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A best on-line algorithm for the single machine parallel-batch scheduling with restricted delivery times

Author

Listed:
  • Jinjiang Yuan

    (Zhengzhou University)

  • Shisheng Li

    (Zhengzhou University)

  • Ji Tian

    (Zhengzhou University)

  • Ruyan Fu

    (Zhengzhou University)

Abstract

We consider a single batch machine on-line scheduling problem with delivery times. In this paper on-line means that jobs arrive over time and the characteristics of jobs are unknown until their arrival times. Once the processing of a job is completed it is delivered to the destination. The objective is to minimize the time by which all jobs have been delivered. For each job J j , its processing time and delivery time are denoted by p j and q j , respectively. We consider two restricted models: (1) the jobs have small delivery times, i.e., for each job J j , q j ≤p j ; (2) the jobs have agreeable processing and delivery times, i.e., for any two jobs J i and J j , p i >p j implies q i ≥q j . We provide an on-line algorithm with competitive ratio $(\sqrt{5}+1)/2$ for both problems, and the results are the best possible.

Suggested Citation

  • Jinjiang Yuan & Shisheng Li & Ji Tian & Ruyan Fu, 2009. "A best on-line algorithm for the single machine parallel-batch scheduling with restricted delivery times," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 206-213, February.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:2:d:10.1007_s10878-007-9108-y
    DOI: 10.1007/s10878-007-9108-y
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    References listed on IDEAS

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    1. Leah Epstein & Lene M. Favrholdt & Jens S. Kohrt, 2006. "Separating online scheduling algorithms with the relative worst order ratio," Journal of Combinatorial Optimization, Springer, vol. 12(4), pages 363-386, December.
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    4. Chung Keung Poon & Wenci Yu, 2005. "On-Line Scheduling Algorithms for a Batch Machine with Finite Capacity," Journal of Combinatorial Optimization, Springer, vol. 9(2), pages 167-186, March.
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    Cited by:

    1. Xing Chai & Wenhua Li & Hang Yuan & Libo Wang, 2022. "Online scheduling on a single machine with linear deteriorating processing times and delivery times," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1900-1912, October.
    2. Yang Fang & Peihai Liu & Xiwen Lu, 2011. "Optimal on-line algorithms for one batch machine with grouped processing times," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 509-516, November.
    3. 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.
    4. Peihai Liu & Xiwen Lu, 2015. "Online unbounded batch scheduling on parallel machines with delivery times," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 228-236, January.
    5. Söhnke Maecker & Liji Shen, 2020. "Solving parallel machine problems with delivery times and tardiness objectives," Annals of Operations Research, Springer, vol. 285(1), pages 315-334, February.
    6. Wenjie Li & Jinjiang Yuan, 2021. "Single-machine online scheduling of jobs with non-delayed processing constraint," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 830-843, May.
    7. Qijia Liu & Jinjiang Yuan, 2018. "Online Scheduling of Incompatible Family Jobs with Equal Length on an Unbounded Parallel-Batch Machine with Job Delivery," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-12, August.
    8. Xing Chai & Wenhua Li & Hang Yuan & Libo Wang, 0. "Online scheduling on a single machine with linear deteriorating processing times and delivery times," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-13.
    9. Peihai Liu & Xiwen Lu, 2015. "Online scheduling on two parallel machines with release dates and delivery times," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 347-359, August.

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