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Two-machine job shop scheduling with optional job rejection

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Abstract

We investigate a two-machine job shop scheduling problem with optional job rejection. The target is to look for a feasible schedule for the set of accepted jobs so that the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs is minimized. We propose an exact pseudo-polynomial dynamic programming algorithm, a greedy \(\frac{\sqrt{5}+1}{2}\)-approximation algorithm, an LP-based \(\frac{e}{e-1}\)-approximation algorithm, and a fully polynomial time approximation scheme to solve it. We demonstrate that the proportionate case is \(\mathcal{N}\mathcal{P}\)-hard and provide an \(O(n^2)\)-time algorithm for the agreeable case.

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Acknowledgements

We would like to thank the two anonymous reviewers for their helpful comments and suggestions on an earlier version of this paper. This research was supported by the Key Research Projects of Henan Higher Education Institutions (24A110014).

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  1. School of Mathematics and Information Science, Zhongyuan University of Technology, Zhengzhou, 450007, People’s Republic of China

    Ren-Xia Chen & Shi-Sheng Li

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  1. Ren-Xia Chen
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Chen, RX., Li, SS. Two-machine job shop scheduling with optional job rejection. Optim Lett 18, 1593–1618 (2024). https://doi.org/10.1007/s11590-023-02077-7

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