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A Parallel Machine Scheduling Problem Maximizing Total Weighted Early Work

Author

Listed:
  • Byung-Cheon Choi

    (School of Business, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Korea)

  • Myoung-Ju Park

    (Department of Industrial and Management Systems Engineering, Kyung Hee University, 1732, Deogyeong-daero, Giheung-gu, Yongin-si, Kyunggi-do 17104, Korea)

  • Kyung Min Kim

    (Department of Industrial Management and Engineering, Myongji University, 116 Myongji-ro, Choein-gu, Yongin-si, Gyeonggido 17058, Korea)

  • Yunhong Min

    (Graduate School of Logistics, Incheon National University, 119, Academy-ro, Yeonsu-gu, Incheon, Gyeonggi-do 22012, Korea)

Abstract

We consider the total weighted early work maximization problem on identical machines in parallel such that the weights are identical, or the due date is the same. First, we present an approach to solve the case with a fixed number of machines in pseudo-polynomial time. Then, we develop approximation algorithms for the two cases with identical weights and with a common due date. For the case with identical weights, furthermore, we show that the parallel-machine and a single-machine cases are strongly NP-hard and weakly NP-hard, respectively, even if the due date of each job is equal to the processing time multiplied by a constant.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:06:n:s021759592150007x
    DOI: 10.1142/S021759592150007X
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    Citations

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    Cited by:

    1. 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.
    2. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    3. Xiaofei Liu & Yajie Li & Weidong Li & Jinhua Yang, 2023. "Combinatorial approximation algorithms for the maximum bounded connected bipartition problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.

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