Skip to main content
SpringerLink
Log in

Variable Neighborhood Search Approach for the Location and Design Problem

  • 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

In this paper the location and design problem is considered. The point of this is that a Company is going to open markets to attract the largest share of total customers demand. This share varies flexibly depending on the markets location and its design variant. The Company vies for consumers demand with some pre-existing competitors markets. The mathematical model is nonlinear, therefore, there are difficulties in the application of exact methods and commercial solvers for it. The ways of constructing upper bounds of the objective function are described. Two algorithms based on the Variable Neighborhood Search approach are proposed. To study the algorithms a series of test instances similar to the real data of the applied problem has been constructed, experimental analysis is carried out. The results of these studies are discussed.

A. Gnusarev—This research was supported by the Russian Foundation for Basic Research, grant 15-07-01141.

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. Aarts, E., Lenstra, J.K.: Local Search in Combinatorial Optimization. Wiley, Hoboken (1997)

    MATH  Google Scholar 

  2. Aboolian, R., Berman, O., Krass, D.: Competitive facility location and design problem. Eur. J. Oper. Res. 182(1), 40–62 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aboolian, R., Berman, O., Krass, D.: Competitive facility location model with concave demand. Eur. J. Oper. Res. 181, 598–619 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Naret, P., Weverbergh, M.: On the predictive power of market share attraction models. J. Mark. Res. 18, 146–153 (1981)

    Article  Google Scholar 

  5. Aboolian, R., Berman, O., Krass, D.: Capturing market share: facility location and design problem. In: International Conference on Discrete Optimization and Operations Research, pp. 7–11. Sobolev Institute of Mathematics, Novosibirsk (2013)

    Google Scholar 

  6. Bonami, P., Biegler, L.T., Conn, A.R., Cornuéjols, G., Grossmann, I.E., Laird, C.D., Lee, J., Lodi, A., Margot, F., Sawaya, N., Wächter, A.: An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optim. 5(2), 186–204 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. The General Algebraic Modeling System (GAMS). http://www.gams.com

  8. Hansen, P., Mladenovic, N.: Variable neighborhood search: principles and applications (invited review). Eur. J. Oper. Res. 130(3), 449–467 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hansen, P., Mladenovic, N., Moreno-Perez, J.F.: Variable neighbourhood search: algorithms and applications. Ann. Oper. Res. 175, 367–407 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Levanova, T., Gnusarev, A.: Heuristic algorithms for the location problem with flexible demand. In: 42th International Symposium on Operations Research, SYM-OP-IS 2015, Belgrad, Serbia, pp. 245–247 (2015)

    Google Scholar 

  11. Kochetov, Y., Alekseeva, E., Levanova, T., Loresh, M.: Large neighborhood local search for the \(p\)-median problem. Yugosl. J. Oper. Res. 15(2), 53–64 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We would like to thank Prof. N. Mladenovic and Prof. Yu. Kochetov for their attention to our paper and helpfull comments.

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Omsk Branch Pevtsova str. 13, 644043, Omsk, Russia

    Tatyana Levanova & Alexander Gnusarev

Authors
  1. Tatyana Levanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Gnusarev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tatyana Levanova .

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

Levanova, T., Gnusarev, A. (2016). Variable Neighborhood Search Approach for the Location and Design Problem. 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_45

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-44914-2_45

  • 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