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Proportionate Flow Shop Scheduling with Rejection

Author

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  • Shi-Sheng Li

    (Department of Information and Computation Science, Zhongyuan University of Technology, Zhengzhou 450007, P. R. China)

  • De-Liang Qian

    (Department of Information and Computation Science, Zhongyuan University of Technology, Zhengzhou 450007, P. R. China)

  • Ren-Xia Chen

    (Department of Information and Computation Science, Zhongyuan University of Technology, Zhengzhou 450007, P. R. China)

Abstract

We consider the problem of scheduling n jobs with rejection on a set of m machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is 𝒩𝒫-hard, then we construct a pseudo-polynomial time algorithm to solve it and an O(n3log n) time for the case where the jobs have the same processing time. For the second problem, we first show that it is 𝒩𝒫-hard, then we design O(n2) time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time.

Suggested Citation

  • Shi-Sheng Li & De-Liang Qian & Ren-Xia Chen, 2017. "Proportionate Flow Shop Scheduling with Rejection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-13, August.
    • Handle: RePEc:wsi:apjorx:v:34:y:2017:i:04:n:s0217595917500154
    DOI: 10.1142/S0217595917500154
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    References listed on IDEAS

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    1. M. L. Smith & S. S. Panwalkar & R. A. Dudek, 1975. "Flowshop Sequencing Problem with Ordered Processing Time Matrices," Management Science, INFORMS, vol. 21(5), pages 544-549, January.
    2. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    3. Zhang, Liqi & Lu, Lingfa & Yuan, Jinjiang, 2009. "Single machine scheduling with release dates and rejection," European Journal of Operational Research, Elsevier, vol. 198(3), pages 975-978, November.
    4. Choi, Byung-Cheon & Chung, Jibok, 2011. "Two-machine flow shop scheduling problem with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(1), pages 66-72, August.
    5. Zhong, Xueling & Ou, Jinwen & Wang, Guoqing, 2014. "Order acceptance and scheduling with machine availability constraints," European Journal of Operational Research, Elsevier, vol. 232(3), pages 435-441.
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    3. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.

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