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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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    1. Zhao, Chuan-Li & Tang, Heng-Yong & Cheng, Cong-Dian, 2009. "Two-parallel machines scheduling with rate-modifying activities to minimize total completion time," European Journal of Operational Research, Elsevier, vol. 198(1), pages 354-357, October.
    2. Gregory Dobson & Uday S. Karmarkar & Jeffrey L. Rummel, 1989. "Batching to Minimize Flow Times on Parallel Heterogeneous Machines," Management Science, INFORMS, vol. 35(5), pages 607-613, May.
    3. Lin, B. M. T. & Jeng, A. A. K., 2004. "Parallel-machine batch scheduling to minimize the maximum lateness and the number of tardy jobs," International Journal of Production Economics, Elsevier, vol. 91(2), pages 121-134, September.
    4. Lee, C. -Y. & Leon, V. J., 2001. "Machine scheduling with a rate-modifying activity," European Journal of Operational Research, Elsevier, vol. 128(1), pages 119-128, January.
    5. 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.
    6. Cheng, T. C. Edwin & Gordon, Valery S. & Kovalyov, Mikhail Y., 1996. "Single machine scheduling with batch deliveries," European Journal of Operational Research, Elsevier, vol. 94(2), pages 277-283, October.
    7. Cheng, T.C.E. & Ng, C.T. & Yuan, J.J., 2008. "Multi-agent scheduling on a single machine with max-form criteria," European Journal of Operational Research, Elsevier, vol. 188(2), pages 603-609, July.
    8. Lodree Jr., Emmett J. & Geiger, Christopher D., 2010. "A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration," European Journal of Operational Research, Elsevier, vol. 201(2), pages 644-648, March.
    9. Wang, Guoqing & Cheng, T. C. Edwin, 2000. "Parallel machine scheduling with batch delivery costs," International Journal of Production Economics, Elsevier, vol. 68(2), pages 177-183, November.
    10. Mor, Baruch & Mosheiov, Gur, 2012. "Scheduling a maintenance activity and due-window assignment based on common flow allowance," International Journal of Production Economics, Elsevier, vol. 135(1), pages 222-230.
    11. Quadt, Daniel & Kuhn, Heinrich, 2007. "Batch scheduling of jobs with identical process times on flexible flow lines," International Journal of Production Economics, Elsevier, vol. 105(2), pages 385-401, February.
    12. 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.
    13. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    14. 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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    Cited by:

    1. Lin, Ran & Wang, Jun-Qiang & Oulamara, Ammar, 2023. "Online scheduling on parallel-batch machines with periodic availability constraints and job delivery," Omega, Elsevier, vol. 116(C).
    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. Gur Mosheiov & Daniel Oron, 2020. "Scheduling problems with a weight-modifying-activity," Annals of Operations Research, Springer, vol. 295(2), pages 737-745, December.
    5. 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.
    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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