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Semi-On-Line Scheduling Problem For Maximizing The Minimum Machine Completion Time On Three Special Uniform Machines

Author

Listed:
  • RUN-ZI LUO

    (Mathematics Department, Shanghai University, Shanghai 200444, P. R. China)

  • SHI-JIE SUN

    (Mathematics Department, Shanghai University, Shanghai 200444, P. R. China)

Abstract

In this paper, we investigate a semi-on-line version for a special case of three machinesM1,M2,M3where the processing time of the largest job is known in advance. A speedsi(s1= s2= 1, 1 ≤ s3= s)is associated with machineMi. Our goal is to maximize theCmin— the minimum workload of three machines. We give aCmin3algorithm and prove its competitive ratio is$\max\!\big\{2,\frac{3s+2}{2+s}\big\}$and the algorithm is the best possible for1 ≤ s ≤ 2. We also claim the competitive ratio of algorithmCmin3is tight.

Suggested Citation

  • Run-Zi Luo & Shi-Jie Sun, 2005. "Semi-On-Line Scheduling Problem For Maximizing The Minimum Machine Completion Time On Three Special Uniform Machines," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 229-237.
    • Handle: RePEc:wsi:apjorx:v:22:y:2005:i:02:n:s0217595905000558
    DOI: 10.1142/S0217595905000558
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