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The Np-Hardness Of Minimizing The Total Late Work On An Unbounded Batch Machine

Author

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  • JIANFENG REN

    (College of Operations Research and Management Sciences, Qufu Normal University, Shangdong, 276826, China)

  • YUZHONG ZHANG

    (Department of Mathematics, Qufu Normal University, Shangdong, 276826, China)

  • GUO SUN

    (Department of Mathematics, Qufu Normal University, Shangdong, 276826, China)

Abstract

We consider the problem of minimizing the total late work$(\sum_{j=1}^{n}\, V_j)$on an unbounded batch processing machine, whereVj=min{Tj, pj}andTj=max{Cj- dj, 0}. The batch processing machine can process up toB (B ≥ n)jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time, respectively. For a batch of jobs, the processing time of the batch is equal to the largest processing time among the jobs in this batch. In this paper, we prove that the problem$1|B \geq n|\sum_{j=1}^{n}V_j$is NP-hard.

Suggested Citation

  • Jianfeng Ren & Yuzhong Zhang & Guo Sun, 2009. "The Np-Hardness Of Minimizing The Total Late Work On An Unbounded Batch Machine," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 351-363.
    • Handle: RePEc:wsi:apjorx:v:26:y:2009:i:03:n:s0217595909002249
    DOI: 10.1142/S0217595909002249
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    Cited by:

    1. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    2. Xin Chen & Malgorzata Sterna & Xin Han & Jacek Blazewicz, 2016. "Scheduling on parallel identical machines with late work criterion: Offline and online cases," Journal of Scheduling, Springer, vol. 19(6), pages 729-736, December.
    3. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    4. Rubing Chen & Jinjiang Yuan & C.T. Ng & T.C.E. Cheng, 2019. "Single‐machine scheduling with deadlines to minimize the total weighted late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 582-595, October.
    5. Chen, Xin & Liang, Yage & Sterna, Małgorzata & Wang, Wen & Błażewicz, Jacek, 2020. "Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date," European Journal of Operational Research, Elsevier, vol. 284(1), pages 67-74.
    6. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    7. Shang-Chia Liu & Jiahui Duan & Win-Chin Lin & Wen-Hsiang Wu & Jan-Yee Kung & Hau Chen & Chin-Chia Wu, 2018. "A Branch-and-Bound Algorithm for Two-Agent Scheduling with Learning Effect and Late Work Criterion," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-24, October.

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