Skip to main content
SpringerLink
Log in

Local search algorithms for the problem of competitive location of enterprises

  • Applications of Mathematical Programming
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

This article deals with the mathematical model that generalizes the known problem of location of enterprises and is represented in the form of the problem of bilevel mathematical programming. In this model two competitive sides sequentially locate enterprises, and each of the sides strives to maximize its profit. As optimal solutions of the investigated problem, optimal cooperative and optimal noncooperative solutions are considered. The method is suggested for calculating the upper bounds of values of the goal function of the problem at optimal cooperative and noncooperative solutions. Simultaneously with the calculation of the upper bound, the initial approximate solution is set up. Algorithms of the local search for improving this solution are suggested. The algorithms involve two stages: at the first stage the locally optimal solution is found, while at the second stage the locally optimal solution relative to the neighborhood called the generalized one is found. The results of computational experiments demonstrating the possibilities of the suggested algorithms are displayed.

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

Similar content being viewed by others

References

  1. Beresnev, V.L., Diskretnye zadachi razmeshcheniya i polinomy ot bulevykh peremennykh (Discrete Problems of Location and Polynomials in Boolean Variables), Novosibirsk: Inst. Mat., 2005.

    Google Scholar 

  2. Discrete Location Theory, Mirchandani, P.B. and Francis, R.L., Eds., New York: Wiley, 1990.

    MATH  Google Scholar 

  3. Stackelberg, H., The Theory of the Market Economy, Oxford: Oxford Univ. Press, 1952.

    Google Scholar 

  4. Dempe, S., Foundations of Bilevel Programming, Dordrecht: Kluwer, 2002.

    MATH  Google Scholar 

  5. Campos, C. and Moreno, J.A., Multiple Voting Location Problems, Eur. J. Oper. Res., 2008, vol. 191, no. 2, pp. 436–452.

    Google Scholar 

  6. Dobson, G. and Karmarkar, U., Competitive Location on Network, Oper. Res., 1987, vol. 35, pp. 565–574.

    Article  MathSciNet  MATH  Google Scholar 

  7. Facility Location: Applications and Theory, Drezner, Z. and Hamacher, H.W., Eds., Berlin: Springer-Verlag, 2002.

    MATH  Google Scholar 

  8. Plastria, F., Static Competitive Facility Location: An Overview of Optimization Approaches, Eur. J. Oper. Res., 2001, vol. 129, pp. 461–470.

    Article  MathSciNet  MATH  Google Scholar 

  9. Plastria, F. and Vanhaverbeke, L., Discrete Model for Competitive Location with Foresight, Comput. Oper. Res. 2008, vol. 35, pp. 683–700.

    Article  MathSciNet  MATH  Google Scholar 

  10. Santos-Penate, D.R., Suarez-Vega, R., and Dorta-Gonzales, P., The Leader-Follower Location Model, Networks Spatial Econ., 2007, vol. 7, pp. 45–61.

    Article  MATH  Google Scholar 

  11. Hakimi, S.L., Locations with Spatial Interactions: Competitive Locations and Games, in Discrete Location Theory, Mirchandani, P.B. and Francis, R.L., Eds., New York: Wiley, 1990, pp. 439–478.

    Google Scholar 

  12. Alekseeva, E., Kochetova, N., Kochetov, Y., and Plyasunov, A., Heuristic and Exact Methods for the Discrete (r/p)-Centroid Problem, in EvoCOP 2010, LNCS 6022, Heidelberg: Springer-Verlag, 2010, pp. 11–22.

    Google Scholar 

  13. Beresnev, V.L., Upper Estimates for Goal Functions of Discrete Problems for Competitive Location of Enterprises, Diskret. Anal. Issled. Oper., 2008, vol. 15, no. 4, pp. 3–24.

    MathSciNet  MATH  Google Scholar 

  14. Beresnev, V.L. and Mel’nikov, A.A., Approximate Algorithms for the Problem of Competitive Location of Enterprises, Diskret. Anal. Issled. Oper., 2010, vol. 17, no. 6, pp. 3–19.

    MATH  Google Scholar 

  15. Beresnev, V.L., Goncharov, E.N., and Mel’nikov, A.A., Local Search over Generalized Neighborhood, Diskret. Anal. Issled. Oper., 2011, vol. 18, no. 4, pp. 3–16.

    MATH  Google Scholar 

  16. Hammer, P.L. and Rudeanu, S., Boolean Method in Operations Research and Related Areas, Berlin: Springer-Verlag, 1968.

    Google Scholar 

  17. Local Search in Combinotorial Optimization, Aarts, E.H.L. and Lenstra, J.K., Eds., Chichester: John Wiley and Sons, 1997.

    Google Scholar 

  18. http://www.math.nsc.ru/AP/benchmarks/

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    V. L. Beresnev

Authors
  1. V. L. Beresnev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.L. Beresnev, 2012, published in Avtomatika i Telemekhanika, 2012, No. 3, pp. 12–27.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beresnev, V.L. Local search algorithms for the problem of competitive location of enterprises. Autom Remote Control 73, 425–439 (2012). https://doi.org/10.1134/S0005117912030022

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117912030022

Keywords

Search

Navigation