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A parallel-machine scheduling problem with an antithetical property to maximize total weighted early work

Author

Listed:
  • Yunhong Min

    (Incheon National University)

  • Byung-Cheon Choi

    (Chungnam National University)

  • Myoung-Ju Park

    (Kyung Hee University)

  • Kyung Min Kim

    (Myongji University)

Abstract

In scheduling with early work, jobs are assigned to a machine by maximizing the parts of non-preemptive jobs executed before their due dates. This paper considers a weighted early work maximization problem on parallel, identical machines with an antithetical property, which holds that $$w_i \le w_j$$ w i ≤ w j implies $$d_i \ge d_j$$ d i ≥ d j for any two jobs i and j where $$w_j$$ w j and $$d_j$$ d j are weight and due date of job j, respectively. We show that the problem is weakly NP-hard. Due to the high complexity of dynamic programming, we develop three solution approaches: mixed-integer programming, heuristics, and a branch-and-bound algorithm. Through numerical experiments, we verify their performance.

Suggested Citation

  • Yunhong Min & Byung-Cheon Choi & Myoung-Ju Park & Kyung Min Kim, 2023. "A parallel-machine scheduling problem with an antithetical property to maximize total weighted early work," 4OR, Springer, vol. 21(3), pages 421-437, September.
    • Handle: RePEc:spr:aqjoor:v:21:y:2023:i:3:d:10.1007_s10288-022-00517-1
    DOI: 10.1007/s10288-022-00517-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Enrique Gerstl & Gur Mosheiov, 2020. "Single machine scheduling to maximize the number of on-time jobs with generalized due-dates," Journal of Scheduling, Springer, vol. 23(3), pages 289-299, June.
    4. Malgorzata Sterna & Kateryna Czerniachowska, 2017. "Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 927-944, September.
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    6. Kenneth R. Baker, 1984. "Sequencing Rules and Due-Date Assignments in a Job Shop," Management Science, INFORMS, vol. 30(9), pages 1093-1104, September.
    7. Byung-Cheon Choi & Myoung-Ju Park & Kyung Min Kim & Yunhong Min, 2021. "A Parallel Machine Scheduling Problem Maximizing Total Weighted Early Work," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(06), pages 1-16, December.
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