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A parallel-machine scheduling problem with periodic maintenance under uncertainty

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Abstract

A parallel-machine scheduling problem with preventive maintenance is studied in the paper. Because of the existence of indeterminacy phenomenon, the processing and maintenance time are assume to be uncertain variables. To address these uncertain parameters, two pessimistic value mathematical programming models are developed and the equivalence is proved. The worst-case bound of longest processing time (LPT) rule for the problem under an uncertain environment is obtained. To solve this problem effectively, an improved LPT rule is proposed according to the result of the theoretical analysis. Finally, numerical experiments show that the improved LPT outperforms the LPT in improving the quality of the optimal value and has a less relative error than that of the LPT.

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Acknowledgements

We are grateful to the editor and the anonymous reviewers for their helpful suggestions on an earlier version of this paper. This work is supported by the National Natural Science Foundation of China (No. 61673011).

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Authors and Affiliations

  1. Department of Public Basic Courses, Nanjing Institute of Industry Technology, Nanjing, 210023, Jiangsu, People’s Republic of China

    Jiayu Shen

  2. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, People’s Republic of China

    Yuanguo Zhu

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  1. Jiayu Shen
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  2. Yuanguo Zhu
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Correspondence to Jiayu Shen.

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Shen, J., Zhu, Y. A parallel-machine scheduling problem with periodic maintenance under uncertainty. J Ambient Intell Human Comput 10, 3171–3179 (2019). https://doi.org/10.1007/s12652-018-1032-8

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  • DOI: https://doi.org/10.1007/s12652-018-1032-8

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