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Optimal algorithm for semi-online scheduling on two machines under GoS levels

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Abstract

Recently, Liu et al. (J Combin Optim 21:138–149, 2011) studied the semi-online scheduling problem on two machines under a grade of service provision. As the sum of jobs’ processing times \(\varSigma \) is known in advance and the processing times are bounded by an interval \([1,\alpha ]\) where \(1< \alpha <2\), they presented an algorithm which is \(\frac{1+\alpha }{2}\)-competitive when \(\varSigma \ge \frac{2\alpha }{\alpha -1}\). In this paper, we give a modified algorithm which is shown to be optimal for arbitrary \(\alpha \) and \(\varSigma \).

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Acknowledgments

This work is supported by National Natural Science Foundation of China under Grants 71071123, 60921003 and 71371129 and Program for Changjiang Scholars and Innovative Research Team in University under Grant IRT1173.

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Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, 610065, China

    Taibo Luo & Yinfeng Xu

  2. State Key Lab for Manufacturing Systems Engineering, Xi’an, 710049, China

    Yinfeng Xu

Authors
  1. Taibo Luo
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  2. Yinfeng Xu
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Correspondence to Yinfeng Xu.

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Luo, T., Xu, Y. Optimal algorithm for semi-online scheduling on two machines under GoS levels. Optim Lett 10, 207–213 (2016). https://doi.org/10.1007/s11590-014-0838-3

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  • DOI: https://doi.org/10.1007/s11590-014-0838-3

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