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An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown

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Abstract

We consider a semi-online scheduling problem on a single machine with an unexpected breakdown period. In the problem, each job has a processing time and a subsequent delivery time. All these data are known in the beginning. The scheduler has to determine a sequence S of these jobs for processing. After S is given, a machine unavailability period may occur where its starting time and length are not known in advance. The objective is to minimize the time by which all jobs are delivered. We present an online algorithm with a competitive ratio of \(\frac{\sqrt{5}+1}{2}\approx 1.618\), which improves the previously known algorithm with \(\frac{2+\sqrt{2}}{2}\approx 1.707\)-competitive.

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Acknowledgements

We would like to thank the associate editor and anonymous referees for their constructive comments and kind suggestions. This work was supported by NSF-Jiangsu (BK20130169) and NSFC (61573362).

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Ji Tian, Yan Zhou & Ruyan Fu

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  1. Ji Tian
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  2. Yan Zhou
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  3. Ruyan Fu
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Correspondence to Ruyan Fu.

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Tian, J., Zhou, Y. & Fu, R. An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown. J Comb Optim 40, 170–180 (2020). https://doi.org/10.1007/s10878-020-00572-6

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  • DOI: https://doi.org/10.1007/s10878-020-00572-6

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