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Single-Machine Scheduling with Step-Deteriorating Jobs and Rejection

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Abstract

In this paper, we consider the single-machine scheduling with step-deteriorating jobs and rejection. Each job is either rejected by paying a rejection penalty, or accepted and processed on the single machine, and the actual processing time of each accepted job is a step function of its starting time and the common deteriorating date. The objective is to minimize the makespan of the accepted jobs plus the total penalty of the rejected jobs. For the case of common deteriorating penalty, we first show that the problem is NP-hard in the ordinary sense. Then we present two pseudo-polynomial algorithms and a 2-approximation algorithm. Furthermore, we propose a fully polynomial time approximation scheme. For the case of common normal processing time, we present two pseudo-polynomial time algorithms, a 2-approximation algorithm and a fully polynomial time approximation scheme.

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Acknowledgements

We thank the review team for their helpful comments on an earlier version of our paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    Fan-Yu Kong, Cui-Xia Miao, Yu-Jia Huo & Jia-Xin Song

  2. Institute of Operations Research, Qufu Normal University, Rizhao, 276826, Shandong, China

    Yu-Zhong Zhang

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  1. Fan-Yu Kong
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  2. Cui-Xia Miao
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  3. Yu-Jia Huo
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  4. Jia-Xin Song
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  5. Yu-Zhong Zhang
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Contributions

All authors contributed to the design of algorithms and the theory analysis of the complexity and the performance of approximation algorithms.

Corresponding author

Correspondence to Cui-Xia Miao.

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The authors declare that there is no conflict of interests regarding the publication of this paper.

Additional information

This research was supported by the National Natural Science Foundation of China (Nos. 12271295 and 12001313) and the Provincial Natural Science Foundation of Shandong (No. ZR2022MA019).

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Kong, FY., Miao, CX., Huo, YJ. et al. Single-Machine Scheduling with Step-Deteriorating Jobs and Rejection. J. Oper. Res. Soc. China (2023). https://doi.org/10.1007/s40305-023-00481-5

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  • DOI: https://doi.org/10.1007/s40305-023-00481-5

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