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On the complexity of open shop scheduling with time lags

Author

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  • Wiesław Kubiak

    (Memorial University)

Abstract

The minimization of makespan in open shop with time lags has been to be shown NP-hard in the strong sense even for the case of two machines and unit-time operations. The minimization of total completion time, however, has remained open for that case though it has been it be shown NP-hard in the strong sense for weighted total completion time or for jobs with release dates. This note shows that the minimization of total completion time for two machines and unit-time operations is NP-hard in the strong sense which answers the long standing open question.

Suggested Citation

  • Wiesław Kubiak, 2023. "On the complexity of open shop scheduling with time lags," Journal of Scheduling, Springer, vol. 26(3), pages 331-334, June.
    • Handle: RePEc:spr:jsched:v:26:y:2023:i:3:d:10.1007_s10951-022-00769-z
    DOI: 10.1007/s10951-022-00769-z
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    References listed on IDEAS

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    1. Peter Brucker & Sigrid Knust & T.C. Cheng & Natalia Shakhlevich, 2004. "Complexity Results for Flow-Shop and Open-Shop Scheduling Problems with Transportation Delays," Annals of Operations Research, Springer, vol. 129(1), pages 81-106, July.
    2. 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.
    3. 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.
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