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Single machine scheduling with two competing agents and equal job processing times

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  • Oron, Daniel
  • Shabtay, Dvir
  • Steiner, George

Abstract

We study various two-agent scheduling problems on a single machine with equal job processing times. The equal processing time assumption enables us to design new polynomial-time or faster-than-known optimization algorithms for many problems. We prove, however, that there exists a subset of problems for which the computational complexity remains NP-hard. The set of hard problems includes different variations where the objective functions of the two agents are either minimizing the weighted sum of completion times or the weighted number of tardy jobs. For these problems, we present pseudo-polynomial time algorithms.

Suggested Citation

  • Oron, Daniel & Shabtay, Dvir & Steiner, George, 2015. "Single machine scheduling with two competing agents and equal job processing times," European Journal of Operational Research, Elsevier, vol. 244(1), pages 86-99.
    • Handle: RePEc:eee:ejores:v:244:y:2015:i:1:p:86-99
    DOI: 10.1016/j.ejor.2015.01.003
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    References listed on IDEAS

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    Cited by:

    1. Zhang, Xingong, 2021. "Two competitive agents to minimize the weighted total late work and the total completion time," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    2. Baruch Mor & Gur Mosheiov, 2016. "Minimizing maximum cost on a single machine with two competing agents and job rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1524-1531, December.
    3. Phosavanh, Johnson & Oron, Daniel, 2024. "Two-agent single-machine scheduling with a rate-modifying activity," European Journal of Operational Research, Elsevier, vol. 312(3), pages 866-876.
    4. Ruyan He & Jinjiang Yuan, 2020. "Two-Agent Preemptive Pareto-Scheduling to Minimize Late Work and Other Criteria," Mathematics, MDPI, vol. 8(9), pages 1-18, September.
    5. Wan, Long & Mei, Jiajie & Du, Jiangze, 2021. "Two-agent scheduling of unit processing time jobs to minimize total weighted completion time and total weighted number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 290(1), pages 26-35.
    6. Shi-Sheng Li & Ren-Xia Chen, 2023. "Competitive two-agent scheduling with release dates and preemption on a single machine," Journal of Scheduling, Springer, vol. 26(3), pages 227-249, June.
    7. 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.
    8. Enrique Gerstl & Baruch Mor & Gur Mosheiov, 2017. "Scheduling with two competing agents to minimize total weighted earliness," Annals of Operations Research, Springer, vol. 253(1), pages 227-245, June.
    9. Shi-Sheng Li & Jin-Jiang Yuan, 2020. "Single-machine scheduling with multi-agents to minimize total weighted late work," Journal of Scheduling, Springer, vol. 23(4), pages 497-512, August.
    10. Fan, B.Q. & Cheng, T.C.E., 2016. "Two-agent scheduling in a flowshop," European Journal of Operational Research, Elsevier, vol. 252(2), pages 376-384.
    11. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    12. Qi Feng & Shisheng Li, 2022. "Algorithms for Multi-Customer Scheduling with Outsourcing," Mathematics, MDPI, vol. 10(9), pages 1-12, May.
    13. Wenjie Li & Jinjiang Yuan, 2021. "Single-machine online scheduling of jobs with non-delayed processing constraint," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 830-843, May.
    14. Zhang Xingong & Wang Yong, 2017. "Two-agent scheduling problems on a single-machine to minimize the total weighted late work," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 945-955, April.
    15. Oron, Daniel, 2021. "Two-agent scheduling problems under rejection budget constraints," Omega, Elsevier, vol. 102(C).
    16. Yuan Gao & Jinjiang Yuan & C. T. Ng & T. C. E. Cheng, 2022. "Pareto-scheduling with family jobs or ND-agent on a parallel-batch machine to minimize the makespan and maximum cost," 4OR, Springer, vol. 20(2), pages 273-287, June.
    17. Zhijun Xu & Dehua Xu, 2018. "Single-machine scheduling with workload-dependent tool change durations and equal processing time jobs to minimize total completion time," Journal of Scheduling, Springer, vol. 21(4), pages 461-482, August.
    18. Yuan Zhang & Jinjiang Yuan & Chi To Ng & Tai Chiu E. Cheng, 2021. "Pareto‐optimization of three‐agent scheduling to minimize the total weighted completion time, weighted number of tardy jobs, and total weighted late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 378-393, April.
    19. Qiulan Zhao & Jinjiang Yuan, 2020. "Bicriteria scheduling of equal length jobs on uniform parallel machines," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 637-661, April.
    20. Ruyan He & Jinjiang Yuan & C. T. Ng & T. C. E. Cheng, 2021. "Two-agent preemptive Pareto-scheduling to minimize the number of tardy jobs and total late work," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 504-525, February.

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