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

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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.

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  1. University of Latvia, Zellu Street 25, Riga, 1002, Latvia

    Ansis Ozolins

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  1. Ansis Ozolins
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Correspondence to Ansis Ozolins.

Appendix

Appendix

See Tables 11 and 12.

Table 11 Calculation of upper bounds: case SDST-JSP
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Table 12 Calculation of lower bounds: case SDST-JSP
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Ozolins, A. Bounded dynamic programming algorithm for the job shop problem with sequence dependent setup times. Oper Res Int J 20, 1701–1728 (2020). https://doi.org/10.1007/s12351-018-0381-6

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