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On the parameterized tractability of the just-in-time flow-shop scheduling problem

Author

Listed:
  • Danny Hermelin

    (Ben-Gurion University of the Negev)

  • Dvir Shabtay

    (Ben-Gurion University of the Negev)

  • Nimrod Talmon

    (Ben-Gurion University of the Negev)

Abstract

We study the parameterized complexity of a set of flow-shop scheduling problems in which the objective is to maximize the weighted number of just-in-time jobs. Our analysis focuses on the case where the number of due dates is considerably smaller than the number of jobs and thus can be considered as a parameter. We prove that the two-machine problem is W[1]-hard with respect to this parameter, even if all processing times on the second machine are of unit length, while the problem is in XP when parameterized by the number of machines combined with the number of different due dates. We then move on to study the tractability of the problem when combining the number of different due dates with either the number of different weights or the number of different processing times on the first machine. We prove that in both cases the problem is fixed-parameter tractable for the two-machine case and is W[1]-hard for three or more machines.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:6:d:10.1007_s10951-019-00617-7
    DOI: 10.1007/s10951-019-00617-7
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    References listed on IDEAS

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    1. White, Richard E. & Prybutok, Victor, 2001. "The relationship between JIT practices and type of production system," Omega, Elsevier, vol. 29(2), pages 113-124, April.
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    3. Kovalyov, Mikhail Y. & Ng, C.T. & Cheng, T.C. Edwin, 2007. "Fixed interval scheduling: Models, applications, computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 178(2), pages 331-342, April.
    4. Shabtay, Dvir, 2012. "The just-in-time scheduling problem in a flow-shop scheduling system," European Journal of Operational Research, Elsevier, vol. 216(3), pages 521-532.
    5. Dvir Shabtay & George Steiner, 2012. "Scheduling to Maximize the Number of Just-in-Time Jobs: A Survey," Springer Optimization and Its Applications, in: Roger Z. Ríos-Mercado & Yasmín A. Ríos-Solís (ed.), Just-in-Time Systems, chapter 0, pages 3-20, Springer.
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    Cited by:

    1. Shabtay, Dvir & Gilenson, Miri, 2023. "A state-of-the-art survey on multi-scenario scheduling," European Journal of Operational Research, Elsevier, vol. 310(1), pages 3-23.
    2. 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.
    3. Klaus Heeger & Danny Hermelin & George B. Mertzios & Hendrik Molter & Rolf Niedermeier & Dvir Shabtay, 2023. "Equitable scheduling on a single machine," Journal of Scheduling, Springer, vol. 26(2), pages 209-225, April.
    4. 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.
    5. 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.

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