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Approximation algorithm for the parallel-machine scheduling problem with release dates and submodular rejection penalties

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Abstract

In this paper, we consider the parallel-machine scheduling problem with release dates and submodular rejection penalties. In this problem, we are given m identical parallel machines and n jobs. Each job has a processing time and a release date. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on one of the m identical parallel machines. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalty of the rejected jobs which is determined by a submodular function. Our main work is to design a 2-approximation algorithm based on the primal-dual framework.

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Acknowledgements

This work was supported by the NSF of China (No. 11971146), the NSF of Hebei Province of China (No. A2019205089, No. A2019205092) and Hebei Province Foundation for Returnees (CL201714).

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Authors and Affiliations

  1. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China

    Hongye Zheng, Suogang Gao, Wen Liu & Bo Hou

  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Weili Wu & Ding-Zhu Du

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  1. Hongye Zheng
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  2. Suogang Gao
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  3. Wen Liu
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  4. Weili Wu
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  5. Ding-Zhu Du
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  6. Bo Hou
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Correspondence to Bo Hou.

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Zheng, H., Gao, S., Liu, W. et al. Approximation algorithm for the parallel-machine scheduling problem with release dates and submodular rejection penalties. J Comb Optim 44, 343–353 (2022). https://doi.org/10.1007/s10878-021-00842-x

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  • DOI: https://doi.org/10.1007/s10878-021-00842-x

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