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Single machine batch scheduling with two non-disjoint agents and splitable jobs

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Abstract

We investigate the scheduling problem on a single bounded parallel-batch machine where jobs belong to two non-disjoint agents (called agent A and agent B) and are of equal length but different size. Each job’s size can be arbitrarily split into two parts and processed in the consecutive batches. It is permitted to process the jobs from different agents in a common batch. We show that it is unary NP-hard for the problem of minimizing the total weighted completion time of the jobs of agent A subject to the maximum cost of the jobs of agent B being upper bounded by a given threshold. For the case of the jobs of agent A having identical weights, we study the version of Pareto problem, and give a polynomial-time algorithm to generate all Pareto optimal points and a Pareto optimal schedule corresponding to each Pareto optimal point.

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Acknowledgements

This research was supported in part by NSFC under Grant Nos. 11671368 and 11771406.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan, People’s Republic of China

    Zhichao Geng

  2. Henan College of Transportation, Zhengzhou, 450001, Henan, People’s Republic of China

    Jiayu Liu

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  1. Zhichao Geng
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  2. Jiayu Liu
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Correspondence to Zhichao Geng.

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Geng, Z., Liu, J. Single machine batch scheduling with two non-disjoint agents and splitable jobs. J Comb Optim 40, 774–795 (2020). https://doi.org/10.1007/s10878-020-00626-9

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  • DOI: https://doi.org/10.1007/s10878-020-00626-9

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