IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v22y2019i5d10.1007_s10951-018-0598-5.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-018-0598-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10951-018-0598-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Omri Dover & Dvir Shabtay, 2016. "Single machine scheduling with two competing agents, arbitrary release dates and unit processing times," Annals of Operations Research, Springer, vol. 238(1), pages 145-178, March.
    3. Donatas Elvikis & Vincent T’kindt, 2014. "Two-agent scheduling on uniform parallel machines with min-max criteria," Annals of Operations Research, Springer, vol. 213(1), pages 79-94, February.
    4. 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.
    5. Shi-Sheng Li & Ren-Xia Chen & Qi Feng, 2016. "Scheduling two job families on a single machine with two competitive agents," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 784-799, October.
    6. Du-Juan Wang & Yunqiang Yin & Shuenn-Ren Cheng & T.C.E. Cheng & Chin-Chia Wu, 2016. "Due date assignment and scheduling on a single machine with two competing agents," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1152-1169, February.
    7. Wenchang Luo & Lin Chen & Guochuan Zhang, 2012. "Approximation schemes for two-machine flow shop scheduling with two agents," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 229-239, October.
    8. 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.
    9. Yaodong Ni & Zhaojun Zhao, 2017. "Two-agent scheduling problem under fuzzy environment," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 739-748, March.
    10. 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.
    11. Cheng He & Joseph Y.-T. Leung, 2017. "Two-agent scheduling of time-dependent jobs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 362-377, August.
    12. 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.
    13. Yunqiang Yin & T. C. E. Cheng & Du-Juan Wang & Chin-Chia Wu, 2017. "Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs," Journal of Scheduling, Springer, vol. 20(4), pages 313-335, August.
    14. Omri Dover & Dvir Shabtay, 2016. "Single machine scheduling with two competing agents, arbitrary release dates and unit processing times," Annals of Operations Research, Springer, vol. 238(1), pages 145-178, March.
    15. Nong, Q.Q. & Cheng, T.C.E. & Ng, C.T., 2011. "Two-agent scheduling to minimize the total cost," European Journal of Operational Research, Elsevier, vol. 215(1), pages 39-44, November.
    16. Byung-Cheon Choi & Myoung-Ju Park, 2016. "An Ordered Flow Shop with Two Agents," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-24, October.
    17. Shesh Narayan Sahu & Yuvraj Gajpal & Swapan Debbarma, 2018. "Two-agent-based single-machine scheduling with switchover time to minimize total weighted completion time and makespan objectives," Annals of Operations Research, Springer, vol. 269(1), pages 623-640, October.
    18. 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.
    19. Koulamas, Christos, 2015. "A note on scheduling problems with competing agents and earliness minimization objectives," European Journal of Operational Research, Elsevier, vol. 245(3), pages 875-876.
    20. Ren-Xia Chen & Shi-Sheng Li, 2019. "Two-agent single-machine scheduling with cumulative deterioration," 4OR, Springer, vol. 17(2), pages 201-219, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jsched:v:22:y:2019:i:5:d:10.1007_s10951-018-0598-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.