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A note on batch scheduling on a two-machine flowshop with machine-dependent processing times

Author

Listed:
  • Gur Mosheiov

    (The Hebrew University)

  • Daniel Oron

    (The University of Sydney)

Abstract

We study a batch scheduling problem on a two-machine flowshop. Unlike most relevant research papers focusing on batching with identical job processing times, we assume machine-dependent processing times. The objective function is minimum makespan. For the relaxed version of the problem, where integer batch sizes are not required, we introduce a constant time solution. It consists of: (i) a closed-form expression for the optimal number of batches; and (ii) a geometric sequence of the batch sizes. This optimal non-integer solution is converted into an integer solution by the application of a simple rounding procedure, which runs in O(nlogn) time (where n is the number of jobs).

Suggested Citation

  • Gur Mosheiov & Daniel Oron, 2023. "A note on batch scheduling on a two-machine flowshop with machine-dependent processing times," 4OR, Springer, vol. 21(3), pages 457-469, September.
    • Handle: RePEc:spr:aqjoor:v:21:y:2023:i:3:d:10.1007_s10288-022-00519-z
    DOI: 10.1007/s10288-022-00519-z
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    References listed on IDEAS

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    1. Gur Mosheiov & Vitaly A. Strusevich, 2017. "Determining optimal sizes of bounded batches with rejection via quadratic min‐cost flow," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 217-224, April.
    2. Onur Ozturk & Mehmet A. Begen & Gregory S. Zaric, 2017. "A branch and bound algorithm for scheduling unit size jobs on parallel batching machines to minimize makespan," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1815-1831, March.
    3. Philippe Baptiste, 2000. "Batching identical jobs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(3), pages 355-367, December.
    4. Gerstl, Enrique & Mosheiov, Gur, 2014. "A two-stage flexible flow shop problem with unit-execution-time jobs and batching," International Journal of Production Economics, Elsevier, vol. 158(C), pages 171-178.
    5. Mosheiov, Gur & Oron, Daniel, 2005. "A note on flow-shop and job-shop batch scheduling with identical processing-time jobs," European Journal of Operational Research, Elsevier, vol. 161(1), pages 285-291, February.
    6. Wang, Jun-Qiang & Fan, Guo-Qiang & Zhang, Yingqian & Zhang, Cheng-Wu & Leung, Joseph Y.-T., 2017. "Two-agent scheduling on a single parallel-batching machine with equal processing time and non-identical job sizes," European Journal of Operational Research, Elsevier, vol. 258(2), pages 478-490.
    7. Mor, Baruch & Mosheiov, Gur, 2011. "Single machine batch scheduling with two competing agents to minimize total flowtime," European Journal of Operational Research, Elsevier, vol. 215(3), pages 524-531, December.
    8. Edward G. Coffman & Ardavan Nozari & Mihalis Yannakakis, 1989. "Optimal Scheduling of Products with Two Subassemblies on a Single Machine," Operations Research, INFORMS, vol. 37(3), pages 426-436, June.
    9. Li, Xueping & Zhang, Kaike, 2018. "Single batch processing machine scheduling with two-dimensional bin packing constraints," International Journal of Production Economics, Elsevier, vol. 196(C), pages 113-121.
    10. Yuan, J.J. & Lin, Y.X. & Cheng, T.C.E. & Ng, C.T., 2007. "Single machine serial-batching scheduling problem with a common batch size to minimize total weighted completion time," International Journal of Production Economics, Elsevier, vol. 105(2), pages 402-406, February.
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