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Open shop cyclic scheduling

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  • Pempera, Jaroslaw
  • Smutnicki, Czeslaw

Abstract

The paper deals with cyclic scheduling problem in the production system working according to the so called open shop policy. The considered case is more general than standard open-shop and job-shop scheduling problems discussed so far in operations research literature. The proposed approach is a nontrivial extension of the permutation-and-graph modelling technology introduced earlier by us for job-shop scheduling. In this paper we provide a mathematical model of the problem and a few graph models. Using these graphs, we formulate several properties employed in the time-efficient method of finding minimal cycle time for the given processing orders. Then, we prove graph properties useful for the elimination of a priori unfeasible or inferior solutions without direct calculation of cycle time. Based on the established theoretical properties, we propose an approximation algorithm of tabu search type. Empirical tests confirm high efficiency of the algorithm.

Suggested Citation

  • Pempera, Jaroslaw & Smutnicki, Czeslaw, 2018. "Open shop cyclic scheduling," European Journal of Operational Research, Elsevier, vol. 269(2), pages 773-781.
    • Handle: RePEc:eee:ejores:v:269:y:2018:i:2:p:773-781
    DOI: 10.1016/j.ejor.2018.02.021
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    References listed on IDEAS

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    1. Kubale, Marek & Nadolski, Adam, 2005. "Chromatic scheduling in a cyclic open shop," European Journal of Operational Research, Elsevier, vol. 164(3), pages 585-591, August.
    2. Peter Brucker & Thomas Kampmeyer, 2008. "Cyclic job shop scheduling problems with blocking," Annals of Operations Research, Springer, vol. 159(1), pages 161-181, March.
    3. Bräsel, Heidemarie & Herms, André & Mörig, Marc & Tautenhahn, Thomas & Tusch, Jan & Werner, Frank, 2008. "Heuristic constructive algorithms for open shop scheduling to minimize mean flow time," European Journal of Operational Research, Elsevier, vol. 189(3), pages 856-870, September.
    4. Blazewicz, Jacek & Domschke, Wolfgang & Pesch, Erwin, 1996. "The job shop scheduling problem: Conventional and new solution techniques," European Journal of Operational Research, Elsevier, vol. 93(1), pages 1-33, August.
    5. J Grabowski & J Pempera, 2001. "New block properties for the permutation flow shop problem with application in tabu search," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(2), pages 210-220, February.
    6. S. Thomas McCormick & Michael L. Pinedo & Scott Shenker & Barry Wolf, 1989. "Sequencing in an Assembly Line with Blocking to Minimize Cycle Time," Operations Research, INFORMS, vol. 37(6), pages 925-935, December.
    7. Eugeniusz Nowicki & Czeslaw Smutnicki, 1996. "A Fast Taboo Search Algorithm for the Job Shop Problem," Management Science, INFORMS, vol. 42(6), pages 797-813, June.
    8. Liaw, Ching-Fang, 2000. "A hybrid genetic algorithm for the open shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 124(1), pages 28-42, July.
    9. Taillard, E., 1993. "Benchmarks for basic scheduling problems," European Journal of Operational Research, Elsevier, vol. 64(2), pages 278-285, January.
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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.
    2. Smutnicki, Czeslaw & Pempera, Jaroslaw & Bocewicz, Grzegorz & Banaszak, Zbigniew, 2022. "Cyclic flow-shop scheduling with no-wait constraints and missing operations," European Journal of Operational Research, Elsevier, vol. 302(1), pages 39-49.

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