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Approximation Algorithms in Batch Processing

Author

Listed:
  • Xiaotie Deng

    (City University of Hong Kong)

  • Chung Keung Poon

    (City University of Hong Kong)

  • Yuzhong Zhang

    (Qufu Normal University)

Abstract

A polynomial approximation scheme for minimizing makespan in a batch processing system under dynamic job arrivals is presented. A lower bound of $${{(\sqrt 5 + 2)} \mathord{\left/ {\vphantom {{(\sqrt 5 + 2)} 2}} \right. \kern-\nulldelimiterspace} 2}$$ on the competitive ratio of any on-line algorithm is proved. This is matched by an on-line algorithm for the special case of unbounded machine capacity.

Suggested Citation

  • Xiaotie Deng & Chung Keung Poon & Yuzhong Zhang, 2003. "Approximation Algorithms in Batch Processing," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 247-257, September.
    • Handle: RePEc:spr:jcomop:v:7:y:2003:i:3:d:10.1023_a:1027316504440
    DOI: 10.1023/A:1027316504440
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    References listed on IDEAS

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    Cited by:

    1. Ruyan Fu & Ji Tian & Shisheng Li & Jinjiang Yuan, 2017. "An optimal online algorithm for the parallel-batch scheduling with job processing time compatibilities," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1187-1197, November.
    2. 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.
    3. Shisheng Li & Jinjiang Yuan, 2010. "Parallel-machine parallel-batching scheduling with family jobs and release dates to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 19(1), pages 84-93, January.
    4. 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.
    5. Hailing Liu & Jinjiang Yuan & Wenjie Li, 2016. "Online scheduling of equal length jobs on unbounded parallel batch processing machines with limited restart," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1609-1622, May.
    6. Ou, Jinwen & Lu, Lingfa & Zhong, Xueling, 2023. "Parallel-batch scheduling with rejection: Structural properties and approximation algorithms," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1017-1032.
    7. Li, Shisheng & Ng, C.T. & Cheng, T.C.E. & Yuan, Jinjiang, 2011. "Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 210(3), pages 482-488, May.
    8. Chengwen Jiao & Jinjiang Yuan & Qi Feng, 2019. "Online Algorithms for Scheduling Unit Length Jobs on Unbounded Parallel-Batch Machines with Linearly Lookahead," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(05), pages 1-8, October.
    9. 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.
    10. Beat Gfeller & Leon Peeters & Birgitta Weber & Peter Widmayer, 2009. "Single machine batch scheduling with release times," Journal of Combinatorial Optimization, Springer, vol. 17(3), pages 323-338, April.
    11. 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.
    12. Nong, Qingqin & Yuan, Jinjiang & Fu, Ruyan & Lin, Lin & Tian, Ji, 2008. "The single-machine parallel-batching on-line scheduling problem with family jobs to minimize makespan," International Journal of Production Economics, Elsevier, vol. 111(2), pages 435-440, February.
    13. 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.
    14. Li, Shuguang, 2017. "Approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities," European Journal of Operational Research, Elsevier, vol. 263(3), pages 815-826.
    15. Li, Shuguang, 2017. "Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan," European Journal of Operational Research, Elsevier, vol. 260(1), pages 12-20.

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