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Online-List Scheduling on a Single Bounded Parallel-Batch Machine to Minimize Makespan

Author

Listed:
  • Wenhua Li

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, People's Republic of China)

  • Jie Gao

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, People's Republic of China)

  • Jinjiang Yuan

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, People's Republic of China)

Abstract

In this paper, we consider the online-list scheduling on a single bounded parallel-batch machine to minimize makespan. In the problem, the jobs arrive online over list. The first unassigned job in the list should be assigned to a batch before the next job is released. Each batch can accommodate up to b jobs. For b = 2, we establish a lower bound 1 + γ of competitive ratio and provide an online algorithm with a competitive ratio of $\frac{\sqrt{5}+1}{2}$, where γ is the positive root of γ(γ + 1)2 = 1. For b = 3, we establish a lower bound 1 + α of competitive ratio and provide an online algorithm with a competitive ratio of 2, where α is the positive root of the equation (1 + α)(1 + α2) = 2.

Suggested Citation

  • Wenhua Li & Jie Gao & Jinjiang Yuan, 2015. "Online-List Scheduling on a Single Bounded Parallel-Batch Machine to Minimize Makespan," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-15.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:04:n:s0217595915500281
    DOI: 10.1142/S0217595915500281
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