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Mixed batch scheduling on identical machines

Author

Listed:
  • Jun-Qiang Wang

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

  • Guo-Qiang Fan

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

  • Zhixin Liu

    (University of Michigan-Dearborn)

Abstract

This paper studies a new mixed batch scheduling problem that arises in vacuum heat treatment. A mixed batch machine can process at most a given number of jobs simultaneously. The processing time of a batch is the weighted sum of the maximum processing time and the total processing time of jobs in the batch. The objective is to minimize the makespan. We first prove that the problem on a single machine can be solved in polynomial time, while the problem on multiple identical machines is NP-hard. Then, we develop a pseudopolynomial time exact algorithm when the number of machines is fixed. Further, we analyze the worst-case performance ratio of a full batch longest processing time algorithm and design Algorithm LPT-Greedy with improved worst-case performance.

Suggested Citation

  • Jun-Qiang Wang & Guo-Qiang Fan & Zhixin Liu, 2020. "Mixed batch scheduling on identical machines," Journal of Scheduling, Springer, vol. 23(4), pages 487-496, August.
    • Handle: RePEc:spr:jsched:v:23:y:2020:i:4:d:10.1007_s10951-019-00623-9
    DOI: 10.1007/s10951-019-00623-9
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    References listed on IDEAS

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    Cited by:

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    3. Ou, Jinwen & Lu, Lingfa & Zhong, Xueling, 2023. "Parallel-batch scheduling with rejection: Structural properties and approximation algorithms," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1017-1032.
    4. Lin, Ran & Wang, Jun-Qiang & Liu, Zhixin & Xu, Jun, 2023. "Best possible algorithms for online scheduling on identical batch machines with periodic pulse interruptions," European Journal of Operational Research, Elsevier, vol. 309(1), pages 53-64.

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