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On the existence of dominating 6-cyclic schedules in four-machine robotic cells

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  • Kats, Vladimir
  • Levner, Eugene

Abstract

We consider a four-machine robotic cell producing identical parts and served by a single robot. We study the no-wait multi-cyclic scheduling problem. Using the forbidden-intervals method, we show that in such a cell the optimal schedule can be k-cyclic with minimum k ≥ 6. This fact refutes Agnetis’ conjecture (Agnetis, 2000) stating that the minimum k for the optimal k-cyclic m-machine schedules does not exceed m−1. In particular, we construct a counter-example to Agnetis’ conjecture.

Suggested Citation

  • Kats, Vladimir & Levner, Eugene, 2018. "On the existence of dominating 6-cyclic schedules in four-machine robotic cells," European Journal of Operational Research, Elsevier, vol. 268(2), pages 755-759.
    • Handle: RePEc:eee:ejores:v:268:y:2018:i:2:p:755-759
    DOI: 10.1016/j.ejor.2018.01.034
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    References listed on IDEAS

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    1. Che, Ada & Chu, Chengbin, 2009. "Multi-degree cyclic scheduling of a no-wait robotic cell with multiple robots," European Journal of Operational Research, Elsevier, vol. 199(1), pages 77-88, November.
    2. Neil Geismar, H. & Dawande, Milind & Sriskandarajah, Chelliah, 2005. "Approximation algorithms for k-unit cyclic solutions in robotic cells," European Journal of Operational Research, Elsevier, vol. 162(2), pages 291-309, April.
    3. Che, Ada & Chu, Chengbin & Levner, Eugene, 2003. "A polynomial algorithm for 2-degree cyclic robot scheduling," European Journal of Operational Research, Elsevier, vol. 145(1), pages 31-44, February.
    4. Agnetis, A., 2000. "Scheduling no-wait robotic cells with two and three machines," European Journal of Operational Research, Elsevier, vol. 123(2), pages 303-314, June.
    5. Levner, Eugene & Kats, Vladimir & Levit, Vadim E., 1997. "An improved algorithm for cyclic flowshop scheduling in a robotic cell," European Journal of Operational Research, Elsevier, vol. 97(3), pages 500-508, March.
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    Cited by:

    1. Hanen, Claire & Hanzalek, Zdenek, 2020. "Grouping tasks to save energy in a cyclic scheduling problem: A complexity study," European Journal of Operational Research, Elsevier, vol. 284(2), pages 445-459.

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