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Two-machine open-shop scheduling with rejection to minimize the makespan

Author

Listed:
  • Liqi Zhang

    (Henan Agricultural University)

  • Lingfa Lu

    (Zhengzhou University)

  • Jinjiang Yuan

    (Zhengzhou University)

Abstract

In this paper, we consider the two-machine open-shop scheduling problem with rejection. The objective is to minimize the sum of the makespan of accepted jobs and the total rejection cost of rejected jobs. We show that the problem is NP-hard even in three special cases and then provide a pseudo-polynomial time algorithm for this problem, which means that the problem is actually NP-hard in the ordinary sense. This answers an open problem posed by Shabtay et al. in (J Schedul 16:3–28, 2013). Finally, a 2-approximation algorithm and an FPTAS are designed for the problem.

Suggested Citation

  • Liqi Zhang & Lingfa Lu & Jinjiang Yuan, 2016. "Two-machine open-shop scheduling with rejection to minimize the makespan," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 519-529, March.
    • Handle: RePEc:spr:orspec:v:38:y:2016:i:2:d:10.1007_s00291-015-0409-8
    DOI: 10.1007/s00291-015-0409-8
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    References listed on IDEAS

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    1. Kellerer, Hans & Strusevich, Vitaly, 2013. "Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product," European Journal of Operational Research, Elsevier, vol. 228(1), pages 24-32.
    2. 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.
    3. George Steiner & Rui Zhang, 2011. "Revised Delivery-Time Quotation in Scheduling with Tardiness Penalties," Operations Research, INFORMS, vol. 59(6), pages 1504-1511, December.
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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. Rainer Kolisch & Erik Demeulemeester & Rubén Ruiz Garcia & Vincent T’Kindt & Jan Węglarz, 2016. "Editorial “Project Management and Scheduling”," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 279-281, March.

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