IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v74y2019i3d10.1007_s10898-019-00750-9.html
   My bibliography  Save this article

On seeking efficient Pareto optimal points in multi-player minimum cost flow problems with application to transportation systems

Author

Listed:
  • Shuvomoy Das Gupta

    (Thales Canada, Transportation Solutions)

  • Lacra Pavel

    (University of Toronto)

Abstract

In this paper, we propose a multi-player extension of the minimum cost flow problem inspired by a transportation problem that arises in modern transportation industry. We associate one player with each arc of a directed network, each trying to minimize its cost function subject to the network flow constraints. In our model, the cost function can be any general nonlinear function, and the flow through each arc is an integer. We present algorithms to compute efficient Pareto optimal point(s), where the maximum possible number of players (but not all) minimize their cost functions simultaneously. The computed Pareto optimal points are Nash equilibriums if the problem is transformed into a finite static game in normal form.

Suggested Citation

  • Shuvomoy Das Gupta & Lacra Pavel, 2019. "On seeking efficient Pareto optimal points in multi-player minimum cost flow problems with application to transportation systems," Journal of Global Optimization, Springer, vol. 74(3), pages 523-548, July.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:3:d:10.1007_s10898-019-00750-9
    DOI: 10.1007/s10898-019-00750-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-019-00750-9
    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/s10898-019-00750-9?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. Efraim Turban & Jon Outland & David King & Jae Kyu Lee & Ting-Peng Liang & Deborrah C. Turban, 2018. "Electronic Commerce 2018," Springer Texts in Business and Economics, Springer, edition 9, number 978-3-319-58715-8, April.
    2. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    3. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    4. Balachandran Vaidyanathan & Ravindra K. Ahuja, 2010. "Fast Algorithms for Specially Structured Minimum Cost Flow Problems with Applications," Operations Research, INFORMS, vol. 58(6), pages 1681-1696, December.
    5. Shangyao Yan & Yu-Lin Shih & Wang-Tsang Lee, 2011. "A particle swarm optimization-based hybrid algorithm for minimum concave cost network flow problems," Journal of Global Optimization, Springer, vol. 49(4), pages 539-559, April.
    6. Willard I. Zangwill, 1968. "Minimum Concave Cost Flows in Certain Networks," Management Science, INFORMS, vol. 14(7), pages 429-450, March.
    7. Dimitris Bertsimas & Ebrahim Nasrabadi & Sebastian Stiller, 2013. "Robust and Adaptive Network Flows," Operations Research, INFORMS, vol. 61(5), pages 1218-1242, October.
    8. Jorjani, S & Lamar, BW, 1994. "Cash flow management network models with quantity discounting," Omega, Elsevier, vol. 22(2), pages 149-155, March.
    9. David Gamarnik & Devavrat Shah & Yehua Wei, 2012. "Belief Propagation for Min-Cost Network Flow: Convergence and Correctness," Operations Research, INFORMS, vol. 60(2), pages 410-428, April.
    10. Hernández, Salvador & Peeta, Srinivas & Kalafatas, George, 2011. "A less-than-truckload carrier collaboration planning problem under dynamic capacities," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 933-946.
    11. Ling Li, 2014. "Managing Supply Chain and Logistics:Competitive Strategy for a Sustainable Future," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9151, February.
    12. Lee, Haijune & Simin Pulat, P., 1993. "Bicriteria network flow problems: Integer case," European Journal of Operational Research, Elsevier, vol. 66(1), pages 148-157, April.
    Full references (including those not matched with items on IDEAS)

    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. Lai, Minghui & Cai, Xiaoqiang & Li, Xiang, 2017. "Mechanism design for collaborative production-distribution planning with shipment consolidation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 137-159.
    2. Fontes, Dalila B.M.M. & Hadjiconstantinou, Eleni & Christofides, Nicos, 2006. "A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1205-1219, October.
    3. Jenn-Rong Lin & Linda Nozick & Mark Turnquist, 2006. "Strategic design of distribution systems with economies of scale in transportation," Annals of Operations Research, Springer, vol. 144(1), pages 161-180, April.
    4. El Mehdi, Er Raqabi & Ilyas, Himmich & Nizar, El Hachemi & Issmaïl, El Hallaoui & François, Soumis, 2023. "Incremental LNS framework for integrated production, inventory, and vessel scheduling: Application to a global supply chain," Omega, Elsevier, vol. 116(C).
    5. Oliver Stein & Maximilian Volk, 2023. "Generalized Polarity and Weakest Constraint Qualifications in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1156-1190, September.
    6. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    7. Petersen, E. R. & Taylor, A. J., 2001. "An investment planning model for a new North-Central railway in Brazil," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(9), pages 847-862, November.
    8. Agarwal, Y.K. & Aneja, Y.P. & Jayaswal, Sachin, 2022. "Directed fixed charge multicommodity network design: A cutting plane approach using polar duality," European Journal of Operational Research, Elsevier, vol. 299(1), pages 118-136.
    9. Alberto Pajares & Xavier Blasco & Juan Manuel Herrero & Miguel A. Martínez, 2021. "A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization," Mathematics, MDPI, vol. 9(9), pages 1-28, April.
    10. Wu, Dexiang & Wu, Desheng Dash, 2020. "A decision support approach for two-stage multi-objective index tracking using improved lagrangian decomposition," Omega, Elsevier, vol. 91(C).
    11. Joseph Y. J. Chow & Amelia C. Regan, 2011. "Real Option Pricing of Network Design Investments," Transportation Science, INFORMS, vol. 45(1), pages 50-63, February.
    12. Melkote, Sanjay & Daskin, Mark S., 2001. "Capacitated facility location/network design problems," European Journal of Operational Research, Elsevier, vol. 129(3), pages 481-495, March.
    13. Zvi Drezner & Said Salhi, 2002. "Using hybrid metaheuristics for the one‐way and two‐way network design problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(5), pages 449-463, August.
    14. Ospina, Juan P. & Duque, Juan C. & Botero-Fernández, Verónica & Montoya, Alejandro, 2022. "The maximal covering bicycle network design problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 159(C), pages 222-236.
    15. Cortés, Pablo & Muñuzuri, Jesús & Guadix, José & Onieva, Luis, 2013. "Optimal algorithm for the demand routing problem in multicommodity flow distribution networks with diversification constraints and concave costs," International Journal of Production Economics, Elsevier, vol. 146(1), pages 313-324.
    16. David Canca & Belén Navarro-Carmona & Gabriel Villa & Alejandro Zarzo, 2023. "A Multilayer Network Approach for the Bimodal Bus–Pedestrian Line Planning Problem," Mathematics, MDPI, vol. 11(19), pages 1-36, October.
    17. Hark‐Chin Hwang & Wilco van den Heuvel, 2012. "Improved algorithms for a lot‐sizing problem with inventory bounds and backlogging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 244-253, April.
    18. Karla E. Bourland & Candace Arai Yano, 1996. "Lot sizing when yields increase during the production run," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1035-1047, December.
    19. Bernard Gendron & Luis Gouveia, 2017. "Reformulations by Discretization for Piecewise Linear Integer Multicommodity Network Flow Problems," Transportation Science, INFORMS, vol. 51(2), pages 629-649, May.
    20. Li, Yuan & Chen, Haoxun & Prins, Christian, 2016. "Adaptive large neighborhood search for the pickup and delivery problem with time windows, profits, and reserved requests," European Journal of Operational Research, Elsevier, vol. 252(1), pages 27-38.

    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:jglopt:v:74:y:2019:i:3:d:10.1007_s10898-019-00750-9. 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.