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On-Line Scheduling Algorithms for a Batch Machine with Finite Capacity

Author

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  • Chung Keung Poon

    (City U. of Hong Kong)

  • Wenci Yu

    (East China U. of Science and Technology)

Abstract

We study the problem of on-line scheduling jobs with release dates on a batch machine of finite capacity with the objective of minimizing the makespan. We generalize several existing algorithms for the problem to a class of on-line algorithms that are 2-competitive for any arbitrary finite machine capacity. Then, we show that one of these generalized algorithms is in fact 7/4-competitive for machine capacity 2. This is the first on-line algorithm for a finite machine capacity with competitive ratio less than 2.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:9:y:2005:i:2:d:10.1007_s10878-005-6855-5
    DOI: 10.1007/s10878-005-6855-5
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    References listed on IDEAS

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    6. Gouchuan Zhang & Xiaoqiang Cai & C.K. Wong, 2001. "On‐line algorithms for minimizing makespan on batch processing machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 241-258, April.
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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. 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. Averbakh, Igor, 2010. "On-line integrated production-distribution scheduling problems with capacitated deliveries," European Journal of Operational Research, Elsevier, vol. 200(2), pages 377-384, January.
    4. Zhang, Jun & Wang, Xuping & Huang, Kai, 2018. "On-line scheduling of order picking and delivery with multiple zones and limited vehicle capacity," Omega, Elsevier, vol. 79(C), pages 104-115.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Ridouard, Frédéric & Richard, Pascal & Martineau, Patrick, 2008. "On-line scheduling on a batch processing machine with unbounded batch size to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1327-1342, September.

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