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Two-agent scheduling problems under rejection budget constraints

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  • Oron, Daniel

Abstract

We study two single machine scheduling problems with two competing agents and the option of rejecting jobs. We seek to minimize the scheduling criterion of one agent under the condition that the maximum completion time of the second agent does not exceed a given upper-bound. Moreover, we assume that jobs are either scheduled or rejected (incurring job-dependent penalties) subject to an upper bound on the total rejection cost. The scheduling objective for the first agent is either the makespan or the total completion time, while that of the second agent is the makespan. As both problems are known to be NP-hard, we develop efficient pseudo-polynomial dynamic programming algorithms to obtain optimal solutions. The algorithms are shown to efficiently solve medium to large size problems through an extensive numerical study.

Suggested Citation

  • Oron, Daniel, 2021. "Two-agent scheduling problems under rejection budget constraints," Omega, Elsevier, vol. 102(C).
    • Handle: RePEc:eee:jomega:v:102:y:2021:i:c:s0305048320306678
    DOI: 10.1016/j.omega.2020.102313
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    11. Hermelin, Danny & Kubitza, Judith-Madeleine & Shabtay, Dvir & Talmon, Nimrod & Woeginger, Gerhard J., 2019. "Scheduling two agents on a single machine: A parameterized analysis of NP-hard problems," Omega, Elsevier, vol. 83(C), pages 275-286.
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    Cited by:

    1. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
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    3. Lingfa Lu & Liqi Zhang, 2023. "Scheduling problems with rejection to minimize the k-th power of the makespan plus the total rejection cost," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-17, August.
    4. Zhang, Zhe & Gong, Xue & Song, Xiaoling & Yin, Yong & Lev, Benjamin & Chen, Jie, 2022. "A column generation-based exact solution method for seru scheduling problems," Omega, Elsevier, vol. 108(C).

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