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Online scheduling on batching machines to minimise the total weighted completion time of jobs with precedence constraints and identical processing times

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  • Jianfa Cao
  • Jinjiang Yuan
  • Wenjie Li
  • Hailin Bu

Abstract

This article studies online scheduling of equal length jobs with precedence constraints on m parallel batching machines. The jobs arrive over time. The objective is to minimise the total weighted completion time of jobs. Denote the size of each batch by b with b = ∞ in the unbounded batching and b < ∞ in the bounded batching. For the unbounded batching version, we provide an online algorithm with a best possible competitive ratio of ρm, where ρm is the positive solution of ρm+1 − ρ = 1. The algorithm is also best possible when the jobs have identical weights. For the bounded batching version with identical weights of jobs, we provide an online algorithm with a competitive ratio of 2.

Suggested Citation

  • Jianfa Cao & Jinjiang Yuan & Wenjie Li & Hailin Bu, 2011. "Online scheduling on batching machines to minimise the total weighted completion time of jobs with precedence constraints and identical processing times," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(1), pages 51-55.
    • Handle: RePEc:taf:tsysxx:v:42:y:2011:i:1:p:51-55
    DOI: 10.1080/00207720903428906
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    Citations

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    Cited by:

    1. Xing Chai & Wenhua Li & Yuejuan Zhu, 2021. "Online scheduling to minimize maximum weighted flow-time on a bounded parallel-batch machine," Annals of Operations Research, Springer, vol. 298(1), pages 79-93, March.
    2. Wenhua Li & Xing Chai, 2019. "The medical laboratory scheduling for weighted flow-time," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 83-94, January.
    3. Wenhua Li & Weina Zhai & Xing Chai, 2019. "Online Bi-Criteria Scheduling on Batch Machines with Machine Costs," Mathematics, MDPI, vol. 7(10), pages 1-11, October.
    4. Zhang, Jun & Liu, Feng & Tang, Jiafu & Li, Yanhui, 2019. "The online integrated order picking and delivery considering Pickers’ learning effects for an O2O community supermarket," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 123(C), pages 180-199.
    5. Christoph Hertrich & Christian Weiß & Heiner Ackermann & Sandy Heydrich & Sven O. Krumke, 2022. "Online algorithms to schedule a proportionate flexible flow shop of batching machines," Journal of Scheduling, Springer, vol. 25(6), pages 643-657, December.

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