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Single Machine Scheduling with Rejection to Minimize the Weighted Makespan

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Algorithmic Aspects in Information and Management (AAIM 2021)

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Abstract

In this paper, we consider the single machine scheduling problem with rejection to minimize the weighted makespan. In this problem, each job is either accepted and processed on the single machine, or is rejected by paying a rejection cost. The objective is to minimize the sum of the weighted makespan (the maximum weighted completion time) of accepted jobs and the total rejection cost of rejected jobs. We first show that this problem is binary NP-hard and then propose a pseudo-polynomial dynamic programming algorithm. Furthermore, based on the relaxed integral programming, we propose a 2-approximation algorithm for this problem. Finally, based on the dynamic programming algorithm and the vector trimming technique, we also obtain a fully polynomial-time approximation scheme (FPTAS) for this problem.

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Acknowledgments

This research was supported by NSFCs (11901168, 11971443 and 11771406).

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Authors and Affiliations

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

    Lingfa Lu

  2. College of Information and Management Science, Henan Agricultural University, Zhengzhou, Henan, People’s Republic of China

    Liqi Zhang

  3. Department of Administrative Management, Jinan University, Guangzhou, Guangdong, People’s Republic of China

    Jinwen Ou

Authors
  1. Lingfa Lu
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  2. Liqi Zhang
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  3. Jinwen Ou
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Corresponding author

Correspondence to Lingfa Lu .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

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Lu, L., Zhang, L., Ou, J. (2021). Single Machine Scheduling with Rejection to Minimize the Weighted Makespan. In: Wu, W., Du, H. (eds) Algorithmic Aspects in Information and Management. AAIM 2021. Lecture Notes in Computer Science(), vol 13153. Springer, Cham. https://doi.org/10.1007/978-3-030-93176-6_9

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  • DOI: https://doi.org/10.1007/978-3-030-93176-6_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-93175-9

  • Online ISBN: 978-3-030-93176-6

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