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Bounded dynamic programming algorithm for the job shop problem with sequence dependent setup times

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  • Ansis Ozolins

    (University of Latvia)

Abstract

In this paper, the job shop scheduling problem (JSP) with a makespan minimization criterion is investigated. Various approximate algorithms exist that can solve moderate JSP instances within a reasonable time limit. However, only a few exact algorithms are known in the literature. We have developed an exact algorithm by means of a bounded dynamic programming (BDP) approach. This approach combines elements of a dynamic programming with elements of a branch and bound method. In addition, a generalization is investigated: the JSP with sequence dependent setup times (SDST-JSP). The BDP algorithm is adapted for this problem. To the best of our knowledge, the dynamic programming approach has never been applied to the SDST-JSP before. The BDP algorithm can directly be used as a heuristic. Computational results show that the proposed algorithm can solve benchmark instances up to 20 jobs and 15 machines for the JSP. For the SDST-JSP, the proposed algorithm outperforms all the state-of-the-art exact algorithms and the best-known lower bounds are improved for 5 benchmark instances.

Suggested Citation

  • Ansis Ozolins, 2020. "Bounded dynamic programming algorithm for the job shop problem with sequence dependent setup times," Operational Research, Springer, vol. 20(3), pages 1701-1728, September.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:3:d:10.1007_s12351-018-0381-6
    DOI: 10.1007/s12351-018-0381-6
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    References listed on IDEAS

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    1. Carlier, Jacques, 1982. "The one-machine sequencing problem," European Journal of Operational Research, Elsevier, vol. 11(1), pages 42-47, September.
    2. Joseph Adams & Egon Balas & Daniel Zawack, 1988. "The Shifting Bottleneck Procedure for Job Shop Scheduling," Management Science, INFORMS, vol. 34(3), pages 391-401, March.
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    4. 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.
    5. Waiman Cheung & Hong Zhou, 2001. "Using Genetic Algorithms and Heuristics for Job Shop Scheduling with Sequence-Dependent Setup Times," Annals of Operations Research, Springer, vol. 107(1), pages 65-81, October.
    6. Christian Artigues & Dominique Feillet, 2008. "A branch and bound method for the job-shop problem with sequence-dependent setup times," Annals of Operations Research, Springer, vol. 159(1), pages 135-159, March.
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    Cited by:

    1. Bin Ji & Shujing Zhang & Samson S. Yu & Binqiao Zhang, 2023. "Mathematical Modeling and A Novel Heuristic Method for Flexible Job-Shop Batch Scheduling Problem with Incompatible Jobs," Sustainability, MDPI, vol. 15(3), pages 1-26, January.

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