Skip to main content
SpringerLink
Log in

Competitive Resource Allocation Among Urban Congestion Areas in a Modern Big City

  • Published:
Journal of the Operations Research Society of China Aims and scope Submit manuscript

Abstract

The continuing growth of modern big cities leads to their spatial expansion and the emergence of new road connections and urban areas. Areas where large transportation flows of pedestrians, passengers, and drivers come together create demand points, which attract business companies that strive to allocate their resources in the most sought-after places. However, the law of supply and demand restrains companies from allocating all their resources solely in the most popular congestion areas since the more valuable an urban area, the higher the cost to be paid for a resource unit allocation there. As a result, companies act in a non-cooperative manner and try to minimize their own overall costs when allocating resources across available commercial areas in a big city. Non-cooperative behavior of companies leads to the problem of Nash equilibrium search in the game of competing entrepreneurs. In this paper, we study the corresponding resource allocation game under affine cost functions and obtain Nash equilibrium strategies in explicit form. These findings allow us to develop a simple procedure for computing Nash equilibria in the game of companies allocating their resources among urban congestion areas. The computational study demonstrates the dependence of the average price for resource allocation on the number of players and their resource volumes. The outcome of the paper contributes to flow theory and seems to be fresh and useful for managers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Algorithm 2
Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Bennington, G., Lubore, S.: Resource allocation for transportation. Naval Res. Logist. Q. 17(4), 471–484 (1970)

    Article  Google Scholar 

  2. Mills, E.S.: Markets and efficient resource allocation in urban areas. Swed. J. Econ. 74(1), 100–113 (1972)

    Article  Google Scholar 

  3. Zargayouna, M., Balbo, F., Ndiaye, K.: Generic model for resource allocation in transportation. Application to urban parking management. Transp. Res. Part C 71, 538–554 (2016)

    Article  Google Scholar 

  4. Gonzales, E.J., Geroliminis, N., Cassidy, M.J., Daganzo, C.F.: On the allocation of city space to multiple transport modes. Transp. Plan. Technol. 33(8), 643–656 (2010)

    Article  Google Scholar 

  5. Feng, C.M., Hsieh, C.H.: Effect of resource allocation policies on urban transport diversity. Comput.-Aided Civ. Infrastruct. Eng. 24, 525–533 (2009)

    Article  Google Scholar 

  6. Feng, C.M., Hsieh, C.H.: Resource allocation for sustainable urban transit from a transport diversity perspective. Sustainability 1, 960–977 (2009)

    Article  Google Scholar 

  7. Shariat, A., Babaei, M.: Optimal resource allocation in urban transportation networks considering capacity reliability and connectivity reliability: A multi-objective approach. Int. J. Civ. Eng. 11(1), 33–42 (2013)

    Google Scholar 

  8. Zakharov, V.V., Krylatov, AYu.: Competitive routing of traffic flows by navigation providers. Autom. Remote Control 77(1), 179–189 (2016)

    Article  MathSciNet  Google Scholar 

  9. Holzapfel, A., Kuhn, H., Sternbeck, M.G.: Product allocation to different types of distribution center in retail logistics networks. Eur. J. Oper. Res. 264(3), 948–966 (2018)

    Article  MathSciNet  Google Scholar 

  10. Gupta, A., Pachar, N., Jain, A., Govindan, K., Jha, P.C.: Resource reallocation strategies for sustainable efficiency improvement of retail chains. J. Retail. Consum. Serv. 73, 103309 (2023)

    Article  Google Scholar 

  11. Soleimanynanadegany, A., Hassan, A., Galankashi, M.R.: Product allocation of warehousing and cross docking: a genetic algorithm approach. Int. J. Serv. Oper. Manag. 27(2), 239–261 (2017)

    Google Scholar 

  12. Xu, D., Zhang, C.W., Miao, Z., Cheung, R.K.: A flow allocation strategy for routing over multiple flow classes with an application to air cargo terminals. Comput. Oper. Res. 51, 1–10 (2014)

    Article  ADS  Google Scholar 

  13. Elhedhli, S., Hu, F.X.: Hub-and-spoke network design with congestion. Comput. Oper. Res. 32(6), 1615–1632 (2005)

    Article  Google Scholar 

  14. Flores-Fillol, R.: Congested hubs. Transp. Res. Part B Methodol. 44(3), 358–370 (2010)

    Article  Google Scholar 

  15. Patriksson, M.: A survey on the continuous nonlinear resource allocation problem. Eur. J. Oper. Res. 185(1), 1–46 (2008)

    Article  MathSciNet  Google Scholar 

  16. Ziegler, H.: Solving certain singly constrained convex optimization problems in production planning. Oper. Res. Lett. 1, 246–252 (1982)

    Article  MathSciNet  Google Scholar 

  17. Bitran, G.R., Hax, A.C.: On the design of hierarchical production planning systems. Decis. Sci. 8, 28–55 (1977)

    Article  Google Scholar 

  18. Zipkin, P.H.: Simple ranking methods for allocation of one resource. Manage. Sci. 26, 34–43 (1980)

    Article  MathSciNet  Google Scholar 

  19. Ibaraki, T., Katoh, N.: Resource Allocation Problems: Algorithmic Approaches Foundations of Computing Series. The MIT Press, Cambridge (1988)

    Google Scholar 

  20. Pardalos, P., Kovoor, N.: An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds. Math. Program. 46, 321–328 (1990)

    Article  MathSciNet  Google Scholar 

  21. Katoh, N., Ibaraki, T.: Resource allocation problems. In: Du, D.-Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, vol. 2, pp. 159–260. Kluwer Academic Publishers, Amsterdam (1998)

    Google Scholar 

  22. Johansson, B., Johansson, M.: Distributed non-smooth resource allocation over a network. In: Proceedings of the 48h IEEE Conference on Decision and Control jointly with 2009 28th Chinese Control Conference, pp. 1678-1683 (2009)

  23. Orda, A., Rom, R., Shimkin, N.: Competitive routing in multiuser communication networks. IEEE/ACM Trans. Netw. 1(5), 510–521 (1993)

    Article  Google Scholar 

  24. Altman, E., Kameda, H.: Equilibria for multiclass routing in multi-agent networks. In: Proceedings of the 40th IEEE Conference on Decision and Control, 1 pp. 604-609 (2001)

  25. Altman, E., Basar, T., Jimenez, T., Shimkin, N.: Competitive routing in networks with polynomial costs. IEEE Trans. Autom. Control 47(1), 92–96 (2002)

    Article  MathSciNet  Google Scholar 

  26. Altman, E., Wynter, L.: Eguilibrium, games, and pricing in transportation and telecommunication networks. Netw. Spat. Econ. 4, 7–21 (2004)

    Article  Google Scholar 

  27. Altman, E., Combes, R., Altman, Z., Sorin, S.: Routing games in the many players regime. In: Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools, pp. 525–527 (2011)

  28. Brun, O., Prabhu, B.J., Seregina, T.: On the convergence of the best-response algorithm in routing games. In: Proceedings of the 7th International Conference on Performance Evaluation Methodologies and Tools, pp. 136–44 (2013)

  29. Krylatov, AYu., Zakharov, V.V., Malygin, I.G.: Competitive traffic assignment in road networks. Transp. Telecommun. 17(3), 212–221 (2016)

    Google Scholar 

  30. Krylatov, A., Zakharov, V., Tuovinen, T.: Nash equilibrium in a road network with many groups of users. Springer Tracts Transp. Traffic 15, 45–70 (2020)

    Article  Google Scholar 

  31. Xie, F., Levinson, D.: Modeling the growth of transportation networks: a comprehensive review. Netw. Spat. Econ. 9, 291–307 (2009)

    Article  MathSciNet  Google Scholar 

  32. Xie, F., Levinson, D.: Topological evolution of surface transportation networks. Comput. Environ. Urban Syst. 33, 211–223 (2009)

    Article  Google Scholar 

  33. Ciardiello, F., Genovese, A., Luo, S., Sgalambro, A.: A game-theoretic multi-stakeholder model for cost allocation in urban consolidation centres. Ann. Oper. Res. 324, 663–686 (2023)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences, Petrozavodsk, 185910, Russia

    Alexander Krylatov

  2. Saint Petersburg State University, Saint Petersburg, 199034, Russia

    Alexander Krylatov & Anastasiya Raevskaya

Authors
  1. Alexander Krylatov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anastasiya Raevskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Alexander Krylatov proved mathematical propositions, while Anastasiya Raevskaya developed computation procedures.

Corresponding author

Correspondence to Alexander Krylatov.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

The work was supported by a grant from the Russian Science Foundation (No. 22-11-20015 Research and development of mathematical models and software for finding equilibrium traffic flows and optimization of a transportation network on the case of Petrozavodsk city).

The work was supported by a grant from the Russian Science Foundation (No. 22-11-20015, Research and development of mathematical models and software for finding equilibrium traffic flows and optimization of a transportation network on the case of Petrozavodsk city).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krylatov, A., Raevskaya, A. Competitive Resource Allocation Among Urban Congestion Areas in a Modern Big City. J. Oper. Res. Soc. China 12, 133–153 (2024). https://doi.org/10.1007/s40305-023-00530-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40305-023-00530-z

Keywords

Mathematics Subject Classification

Search

Navigation