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Minimizing the Number of Late Jobs under the Group Technology Assumption

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  • Zhaohui Liu

    (East China University of Science and Technology)

  • Wenci Yu

    (East China University of Science and Technology)

Abstract

We consider the one-machine scheduling problem to minimize the number of late jobs under the group technology assumption, where jobs are classified into groups and all jobs from the same group must be processed contiguously. This problem is shown to be strongly NP-hard, even for the case of unit processing time and zero set-up time. A polynomial time algorithm is developed for the restricted version in which the jobs in each group have the same due date. However, the problem is proved to be ordinarily NP-hard if the jobs in a group have the same processing time as well as the same due date.

Suggested Citation

  • Zhaohui Liu & Wenci Yu, 1999. "Minimizing the Number of Late Jobs under the Group Technology Assumption," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 5-15, July.
    • Handle: RePEc:spr:jcomop:v:3:y:1999:i:1:d:10.1023_a:1009841719644
    DOI: 10.1023/A:1009841719644
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    References listed on IDEAS

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    1. Scott Webster & Kenneth R. Baker, 1995. "Scheduling Groups of Jobs on a Single Machine," Operations Research, INFORMS, vol. 43(4), pages 692-703, August.
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    Cited by:

    1. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    2. Janiak, Adam & Kovalyov, Mikhail Y. & Portmann, Marie-Claude, 2005. "Single machine group scheduling with resource dependent setup and processing times," European Journal of Operational Research, Elsevier, vol. 162(1), pages 112-121, April.

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