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Single-machine online scheduling of jobs with non-delayed processing constraint

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Abstract

This paper introduces a new environment of online scheduling in which jobs are scheduled under the non-delayed processing (NDP) constraint, where NDP means that the available jobs cannot be delayed for processing when some machine is idle. We study in this paper the single-machine online scheduling to minimize the maximum weighted completion time (\({\textit{WC}}_{\mathrm{max}}\)) or the maximum delivery completion time (\(L_{\mathrm{max}}\)) under the NDP constraint. For the first problem, we establish a lower bound 2 and provide an online algorithm which has a competitive ratio of \((3+\sqrt{5})/2\approx 2.618\). We present a 3/2-competitive best possible online algorithm for the second problem.

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Acknowledgements

The authors would like to thank the associate editor and four anonymous referees for their comments and suggestions. This work was supported by NSFC (Nos. 11701148, 12071442, 11501279) and the Young Backbone Teachers of Luoyang Normal University (2018XJGGJS-10) and Henan Colleges (2019GGJS202).

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Authors and Affiliations

  1. School of Mathematical Sciences, Luoyang Normal University, Luoyang, 471934, Henan, People’s Republic of China

    Wenjie Li

  2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan, People’s Republic of China

    Jinjiang Yuan

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  1. Wenjie Li
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  2. Jinjiang Yuan
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Correspondence to Wenjie Li.

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Li, W., Yuan, J. Single-machine online scheduling of jobs with non-delayed processing constraint. J Comb Optim 41, 830–843 (2021). https://doi.org/10.1007/s10878-021-00722-4

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