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Two-machine open shop scheduling with special transportation times

Author

Listed:
  • D Rebaine

    (University of Tizi-Ouzou)

  • V A Strusevich

    (University of Greenwich)

Abstract

The paper considers a problem of scheduling n jobs in a two-machine open shop to minimise the makespan, provided that preemption is not allowed and the interstage transportation times are involved. In general, this problem is known to be NP-hard. We present a linear time algorithm that finds an optimal schedule if no transportation time exceeds the smallest of the processing times. We also describe an algorithm that creates a heuristic solution to the problem with job-independent transportation times. Our algorithm provides a worst-case performance ratio of 8/5 if the transportation time of a job depends on the assigned processing route. The ratio reduces to 3/2 if all transportation times are equal.

Suggested Citation

  • D Rebaine & V A Strusevich, 1999. "Two-machine open shop scheduling with special transportation times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 756-764, July.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:7:d:10.1057_palgrave.jors.2600769
    DOI: 10.1057/palgrave.jors.2600769
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    Citations

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    Cited by:

    1. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    2. Averbakh, Igor & Berman, Oded & Chernykh, Ilya, 2005. "A -approximation algorithm for the two-machine routing open-shop problem on a two-node network," European Journal of Operational Research, Elsevier, vol. 166(1), pages 3-24, October.
    3. Munier-Kordon, Alix & Rebaine, Djamal, 2010. "The two-machine open-shop problem with unit-time operations and time delays to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 203(1), pages 42-49, May.
    4. Haiyan Wang & Chung‐Yee Lee, 2005. "Production and transport logistics scheduling with two transport mode choices," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 796-809, December.
    5. Zhang, Xiandong & van de Velde, Steef, 2010. "On-line two-machine open shop scheduling with time lags," European Journal of Operational Research, Elsevier, vol. 204(1), pages 14-19, July.
    6. Wiesław Kubiak, 2023. "On the complexity of open shop scheduling with time lags," Journal of Scheduling, Springer, vol. 26(3), pages 331-334, June.
    7. Hosseini, Amir & Otto, Alena & Pesch, Erwin, 2024. "Scheduling in manufacturing with transportation: Classification and solution techniques," European Journal of Operational Research, Elsevier, vol. 315(3), pages 821-843.

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