Skip to main content
SpringerLink
Log in

Facility Location in Unfair Competition

  • Conference paper
  • First Online:
Discrete Optimization and Operations Research (DOOR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9869))

Abstract

We consider a mathematical model belonging to the family of competitive location problems. In the model, there are two competing parties called Leader and Follower, which open their facilities with the goal to capture customers and maximize profit. In our model we assume that Follower is able to open own facilities as well as to close the Leader’s ones. The model can be written as a pessimistic bilevel integer programming problem. We show that the problem of Leader’s profit maximization can be represented as a problem of pseudo–Boolean function maximization. The number of variables the function depends on equals to the number of sites available for opening a facility. We suggest a method of calculation of an upper bound for the optimal value of the function based on strengthening of a bilevel model with valid inequalities and further relaxation of the model by removing the lower–level optimization problem.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aksen, D., Piyade, N., Aras, N.: The budget constrained r-interdiction median problem with capacity expansion. Cent. Eur. J. Oper. Res. 18(3), 269–291 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aksen, D., Aras, N.: A matheuristic for leader-follower games involving facility location-protection-interdiction decisions. In: Talbi, E.-G., Brotcorne, L. (eds.) Metaheuristics for Bi-level Optimization. SCI, vol. 482, pp. 115–152. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  3. Aliakbarian, N., Dehghanian, F., Salari, M.: A bi-level programming model for protection of hierarchical facilities under imminent attacks. Comp. Oper. Res. 64, 210–224 (2015)

    Article  MathSciNet  Google Scholar 

  4. Beresnev, V.: Branch-and-bound algorithm for competitive facility location problem. Comput. Oper. Res. 40, 2062–2070 (2013)

    Article  MathSciNet  Google Scholar 

  5. Beresnev, V.: On the competitive facility location problem with a free choice of suppliers. Autom. Remote Control 75, 668–676 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Beresnev, V., Mel’nikov, A.: The branch-and-bound algorithm for a competitive facility location problem with the prescribed choice of suppliers. J. Appl. Ind. Math. 8, 177–189 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Davydov, I.A., Kochetov, Y.A., Mladenovic, N., Urosevic, D.: Fast metaheuristics for the discrete \((r|p)\)-centroid problem. Autom. Remote Control 75, 677–687 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dempe, S.: Foundations of Bilevel Programming. Kluwer Acad. Publ, Dortrecht (2002)

    MATH  Google Scholar 

  9. Krarup, J., Pruzan, P.M.: The simple plant location problem: survey and synthesis. Eur. J. Oper. Res. 12(1), 36–81 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kress, D., Pesch, E.: Sequential competitive location on networks. Eur. J. Oper. Res. 217, 483–499 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liberatore, F., Scaparra, M.P., Daskin, M.S.: Analysis of facility protection strategies against an uncertain number of attacks: the stochastic r-interdiction median problem with fortification. Comp. Oper. Res. 38, 357–366 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mel’nikov, A.: Randomized local search for the discrete competitive facility location problem. Autom. Remote Control 75, 700–714 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Santos-Penate, D.R., Suarez-Vega, R., Dorta-Gonzalez, P.: The leader follower location model. Netw. Spat. Econ. 7, 45–61 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Scaparra, M.P., Church, R.L.: A bilevel mixed-integer program for critical infrastructure protection planning. Comp. Oper. Res. 35, 1905–1923 (2008)

    Article  MATH  Google Scholar 

  15. Stackelberg, H.: The Theory of the Market Economy. Oxford Univ. Press, Oxford (1952)

    Google Scholar 

  16. Zhu, Y., Zheng, Z., Zhang, X., Cai, K.Y.: The r-interdiction median problem with probabilistic protection and its solution algorithm. Comp. Oper. Res. 40, 451–462 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The research is supported by Russian Foundation for Basic Research (project 15-01-01446) and Presidium of Russian Academy of Sciences (program 15, project 227). We deeply grateful to Alexander Ageev for his assistance in preparing the English text.

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Vladimir Beresnev & Andrey Melnikov

  2. Novosibirsk State University, Novosibirsk, Russia

    Vladimir Beresnev & Andrey Melnikov

Authors
  1. Vladimir Beresnev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrey Melnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Beresnev .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Yury Kochetov

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Vladimir Beresnev

  4. Far Eastern Federal University , Vladivostik, Russia

    Evgeni Nurminski

  5. University of Florida , Gainesville, Florida, USA

    Panos Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Beresnev, V., Melnikov, A. (2016). Facility Location in Unfair Competition. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-44914-2_26

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44913-5

  • Online ISBN: 978-3-319-44914-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation