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Complexity results for flow shop problems with synchronous movement

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  • Waldherr, Stefan
  • Knust, Sigrid

Abstract

In this paper we present complexity results for flow shop problems with synchronous movement which are a variant of a non-preemptive permutation flow shop. Jobs have to be moved from one machine to the next by an unpaced synchronous transportation system, which implies that the processing is organized in synchronized cycles. This means that in each cycle the current jobs start at the same time on the corresponding machines and after processing have to wait until the last job is finished. Afterwards, all jobs are moved to the next machine simultaneously. Besides the general situation we also investigate special cases involving machine dominance which means that the processing times of all jobs on a dominating machine are at least as large as the processing times of all jobs on the other machines. Especially, we study flow shops with synchronous movement for a small number of dominating machines (one or two) and different objective functions.

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  • Waldherr, Stefan & Knust, Sigrid, 2015. "Complexity results for flow shop problems with synchronous movement," European Journal of Operational Research, Elsevier, vol. 242(1), pages 34-44.
    • Handle: RePEc:eee:ejores:v:242:y:2015:i:1:p:34-44
    DOI: 10.1016/j.ejor.2014.09.053
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    References listed on IDEAS

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    1. Karabati, Selcuk & Sayin, Serpil, 2003. "Assembly line balancing in a mixed-model sequencing environment with synchronous transfers," European Journal of Operational Research, Elsevier, vol. 149(2), pages 417-429, September.
    2. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
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    4. J. Michael Moore, 1968. "An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs," Management Science, INFORMS, vol. 15(1), pages 102-109, September.
    5. Xiang, S. & Tang, G. & Cheng, T. C. E., 2000. "Solvable cases of permutation flowshop scheduling with dominating machines," International Journal of Production Economics, Elsevier, vol. 66(1), pages 53-57, June.
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    Cited by:

    1. S. S. Panwalkar & Christos Koulamas, 2020. "Three-stage ordered flow shops with either synchronous flow, blocking or no-idle machines," Journal of Scheduling, Springer, vol. 23(1), pages 145-154, February.
    2. Waldherr, Stefan & Knust, Sigrid, 2017. "Decomposition algorithms for synchronous flow shop problems with additional resources and setup times," European Journal of Operational Research, Elsevier, vol. 259(3), pages 847-863.
    3. Waldherr, Stefan & Knust, Sigrid & Briskorn, Dirk, 2017. "Synchronous flow shop problems: How much can we gain by leaving machines idle?," Omega, Elsevier, vol. 72(C), pages 15-24.
    4. C. Weiß & S. Waldherr & S. Knust & N. V. Shakhlevich, 2017. "Open Shop Scheduling with Synchronization," Journal of Scheduling, Springer, vol. 20(6), pages 557-581, December.
    5. S. S. Panwalkar & Christos Koulamas, 2019. "The evolution of schematic representations of flow shop scheduling problems," Journal of Scheduling, Springer, vol. 22(4), pages 379-391, August.
    6. Matthias Bultmann & Sigrid Knust & Stefan Waldherr, 2018. "Flow shop scheduling with flexible processing times," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 809-829, July.

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