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Optimal on-line algorithms for one batch machine with grouped processing times

Author

Listed:
  • Yang Fang

    (East China University of Science and Technology)

  • Peihai Liu

    (East China University of Science and Technology)

  • Xiwen Lu

    (East China University of Science and Technology)

Abstract

In this paper, we study on-line scheduling problems on a batch machine with the assumption that all jobs have their processing times in [p, (1+φ)p], where p>0 and $\phi=(\sqrt{5}-1)/2$ . Jobs arrive over time. First, we deal with the on-line problem on a bounded batch machine with the objective to minimize makespan. A class of algorithms with competitive ratio $(\sqrt{5}+1)/2$ are given. Then we consider the scheduling on an unbounded batch machine to minimize the time by which all jobs have been delivered, and provide a class of on-line algorithms with competitive ratio $(\sqrt{5}+1)/2$ . The two class of algorithms are optimal for the problems studied here.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9298-6
    DOI: 10.1007/s10878-010-9298-6
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    References listed on IDEAS

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    1. Chung-Yee Lee & Reha Uzsoy & Louis A. Martin-Vega, 1992. "Efficient Algorithms for Scheduling Semiconductor Burn-In Operations," Operations Research, INFORMS, vol. 40(4), pages 764-775, August.
    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. 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.
    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.
    5. 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.
    6. Chung Poon & Wenci Yu, 2005. "A Flexible On-line Scheduling Algorithm for Batch Machine with Infinite Capacity," Annals of Operations Research, Springer, vol. 133(1), pages 175-181, January.
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    Cited by:

    1. 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.
    2. 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.
    3. 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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