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Mixed batch scheduling with non-identical job sizes to minimize makespan

Author

Listed:
  • Guo-Qiang Fan

    (Xidian University)

  • Jun-Qiang Wang

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

  • Zhixin Liu

    (University of Michigan-Dearborn)

Abstract

This paper studies a mixed batch scheduling problem with non-identical job sizes to minimize the makespan. Multiple jobs can be processed simultaneously as a batch on a mixed batch machine as long as the total size of the jobs in the batch does not exceed the machine capacity. The processing time of a batch is the weighted sum of the maximum processing time and total processing time of the jobs in the batch. We show that the problem is strongly NP-hard even with a single machine, and analyze the worst-case performance ratio of the longest processing time first fit (LPTFF) algorithm. Furthermore, we present the longest processing time first fit greedy (LPTFFG) algorithm, and show that the worst-case performance ratio of algorithm LPTFFG is better than that of algorithm LPTFF. Computational experiments show that algorithm LPTFFG fits the case with a large number of machines, small job sizes, and small weight of the maximum processing time.

Suggested Citation

  • Guo-Qiang Fan & Jun-Qiang Wang & Zhixin Liu, 2025. "Mixed batch scheduling with non-identical job sizes to minimize makespan," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(1), pages 105-127, March.
    • Handle: RePEc:spr:orspec:v:47:y:2025:i:1:d:10.1007_s00291-024-00770-2
    DOI: 10.1007/s00291-024-00770-2
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    References listed on IDEAS

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    1. Jia, Zhao-hong & Leung, Joseph Y.-T., 2015. "A meta-heuristic to minimize makespan for parallel batch machines with arbitrary job sizes," European Journal of Operational Research, Elsevier, vol. 240(3), pages 649-665.
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    6. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    7. Wang, Jun-Qiang & Leung, Joseph Y.-T., 2014. "Scheduling jobs with equal-processing-time on parallel machines with non-identical capacities to minimize makespan," International Journal of Production Economics, Elsevier, vol. 156(C), pages 325-331.
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    11. Muter, İbrahim, 2020. "Exact algorithms to minimize makespan on single and parallel batch processing machines," European Journal of Operational Research, Elsevier, vol. 285(2), pages 470-483.
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