IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v7y2007i1p19-44.html
   My bibliography  Save this article

Planar Location and Design of a New Facility with Inner and Outer Competition: An Interval Lexicographical-like Solution Procedure

Author

Listed:
  • José Fernández
  • Blas Pelegrín
  • Frank Plastria
  • Boglárka Tóth

Abstract

A chain has to decide the location and design for a single new facility in a region where a set of facilities already exists offering the same type of product. Some of the existing facilities belong to the chain and the others are competitors. Since competition comes from outside the chain, the maximization of the profit is the main objective of the chain’s owner. Customers are supposed to patronize all the facilities, the old and the new, proportionally to the attraction they feel for them. The entrance of the new facility may thus also have a detrimental effect on the market shares of the existing chain-owned facilities, and this cannibalization should be minimized as a secondary objective. This problem is formulated as a biobjective optimization problem, and a variant of the lexicographic method is proposed to generate certain efficient solutions. This requires solving two related optimization problems, both neither convex nor concave, for which a unified interval branch and bound method is developed. Computational experiments on randomly generated problems show the feasibility of the approach, while an application of the model with real data demonstrates its use for economical analysis. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • José Fernández & Blas Pelegrín & Frank Plastria & Boglárka Tóth, 2007. "Planar Location and Design of a New Facility with Inner and Outer Competition: An Interval Lexicographical-like Solution Procedure," Networks and Spatial Economics, Springer, vol. 7(1), pages 19-44, March.
    • Handle: RePEc:kap:netspa:v:7:y:2007:i:1:p:19-44
    DOI: 10.1007/s11067-006-9005-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11067-006-9005-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-006-9005-4?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. Kilkenny, Maureen & Thisse, Jacques, 1999. "The Economics of Location: A Selective Survey," Staff General Research Papers Archive 1693, Iowa State University, Department of Economics.
    2. H. A. Eiselt & Gilbert Laporte & Jacques-François Thisse, 1993. "Competitive Location Models: A Framework and Bibliography," Transportation Science, INFORMS, vol. 27(1), pages 44-54, February.
    3. SCHMALENSEE, Richard & THISSE, Jacques-François, 1988. "Perceptual maps and the optimal location of new products: an integrative essay," LIDAM Reprints CORE 840, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. R. Suárez-Vega & D. Santos-Peñate & P. Dorta-González, 2004. "Discretization and resolution of the (r|X p )-medianoid problem involving quality criteria," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 111-133, June.
    5. Wendell, R. E. & McKelvey, R. D., 1981. "New perspectives in competitive location theory," European Journal of Operational Research, Elsevier, vol. 6(2), pages 174-182, February.
    6. Tammy Drezner & Zvi Drezner, 2004. "Finding the optimal solution to the Huff based competitive location model," Computational Management Science, Springer, vol. 1(2), pages 193-208, July.
    7. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
    8. Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
    9. Daniel Serra & Rosa Colomé, 1998. "Consumer choice in competitive location models: Formulations and heuristics," Economics Working Papers 290, Department of Economics and Business, Universitat Pompeu Fabra.
    10. repec:cor:louvrp:-1435 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Blas Pelegrín & Pascual Fernández & María Dolores García Pérez, 2016. "Profit maximization and reduction of the cannibalization effect in chain expansion," Annals of Operations Research, Springer, vol. 246(1), pages 57-75, November.
    2. Schöbel, Anita & Scholz, Daniel, 2014. "A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables," European Journal of Operational Research, Elsevier, vol. 232(2), pages 266-275.
    3. Tammy Drezner, 2011. "Cannibalization in a Competitive Environment," International Regional Science Review, , vol. 34(3), pages 306-322, July.
    4. Suárez-Vega, Rafael & Gutiérrez-Acuña, José Luis & Rodríguez-Díaz, Manuel, 2019. "Using a productivity function based method to design a new shopping centre," Journal of Retailing and Consumer Services, Elsevier, vol. 51(C), pages 176-185.
    5. Pelegrín, Blas & Fernández, Pascual & Dolores García Pérez, María & Cano Hernández, Saúl, 2012. "On the location of new facilities for chain expansion under delivered pricing," Omega, Elsevier, vol. 40(2), pages 149-158, April.
    6. Küçükaydin, Hande & Aras, Necati & Kuban AltInel, I., 2011. "Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution," European Journal of Operational Research, Elsevier, vol. 208(3), pages 206-220, February.
    7. Blanquero, Rafael & Carrizosa, Emilio & Schöbel, Anita & Scholz, Daniel, 2011. "A global optimization procedure for the location of a median line in the three-dimensional space," European Journal of Operational Research, Elsevier, vol. 215(1), pages 14-20, November.
    8. H Küçükaydın & N Aras & İ K Altınel, 2011. "A discrete competitive facility location model with variable attractiveness," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1726-1741, September.

    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. Tammy Drezner, 2009. "Location of retail facilities under conditions of uncertainty," Annals of Operations Research, Springer, vol. 167(1), pages 107-120, March.
    2. Rafael Blanquero & Emilio Carrizosa & Amaya Nogales-Gómez & Frank Plastria, 2014. "Single-facility huff location problems on networks," Annals of Operations Research, Springer, vol. 222(1), pages 175-195, November.
    3. Fernandez, Pascual & Pelegrin, Blas & Garcia Perez, Maria Dolores & Peeters, Peter H., 2007. "A discrete long-term location-price problem under the assumption of discriminatory pricing: Formulations and parametric analysis," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1050-1062, June.
    4. Blanquero, Rafael & Carrizosa, Emilio & G.-Tóth, Boglárka & Nogales-Gómez, Amaya, 2016. "p-facility Huff location problem on networks," European Journal of Operational Research, Elsevier, vol. 255(1), pages 34-42.
    5. Buechel, Berno & Roehl, Nils, 2015. "Robust equilibria in location games," European Journal of Operational Research, Elsevier, vol. 240(2), pages 505-517.
    6. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.
    7. Haase, Knut & Hoppe, Mirko, 2008. "Standortplanung unter Wettbewerb - Teil 1: Grundlagen," Discussion Papers 2/2008, Technische Universität Dresden, "Friedrich List" Faculty of Transport and Traffic Sciences, Institute of Transport and Economics.
    8. Tammy Drezner, 2011. "Cannibalization in a Competitive Environment," International Regional Science Review, , vol. 34(3), pages 306-322, July.
    9. Fernandez, Jose & Pelegri'n, Blas & Plastria, Frank & Toth, Boglarka, 2007. "Solving a Huff-like competitive location and design model for profit maximization in the plane," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1274-1287, June.
    10. Gunhak Lee & Morton E. O'Kelly, 2009. "Exploring Locational Equilibria In A Competitive Broadband Access Market: Theoretical Modeling Approach," Journal of Regional Science, Wiley Blackwell, vol. 49(5), pages 953-975, December.
    11. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
    12. Wuyang Yu, 2019. "A leader-follower model for discrete competitive facility location problem under the partially proportional rule with a threshold," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-16, December.
    13. Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
    14. Abdullah Dasci & Gilbert Laporte, 2005. "A Continuous Model for Multistore Competitive Location," Operations Research, INFORMS, vol. 53(2), pages 263-280, April.
    15. Blas Pelegrín & Pascual Fernández & María Dolores García Pérez, 2016. "Profit maximization and reduction of the cannibalization effect in chain expansion," Annals of Operations Research, Springer, vol. 246(1), pages 57-75, November.
    16. Fernández, José & Hendrix, Eligius M.T., 2013. "Recent insights in Huff-like competitive facility location and design," European Journal of Operational Research, Elsevier, vol. 227(3), pages 581-584.
    17. T Drezner & Z Drezner, 2008. "Lost demand in a competitive environment," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 362-371, March.
    18. J. Redondo & J. Fernández & I. García & P. Ortigosa, 2009. "A robust and efficient algorithm for planar competitive location problems," Annals of Operations Research, Springer, vol. 167(1), pages 87-105, March.
    19. Küçükaydin, Hande & Aras, Necati & Kuban AltInel, I., 2011. "Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution," European Journal of Operational Research, Elsevier, vol. 208(3), pages 206-220, February.
    20. Sáiz, M. Elena & Hendrix, Eligius M.T. & Pelegrín, Blas, 2011. "On Nash equilibria of a competitive location-design problem," European Journal of Operational Research, Elsevier, vol. 210(3), pages 588-593, May.

    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:kap:netspa:v:7:y:2007:i:1:p:19-44. 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.