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An on-line scheduling problem of parallel machines with common maintenance time

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Abstract

In this paper, the authors consider an on-line scheduling problem of m (m ≥ 3) identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive ratio \(4 - \tfrac{1} {m} \). In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is \(\tfrac{{10}} {3} \).

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Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, Zhengzhou, 450001, China

    Qi Feng, Wenjie Li, Weiping Shang & Yuhua Cai

  2. College of Science, Zhongyuan University of Technology, Zhengzhou, 450007, China

    Qi Feng

Authors
  1. Qi Feng
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  2. Wenjie Li
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  3. Weiping Shang
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  4. Yuhua Cai
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Corresponding author

Correspondence to Wenjie Li.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant Nos. 11271338, 11171313, 61070229, 10901144, 11001117, and supported by the Ph.D. Programs Foundation of Ministry of Education of China under Grant No. 20111401110005, and the Henan Province Natural Science Foundation under Grant No. 112300410047.

This paper was recommended for publication by Editor ZHANG Hanqin.

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Feng, Q., Li, W., Shang, W. et al. An on-line scheduling problem of parallel machines with common maintenance time. J Syst Sci Complex 26, 201–208 (2013). https://doi.org/10.1007/s11424-013-0335-2

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  • DOI: https://doi.org/10.1007/s11424-013-0335-2

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