IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v294y2021i1p29-41.html
   My bibliography  Save this article

Nash equilibrium solutions in multi-agent project scheduling with milestones

Author

Listed:
  • Šůcha, Přemysl
  • Agnetis, Alessandro
  • Šidlovský, Marko
  • Briand, Cyril

Abstract

This paper addresses a project scheduling environment in which the activities are partitioned among a set of agents. The project owner is interested in completing the project as soon as possible. Therefore, she/he defines rewards and penalties to stimulate the agents to complete the project faster. The project owner offers a per-day reward for early project completion and defines intermediate project milestones to be met within specific due dates, with associated per-day penalties. Each agent can, therefore, decide the duration of her/his activities, taking into account linear activity crashing costs, the reward for early project completion, and the penalty arising from violating milestone due-dates. We consider Nash equilibria, i.e., situations in which no agent has an interest in individually changing the duration of any of her/his activities, and in particular, the problem of finding a minimum-makespan equilibrium. This problem is known to be NP-hard, and in this paper, we (i) propose a new and efficient exact algorithmic approach for finding the minimum-makespan equilibrium and (ii) through an extensive computational campaign we evaluate the role played by milestones in driving the project towards the owner’s goal.

Suggested Citation

  • Šůcha, Přemysl & Agnetis, Alessandro & Šidlovský, Marko & Briand, Cyril, 2021. "Nash equilibrium solutions in multi-agent project scheduling with milestones," European Journal of Operational Research, Elsevier, vol. 294(1), pages 29-41.
    • Handle: RePEc:eee:ejores:v:294:y:2021:i:1:p:29-41
    DOI: 10.1016/j.ejor.2021.01.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721000400
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.01.023?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. Kolisch, Rainer & Sprecher, Arno & Drexl, Andreas, 1992. "Characterization and generation of a general class of resource-constrained project scheduling problems: Easy and hard instances," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 301, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Rodica Brânzei & Giulio Ferrari & Vito Fragnelli & Stef Tijs, 2002. "Two Approaches to the Problem of Sharing Delay Costs in Joint Projects," Annals of Operations Research, Springer, vol. 109(1), pages 359-374, January.
    3. Cyril Briand & Sandra Ulrich Ngueveu & Přemysl Šůcha, 2017. "Finding an optimal Nash equilibrium to the multi-agent project scheduling problem," Journal of Scheduling, Springer, vol. 20(5), pages 475-491, October.
    4. Averbakh, Igor, 2010. "Nash equilibria in competitive project scheduling," European Journal of Operational Research, Elsevier, vol. 205(3), pages 552-556, September.
    5. Dominik Kress & Sebastian Meiswinkel & Erwin Pesch, 2018. "Mechanism design for machine scheduling problems: classification and literature overview," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 583-611, July.
    6. G. B. Dantzig & D. R. Fulkerson & S. M. Johnson, 1959. "On a Linear-Programming, Combinatorial Approach to the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 7(1), pages 58-66, February.
    7. Bergantiños, Gustavo & Lorenzo, Leticia, 2019. "How to apply penalties to avoid delays in projects," European Journal of Operational Research, Elsevier, vol. 275(2), pages 608-620.
    8. Oğuzhan Ahmet Arık & Erkan Köse & Jeffrey Yi-Lin Forrest, 2019. "Project Staff Scheduling with Theory of Coalition," Group Decision and Negotiation, Springer, vol. 28(4), pages 827-847, August.
    9. Giuseppe Confessore & Stefano Giordani & Silvia Rismondo, 2007. "A market-based multi-agent system model for decentralized multi-project scheduling," Annals of Operations Research, Springer, vol. 150(1), pages 115-135, March.
    10. Steve Phillips, Jr. & Mohamed I. Dessouky, 1977. "Solving the Project Time/Cost Tradeoff Problem Using the Minimal Cut Concept," Management Science, INFORMS, vol. 24(4), pages 393-400, December.
    11. Brucker, Peter & Drexl, Andreas & Mohring, Rolf & Neumann, Klaus & Pesch, Erwin, 1999. "Resource-constrained project scheduling: Notation, classification, models, and methods," European Journal of Operational Research, Elsevier, vol. 112(1), pages 3-41, January.
    12. Alessandro Agnetis & Cyril Briand & Sandra Ulrich Ngueveu & Přemysl Šůcha, 2020. "Price of anarchy and price of stability in multi-agent project scheduling," Annals of Operations Research, Springer, vol. 285(1), pages 97-119, February.
    13. W Herroelen & B De Reyck, 1999. "Phase transitions in project scheduling," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(2), pages 148-156, February.
    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.

    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. Alessandro Agnetis & Cyril Briand & Sandra Ulrich Ngueveu & Přemysl Šůcha, 2020. "Price of anarchy and price of stability in multi-agent project scheduling," Annals of Operations Research, Springer, vol. 285(1), pages 97-119, February.
    2. J. C. Gonçalves-Dosantos & I. García-Jurado & J. Costa, 2020. "Sharing delay costs in stochastic scheduling problems with delays," 4OR, Springer, vol. 18(4), pages 457-476, December.
    3. Hartmann, Sönke & Briskorn, Dirk, 2010. "A survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 1-14, November.
    4. Hartmann, Sönke & Briskorn, Dirk, 2008. "A survey of variants and extensions of the resource-constrained project scheduling problem," Working Paper Series 02/2008, Hamburg School of Business Administration (HSBA).
    5. V. Van Peteghem & M. Vanhoucke, 2009. "Using Resource Scarceness Characteristics to Solve the Multi-Mode Resource-Constrained Project Scheduling Problem," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 09/595, Ghent University, Faculty of Economics and Business Administration.
    6. D. Debels & M. Vanhoucke, 2006. "The impact of various activity assumptions on the lead-time and resource utilization of resource-constrained projects," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/385, Ghent University, Faculty of Economics and Business Administration.
    7. Rahman Torba & Stéphane Dauzère-Pérès & Claude Yugma & Cédric Gallais & Juliette Pouzet, 2024. "Solving a real-life multi-skill resource-constrained multi-project scheduling problem," Annals of Operations Research, Springer, vol. 338(1), pages 69-114, July.
    8. Xiaowei Lin & Jing Zhou & Lianmin Zhang & Yinlian Zeng, 2021. "Revenue sharing for resource reallocation among project activity contractors," Annals of Operations Research, Springer, vol. 301(1), pages 121-141, June.
    9. Servranckx, Tom & Vanhoucke, Mario, 2019. "A tabu search procedure for the resource-constrained project scheduling problem with alternative subgraphs," European Journal of Operational Research, Elsevier, vol. 273(3), pages 841-860.
    10. Browning, Tyson R. & Yassine, Ali A., 2010. "Resource-constrained multi-project scheduling: Priority rule performance revisited," International Journal of Production Economics, Elsevier, vol. 126(2), pages 212-228, August.
    11. Kolisch, R. & Padman, R., 2001. "An integrated survey of deterministic project scheduling," Omega, Elsevier, vol. 29(3), pages 249-272, June.
    12. Cyril Briand & Sandra Ulrich Ngueveu & Přemysl Šůcha, 2017. "Finding an optimal Nash equilibrium to the multi-agent project scheduling problem," Journal of Scheduling, Springer, vol. 20(5), pages 475-491, October.
    13. Vanhoucke, M., 2006. "A scatter search procedure for maximizing the net present value of a project under renewable resource constraints," Vlerick Leuven Gent Management School Working Paper Series 2006-40, Vlerick Leuven Gent Management School.
    14. Gómez Sánchez, Mariam & Lalla-Ruiz, Eduardo & Fernández Gil, Alejandro & Castro, Carlos & Voß, Stefan, 2023. "Resource-constrained multi-project scheduling problem: A survey," European Journal of Operational Research, Elsevier, vol. 309(3), pages 958-976.
    15. Wuliang Peng & Jiali lin & Jingwen Zhang & Liangwei Chen, 2022. "A bi-objective hierarchical program scheduling problem and its solution based on NSGA-III," Annals of Operations Research, Springer, vol. 308(1), pages 389-414, January.
    16. Buddhakulsomsiri, Jirachai & Kim, David S., 2006. "Properties of multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting," European Journal of Operational Research, Elsevier, vol. 175(1), pages 279-295, November.
    17. Messelis, Tommy & De Causmaecker, Patrick, 2014. "An automatic algorithm selection approach for the multi-mode resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 233(3), pages 511-528.
    18. He, Yukang & Jia, Tao & Zheng, Weibo, 2023. "Tabu search for dedicated resource-constrained multiproject scheduling to minimise the maximal cash flow gap under uncertainty," European Journal of Operational Research, Elsevier, vol. 310(1), pages 34-52.
    19. Debels, D. & Vanhoucke, M., 2006. "Meta-Heuristic resource constrained project scheduling: solution space restrictions and neighbourhood extensions," Vlerick Leuven Gent Management School Working Paper Series 2006-18, Vlerick Leuven Gent Management School.
    20. Estévez-Fernández, Arantza, 2012. "A game theoretical approach to sharing penalties and rewards in projects," European Journal of Operational Research, Elsevier, vol. 216(3), pages 647-657.

    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:eee:ejores:v:294:y:2021:i:1:p:29-41. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.