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The complexity of CO-agent scheduling to minimize the total completion time and total number of tardy jobs

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  • Rubing Chen

    (Zhengzhou University)

  • Jinjiang Yuan

    (Zhengzhou University)

  • Yuan Gao

    (Zhengzhou University)

Abstract

In this paper, we revisit a two-agent scheduling problem on a single machine. In this problem, we have two competing agents A and B, which means that the job set of agent A and the job set of agent B are disjoint. The objective is to minimize the total completion time of agent A, under the constraint that the total number of tardy jobs of agent B is no larger than a given bound. The complexity of this problem was posed as open in Agnetis et al. (Oper Res 52:229–242, 2004). Leung et al. (Oper Res 58:458–469, 2010a, b. https://doi.org/10.1287/opre.1090.0744ec ) showed that the problem is binary NP-hard. However, their NP-hardness proof has a flaw. Here, we present a new NP-hardness proof for this problem. Our research shows that the problem is still NP-hard even if the jobs of agent A have a common processing time.

Suggested Citation

  • Rubing Chen & Jinjiang Yuan & Yuan Gao, 2019. "The complexity of CO-agent scheduling to minimize the total completion time and total number of tardy jobs," Journal of Scheduling, Springer, vol. 22(5), pages 581-593, October.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:5:d:10.1007_s10951-018-0598-5
    DOI: 10.1007/s10951-018-0598-5
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    References listed on IDEAS

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    1. Dorit S. Hochbaum & Ron Shamir, 1991. "Strongly Polynomial Algorithms for the High Multiplicity Scheduling Problem," Operations Research, INFORMS, vol. 39(4), pages 648-653, August.
    2. Joseph Y.-T. Leung & Michael Pinedo & Guohua Wan, 2010. "Competitive Two-Agent Scheduling and Its Applications," Operations Research, INFORMS, vol. 58(2), pages 458-469, April.
    3. C. T. Ng & T. C. E. Cheng & J. J. Yuan, 2006. "A note on the complexity of the problem of two-agent scheduling on a single machine," Journal of Combinatorial Optimization, Springer, vol. 12(4), pages 387-394, December.
    4. Allesandro Agnetis & Pitu B. Mirchandani & Dario Pacciarelli & Andrea Pacifici, 2004. "Scheduling Problems with Two Competing Agents," Operations Research, INFORMS, vol. 52(2), pages 229-242, April.
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    Cited by:

    1. 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.
    2. 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.
    3. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.
    4. 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.
    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. 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.

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