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Online batch scheduling with kind release times and incompatible families to minimize makespan

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Abstract

This paper studies online scheduling of jobs with incompatible families on a single unbounded batch machine under the KRT environment, where jobs arrive over time and “KRT” means that in the online setting no jobs can be released when the machine is busy. The goal is to determine a feasible schedule to minimize the makespan. We provide a best online algorithm with a competitive ratio of \(1+\frac{\sqrt{f^{2}-f+1}-1}{f}\), where f is the number of job families.

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Acknowledgements

The authors would like to thank the Area-in-Chief and the anonymous referee for their comments and suggestions. This research was supported in part NSFC (Nos. 11501279, 11401605, 11401604 and 11671188) and NSF of Henan Province (No. 152300410217).

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Authors and Affiliations

  1. School of Mathematical Sciences, Luoyang Normal University, Luoyang, 471022, Henan, People’s Republic of China

    Wenjie Li

  2. Department of Information and Computation Science, Zhongyuan University of Technology, Zhengzhou, 450007, Henan, People’s Republic of China

    Shisheng Li & Qi Feng

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  1. Wenjie Li
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  2. Shisheng Li
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  3. Qi Feng
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Correspondence to Wenjie Li.

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Li, W., Li, S. & Feng, Q. Online batch scheduling with kind release times and incompatible families to minimize makespan. Optim Lett 12, 301–310 (2018). https://doi.org/10.1007/s11590-017-1113-1

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  • DOI: https://doi.org/10.1007/s11590-017-1113-1

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