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Two-Machine Job-Shop Scheduling with Equal Processing Times on Each Machine

Author

Listed:
  • Evgeny Gafarov

    (V.A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Profsoyuznaya st. 65, 117997 Moscow, Russia)

  • Frank Werner

    (Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, PSF 4120, 39016 Magdeburg, Germany)

Abstract

In this paper, we consider a two-machine job-shop scheduling problem of minimizing total completion time subject to n jobs with two operations and equal processing times on each machine. This problem occurs e.g., as a single-track railway scheduling problem with three stations and constant travel times between any two adjacent stations. We present a polynomial dynamic programming algorithm of the complexity O ( n 5 ) and a heuristic procedure of the complexity O ( n 3 ) . This settles the complexity status of the problem under consideration which was open before and extends earlier work for the two-station single-track railway scheduling problem. We also present computational results of the comparison of both algorithms. For the 30,000 instances with up to 30 jobs considered, the average relative error of the heuristic is less than 1 % . In our tests, the practical running time of the dynamic programming algorithm was even bounded by O ( n 4 ) .

Suggested Citation

  • Evgeny Gafarov & Frank Werner, 2019. "Two-Machine Job-Shop Scheduling with Equal Processing Times on Each Machine," Mathematics, MDPI, vol. 7(3), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:301-:d:216886
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    References listed on IDEAS

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    1. Zigao Wu & Shaohua Yu & Tiancheng Li, 2019. "A Meta-Model-Based Multi-Objective Evolutionary Approach to Robust Job Shop Scheduling," Mathematics, MDPI, vol. 7(6), pages 1-19, June.

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