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Open Shop Scheduling with Synchronization

Author

Listed:
  • C. Weiß

    (University of Leeds)

  • S. Waldherr

    (University of Osnabrück)

  • S. Knust

    (University of Osnabrück)

  • N. V. Shakhlevich

    (University of Leeds)

Abstract

In this paper, we study open shop scheduling problems with synchronization. This model has the same features as the classical open shop model, where each of the n jobs has to be processed by each of the m machines in an arbitrary order. Unlike the classical model, jobs are processed in synchronous cycles, which means that the m operations of the same cycle start at the same time. Within one cycle, machines which process operations with smaller processing times have to wait until the longest operation of the cycle is finished before the next cycle can start. Thus, the length of a cycle is equal to the maximum processing time of its operations. In this paper, we continue the line of research started by Weiß et al. (Discrete Appl Math 211:183–203, 2016). We establish new structural results for the two-machine problem with the makespan objective and use them to formulate an easier solution algorithm. Other versions of the problem, with the total completion time objective and those which involve due dates or deadlines, turn out to be NP-hard in the strong sense, even for $$m=2$$ m = 2 machines. We also show that relaxed models, in which cycles are allowed to contain less than m jobs, have the same complexity status.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jsched:v:20:y:2017:i:6:d:10.1007_s10951-016-0490-0
    DOI: 10.1007/s10951-016-0490-0
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    References listed on IDEAS

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    3. Urban, Timothy L. & Chiang, Wen-Chyuan, 2016. "Designing energy-efficient serial production lines: The unpaced synchronous line-balancing problem," European Journal of Operational Research, Elsevier, vol. 248(3), pages 789-801.
    4. 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.
    5. Maurice Queyranne & Frits Spieksma & Fabio Tardella, 1998. "A General Class of Greedily Solvable Linear Programs," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 892-908, November.
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