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Synchronous flow shop scheduling with pliable jobs

Author

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  • Bultmann, Matthias
  • Knust, Sigrid
  • Waldherr, Stefan

Abstract

In this paper, we consider synchronous flow shop scheduling problems where the processing times of the operations are not fixed in advance. Instead, for each job a total processing time is given which can be distributed freely among the machines, respecting some lower and/or upper bounds on the processing times of the operations. We prove that even if no additional bounds are given, minimizing the makespan is NP-hard already for two machines. On the other hand, we can draw on a more general result to show that for a fixed job permutation optimal corresponding processing times can be determined via a linear program in polynomial time. However, for larger problem instances, this leads to large run times. As a more efficient alternative, we propose direct combinatorial algorithms to determine the processing times. We embed these algorithms in a two-stage approach using the set of all job permutations as search space and calculating corresponding processing times in a second step. Computational results are presented for randomly generated data with varying degrees of allowed flexibility.

Suggested Citation

  • Bultmann, Matthias & Knust, Sigrid & Waldherr, Stefan, 2018. "Synchronous flow shop scheduling with pliable jobs," European Journal of Operational Research, Elsevier, vol. 270(3), pages 943-956.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:3:p:943-956
    DOI: 10.1016/j.ejor.2018.04.024
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    Cited by:

    1. Rossit, Daniel A. & Vásquez, Óscar C. & Tohmé, Fernando & Frutos, Mariano & Safe, Martín D., 2021. "A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems," European Journal of Operational Research, Elsevier, vol. 289(3), pages 841-854.
    2. S. Knust & N. V. Shakhlevich & S. Waldherr & C. Weiß, 2019. "Shop scheduling problems with pliable jobs," Journal of Scheduling, Springer, vol. 22(6), pages 635-661, December.

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