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Batch scheduling with a rate-modifying maintenance activity to minimize total flowtime

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  • Mor, Baruch
  • Mosheiov, Gur

Abstract

We study a single machine batch scheduling problem with unit time jobs and an optional maintenance activity. The maintenance activity is assumed to be rate modifying, i.e. the processing times of the jobs processed after the maintenance are reduced. The objective function is minimum total flowtime. We focus first on the relaxed version of the problem, where batch sizes are not forced to be integers. For a given number of jobs, setup time, duration of the maintenance activity, and a rate-modifying factor, we show that the optimal solution has a unique property: the batch sizes of the jobs scheduled prior to the maintenance, and after it, form two decreasing arithmetic sequences. Based on this property, we introduce an optimal algorithm which is polynomial in the number of jobs. We propose a simple rounding procedure that guarantees an integer solution. Our numerical tests indicate that this procedure leads to very close-to-optimal schedules.

Suggested Citation

  • Mor, Baruch & Mosheiov, Gur, 2014. "Batch scheduling with a rate-modifying maintenance activity to minimize total flowtime," International Journal of Production Economics, Elsevier, vol. 153(C), pages 238-242.
    • Handle: RePEc:eee:proeco:v:153:y:2014:i:c:p:238-242
    DOI: 10.1016/j.ijpe.2014.03.004
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    References listed on IDEAS

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    Cited by:

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    2. Du-Juan Wang & Yunqiang Yin & Mengqi Liu, 2016. "Bicriteria scheduling problems involving job rejection, controllable processing times and rate-modifying activity," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3691-3705, June.
    3. Yin, Yunqiang & Wang, Yan & Cheng, T.C.E. & Liu, Wenqi & Li, Jinhai, 2017. "Parallel-machine scheduling of deteriorating jobs with potential machine disruptions," Omega, Elsevier, vol. 69(C), pages 17-28.
    4. Han, Guanghua & Dong, Ming & Liu, Shaoxuan, 2014. "Yield and allocation management in a continuous make-to-stock system with demand upgrade substitution," International Journal of Production Economics, Elsevier, vol. 156(C), pages 124-131.
    5. Gur Mosheiov & Daniel Oron, 2020. "Scheduling problems with a weight-modifying-activity," Annals of Operations Research, Springer, vol. 295(2), pages 737-745, December.
    6. 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.
    7. Ma, Ran & Wan, Long & Wei, Lijun & Yuan, Jinjiang, 2014. "Online bounded-batch scheduling to minimize total weighted completion time on parallel machines," International Journal of Production Economics, Elsevier, vol. 156(C), pages 31-38.

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