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Minimising makespan for two batch-processing machines with non-identical job sizes in job shop

Author

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  • Bayi Cheng
  • Shanlin Yang
  • Ying Ma

Abstract

In this article, the job shop scheduling problem with two batch-processing machines is considered. The machines have limited capacity and the jobs have non-identical job sizes. The jobs are processed in batches and the total size of each batch cannot exceed the machine capacity. The processing times of a job on the two machines are proportional. We show the problem of minimising makespan is NP-hard in the strong sense. Then we provide an approximation algorithm with worst-case ratio no more than 4, and the running time of the algorithm is O(n log n). Finally, the performance of the proposed algorithm is tested by different levels of instances. Computational results demonstrate the effectiveness of the algorithm for all the instances.

Suggested Citation

  • Bayi Cheng & Shanlin Yang & Ying Ma, 2012. "Minimising makespan for two batch-processing machines with non-identical job sizes in job shop," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(12), pages 2185-2192.
    • Handle: RePEc:taf:tsysxx:v:43:y:2012:i:12:p:2185-2192
    DOI: 10.1080/00207721.2011.577250
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    Cited by:

    1. B.‐Y. Cheng & J.Y.‐T. Leung & K. Li & S.‐L. Yang, 2015. "Single batch machine scheduling with deliveries," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 470-482, September.
    2. Zhang, Hongbin & Yang, Yu & Wu, Feng, 2024. "Scheduling a set of jobs with convex piecewise linear cost functions on a single-batch-processing machine," Omega, Elsevier, vol. 122(C).
    3. Alessandro Druetto & Erica Pastore & Elena Rener, 2023. "Parallel batching with multi-size jobs and incompatible job families," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 440-458, July.

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