springer, vol. 23(4), pages 395-424, May.
    13. 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.
    14. Liqi Zhang & Lingfa Lu & Shisheng Li, 2016. "New results on two-machine flow-shop scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1493-1504, May.
    15. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    16. Uttarayan Bagchi, 1989. "Simultaneous Minimization of Mean and Variation of Flow Time and Waiting Time in Single Machine Systems," Operations Research, INFORMS, vol. 37(1), pages 118-125, February.
    17. Choi, Byung-Cheon & Chung, Jibok, 2011. "Two-machine flow shop scheduling problem with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(1), pages 66-72, August.
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