Skip to main content
SpringerLink
Log in

On agglomeration in competitive location models

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Agglomeration of facilities that compete with each other is common in practice, which suggests the existence of forces driving facilities to locate in clusters. Shopping centers and food courts are everyday examples. Although these agglomeration forces have been adequately analyzed and explained in the economic literature, operational research location models have not taken them into consideration as of today. This is particularly troublesome, as locations prescribed by these models are rather dispersed, which is in blatant disagreement with the examples that can be observed in real life. We present a selective review of the economic literature dealing with agglomeration forces acting in a linear market, classifying these forces into weak and strong. This paper demonstrates the sensitivity of competitive location models with respect to some assumptions that cause agglomeration or dispersion.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Aboolian, R., Berman, O., & Krass, D. (2007). Competitive facility location and design problem. European Journal of Operational Research, 182(1), 40–62.

    Article  Google Scholar 

  • Anas, A., & Kim, I. (1996). General equilibrium models of polycentric urban land use with endogenous congestion and job agglomeration. Journal of Urban Economics, 40, 232–256.

    Article  Google Scholar 

  • Anderson, S. P. (1988). Equilibrium existence in the linear model of spatial competition. Economica, 55(220), 479–491.

    Article  Google Scholar 

  • Aros-Vera, F., Marianov, V., & Mitchell, J. (2013). p-hub approach for the optimal park-and-ride facility location problem. European Journal of Operational Research, 226, 277–285.

    Article  Google Scholar 

  • Blanquero, R., Hendrix, E. M. T., & Carrizosa, E. (2011). Locating a competitive facility in the plane with a robustness criterion. European Journal of Operational Research, 215(1), 21–24.

    Article  Google Scholar 

  • Boulding, K. E. (1966). Economic analysis (4th ed.). New York, NY: Harper & Row.

    Google Scholar 

  • Burkey, M. L., Bhadury, J., & Eiselt, H. A. (2012). A location-based comparison of health care services in four U.S. states with efficiency and equity. Socio-Economic Planning Sciences, 46, 157–163.

  • Canina, L., Enz, C., & Harrison, J. S. (2005). Agglomeration effects and strategic orientations: evidence from the U.S. lodging industry. The Academy of Management Journal, 48(4), 565–581.

    Article  Google Scholar 

  • Christaller, W. (1933). Die zentralen Orte in Süddeutschland. Jena: Gustav Fischer, 1933. (Translated (in part), by Charlisle W. Baskin, as Central places in Southern Germany. Prentice Hall 1966).

  • D’Aspremont, C., Gabszewicz, J. J., & Thisse, J.-F. (1979). On Hotelling’s ‘Stability in competition’. Econometrica, 47, 1145–1150.

    Article  Google Scholar 

  • Dasci, A. (2011). conditional location problems on networks and in the plane. In H. A. Eiselt & V. Marianov (Eds.), Foundations of location analysis. NY: Springer.

    Google Scholar 

  • DePalma, A., Ginsburgh, V., Labbe, M., & Thisse, J.-F. (1985). The principle of minimum differentiation holds under sufficient heterogeneity. Econometrica, 53(4), 767–781.

    Article  Google Scholar 

  • DePalma, A., Ginsburgh, V., & Thisse, J.-F. (1987). On existence of locational equilibria in the 3-firm Hotelling problem. Journal of Industrial Economics, 36, 245–252.

    Article  Google Scholar 

  • Díaz-Báñez, J. M., Heredia, M., Pelegrín, B., Pérez-Lantero, P., & Ventura, I. (2011). Finding all pure strategy Nash equilibria in a planar location game. European Journal of Operational Research, 214, 91–98.

    Article  Google Scholar 

  • Drezner, T. (1994). Optimal continuous location of a retail facility, facility attractiveness and market share: An interaction model. Journal of Retailing, 70, 49–64.

    Article  Google Scholar 

  • Drezner, T. (2014). A review of competitive facility location in the plane. Logistics Research 7, 114. doi:10.1007/s12159-014-0114-z.

  • Drezner, T., & Drezner, Z. (1996). Competitive facilities: Market share and location with random utility. Journal of Regional Science, 36, 1–15.

    Article  Google Scholar 

  • Drezner, T., Drezner, Z., & Kalczynski, P. (2012). Strategic competitive location: Improving existing and establishing new facilities. Journal of the Operational Research Society, 63(12), 1720–1730.

    Article  Google Scholar 

  • Drezner, T., Drezner, Z., & Wesolowsky, G. O. (1998). On the logit approach to competitive facility location. Journal of Regional Science, 38, 313–327.

    Article  Google Scholar 

  • Drezner, T., & Eiselt, H. A. (2002). Consumers in competitive location models. In Z. Drezner & H. Hamacher (Eds.), Facility location: Applications and theory (pp. 151–178). Berlin: Springer.

    Chapter  Google Scholar 

  • Drezner, Z. (1982). Competitive location strategies for two facilities. Regional Science and Urban Economics, 12, 485–493.

    Article  Google Scholar 

  • Eaton, B. C., & Lipsey, R. G. (1975). The principle of minimum differentiation reconsidered: Some new developments in the theory of spatial competition. The Review of Economic Studies, 42(1), 27–49.

    Article  Google Scholar 

  • Eaton, B. C., & Lipsey, R. G. (1979). Comparison shopping and the clustering of homogeneous firms. Journal of Regional Science, 19(4), 421–435.

    Article  Google Scholar 

  • Eaton, B. C., & Lipsey, R. G. (1982). An economic theory of central places. The Economic Journal, 92(365), 56–72.

    Article  Google Scholar 

  • Eiselt, H. A. (1992). Hotelling’s duopoly on a tree. Annals of Operations Research, 40, 195–207.

    Article  Google Scholar 

  • Eiselt, H.A. (2011). Equilibria in competitive location models. In H. A. Eiselt, & V. Marianov (Eds.), Foundations of location analysis (Chapter 7, pp. 139–162). New York/Dordrecht: Springer.

  • Eiselt, H. A., & Laporte, G. (1989). The maximum capture problem in a weighted network. Journal of Regional Science, 29(3), 433–439.

    Article  Google Scholar 

  • Eiselt, H. A., Laporte, G., & Thisse, J.-F. (1993). Competitive location models: A framework and bibliography. Transportation Science, 27(1), 44–54.

    Article  Google Scholar 

  • Eiselt, H. A., & Marianov, V. (2014) Competitive location models. In G. Laporte, S. Nickel, & F. Saldanha-da-Gama (Eds.), Location science (Chapter 14). New York: Springer.

  • Eppli, M., & Benjamin, J. D. (1996). The evolution of whopping center research: A review and analysis. The Journal of Real Estate Research, 9(1), 5–32.

    Google Scholar 

  • Fernández, J., & Hendrix, E. M. T. (2013). Recent insights in Huff-like competitive facility location and design. European Journal of Operational Research, 227, 581–584.

    Article  Google Scholar 

  • Fernández, J., Pelegrín, B., Plastria, F., & Tóth, B. (2007). Solving a Huff-like competitive location and design model for profit maximization in the plane. European Journal of Operational Research, 179, 1274–1287.

    Article  Google Scholar 

  • Fetter, F. A. (1924). The economic law of market areas. Quarterly Journal of Economics, 39, 520–529.

  • Fischer, K. (2011). Central places: The theories of von Thünen, Christaller, and Lösch. In H. A. Eiselt & V. Marianov (Eds.), Foundations of location analysis (pp. 471–505). New York: Springer.

    Chapter  Google Scholar 

  • Fotheringham, A. S. (1985). Spatial competition and agglomeration in urban modelling. Environment and Planning A, 17, 213–230.

    Article  Google Scholar 

  • Fotheringham, A. S. (1988). Consumer store choice and choice set definition. Marketing Science, 7(3), 299–310.

    Article  Google Scholar 

  • Fotheringham, A. S., & Knudsen, D. C. (1986). Modeling discontinuous change in retailing systems: extensions of the Harris–Wilson framework with results from a simulated urban retailing system. Geographical Analysis, 18(4), 295–312.

    Article  Google Scholar 

  • Fujita, M., & Thisse, J.-F. (1996). Economics of agglomeration. Journal of the Japanese and International Economies, 10, 339–378.

    Article  Google Scholar 

  • Fujita, M., & Thisse, J.-F. (2002). Economics of agglomeration: Cities, industrial location, and regional growth. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Gabszewicz, J. J., & Thisse, J.-F. (1986a). Spatial competition and the location of firms. In J. J. Gabszewicz, J.-F. Thisse, M. Fujita, & U. Shweitzer (Eds.), Location theory. Chur: Harwood Academic Publishers.

    Google Scholar 

  • Gabszewicz, J. J., & Thisse, J.-F. (1986b). Spatial competition and the location of firms. Fundamentals of Pure and Applied Economics, 5, 1–71.

    Google Scholar 

  • García-Pérez, M. D., & Pelegrín, B. (2003). All Stackelberg location equilibria in the Hotelling’s Duopoly model on a tree with parametric prices. Annals of Operations Research, 122, 177–192.

    Article  Google Scholar 

  • Gordon, I. R., & McCann, P. (2000). Industrial clusters: Complexes, agglomeration and/or social networks? Urban Studies, 37(3), 513–532.

    Article  Google Scholar 

  • Guimarães, P., Figuereido, O., & Woodward, D. (2004). Measuring the localization of economic activity: A random utility approach. FEP Working paper Nr. 161, October 2004, CEMPRE, Universidade do Porto.

  • Hakimi, S. L. (1983). On locating new facilities in a competitive environment. European Journal of Operational Research, 12, 29–35.

    Article  Google Scholar 

  • Hodgson, M. J. (1978). Toward more realistic allocation in location-allocation models: An interaction approach. Environment and Planning A, 10, 1273–1285.

    Article  Google Scholar 

  • Hodgson, M. J. (1981). A location–allocation model maximizing consumers’ welfare. Regional Studies, 15(6), 493–506.

    Article  Google Scholar 

  • Hotelling, H. (1929). Stability in competition. Economic Journal, 39, 41–57.

    Article  Google Scholar 

  • Huff, D. L. (1963). A probabilistic analysis of shopping center trade areas. Land Economics, 39(1), 81–90.

    Article  Google Scholar 

  • Huff, D. L. (1964). Defining and estimating a trading area. Journal of Marketing, 28, 34–38.

    Article  Google Scholar 

  • Joseph, L., & Kuby, M. (2011). Gravity modeling and its impacts on location analysis. In H. A. Eiselt & V. Marianov (Eds.), Foundations of location analysis (pp. 475–498). New York/Dordrecht: Springer.

    Google Scholar 

  • Kilkenny, M., & Thisse, J.-F. (1999). Economics of location: A selective survey. Computers & Operations Research, 26, 1369–1394.

    Article  Google Scholar 

  • Kohlberg, E. (1983). Equilibrium store locations when consumers minimize travel time plus waiting time. Economics Letters, 11, 211–216.

    Article  Google Scholar 

  • Konishi, H. (2005). Concentration of competing retail stores. Journal of Urban Economics, 58, 488–512.

    Article  Google Scholar 

  • Kress, D., & Pesch, E. (2012). Sequential competitive location on networks. European Journal of Operational Research, 217, 483–499.

    Article  Google Scholar 

  • Krider, R. E., & Putler, D. S. (2013). Which birds of a feather flock together? Clustering and avoidance patterns of similar retail outlets. Geographical Analysis, 45, 123–149.

    Article  Google Scholar 

  • Krugman, P. (1991a). Increasing returns and economic geography. The Journal of Political Economy, 99, 99–483.

    Article  Google Scholar 

  • Krugman, P. (1991b). First nature, second nature and metropolitan location. Working Paper No 3740, National Bureau of Economic Research, June 1991.

  • Küçükaydin, H., Aras, N., & Altinel, I. K. (2011). Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution. European Journal of Operational Research, 208(3), 206–220.

    Article  Google Scholar 

  • Küçükaydin, H., Aras, N., & Altinel, I. K. (2012). A leader-follower game in competitive facility location. Computers and Operations Research, 39(2), 437–448.

    Article  Google Scholar 

  • Lerner, A. P., & Singer, H. W. (1937). Some notes on duopoly and spatial competition. Journal of Political Economy, 45(2), 145–186.

    Article  Google Scholar 

  • Lösch, A. (1954). Economics of location (2d ed.). New Heaven: Yale University Press.

    Google Scholar 

  • Lüer-Villagra, A., & Marianov, V. (2013). The competitive hub location and pricing problem. European Journal of Operational Research, 231, 734–744.

    Article  Google Scholar 

  • Magionni, M. A. (1999). Clustering dynamics and the location of high tech firms. PhD thesis, Warwick Business School, University of Warwick. http://wrap.warwick.ac.uk/3704/. Accessed 17 July 2014.

  • Marianov, V., Ríos, M., & Icaza, M. J. (2008). Facility location for market capture when users rank facilities by travel and waiting times. European Journal of Operational Research, 191(1), 32–44.

    Article  Google Scholar 

  • Marshall, A. (1920). Principles of economics (8th ed.). London: Macmillan.

    Google Scholar 

  • McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in econometrics. New York, NY: Academic Press.

    Google Scholar 

  • McLafferty, S., & Ghosh, A. (1987). Optimal location and allocation with multipurpose shopping. In A. Ghosh & G. Rushton (Eds.), Spatial analysis and location–allocation models (pp. 55–75). New York: Von Nostrand Reinhold.

    Google Scholar 

  • Mulligan, G. F. (1984). Agglomeration and central place theory: A review of the literature. International Regional Science Review, 9(1), 1–42.

    Article  Google Scholar 

  • Mulligan, G. F. (1987). Consumer travel behavior: Extensions of a multipurpose shopping model. Geographical Analysis, 19(4), 364–375.

    Article  Google Scholar 

  • Mulligan, G. F., Partridge, M. D., & Carruthers, G. I. (2012). Central place theory and its reemergence in regional science. The Annals of Regional Science, 48, 405–431.

    Article  Google Scholar 

  • Nakashani, M., & Cooper, L. G. (1974). Parameter estimation for a multiplicative competitive interaction mode-least squares approach. Journal of Marketing Research, XI, 303–311.

  • O’Kelly, M. (1981). A model of the demand for retail facilities, incorporating multistop, multipurpose trips. Geographical Analysis, 13(2), 134–148.

    Article  Google Scholar 

  • O’Kelly, M. (1983). Impacts of multistop, multipurpose trips on retail distributions. Urban Geography, 4(2), 173–190.

    Google Scholar 

  • Ortúzar, J. d. D., & Willumsen, L. G. (2011). Modelling transport (4th ed., Chapter 7, pp. 227–268). West Sussex: Blackwell.

  • Papageorgiou, Y. Y., & Thisse, J.-F. (1985). Agglomeration as spatial interdependence between firms and households. Journal of Economic Theory, 37, 19–31.

    Article  Google Scholar 

  • Pelegrín-Pelegrín, B., Dorta-González, P., & Fernández-Hernández, P. (2011). Finding location equilibria for competing firms under delivered pricing. Journal of the Operational Research Society, 62, 729–741.

    Article  Google Scholar 

  • Porter, M. E. (1998). Clusters and the new economics of competition. Harvard Business Review, 76(6), 77–90.

    Google Scholar 

  • Prescott, E. C., & Visscher, M. (1977). Sequential location among firms with foresight. The Bell Journal of Economics, 8(2), 378–393.

    Article  Google Scholar 

  • Reilly, W. J. (1931). The law of retail gravitation. New York: Knickerbocker Press, New York.

    Google Scholar 

  • ReVelle, C. (1986). The maximum capture or “Sphere of influence” location problem: Hotelling revisited on a network. Journal of Regional Science, 26(2), 343–358.

    Article  Google Scholar 

  • ReVelle, C., & Serra, D. (1991). The maximum capture problem including relocation. INFOR, 29(2), 130–138.

    Google Scholar 

  • Roy, J., & Thill, J.-C. (2004). Spatial interaction modelling. Papers in Regional Science, 83, 339–361.

    Article  Google Scholar 

  • Saíz, M. E., Hendrix, E. M. T., Fernández, J., & Pelegrín, B. (2009). On a branch-and-bound approach for a Huff-like Stackelberg location problem. OR Spectrum, 31, 679–705.

    Article  Google Scholar 

  • Sáiz, M. E., Hendrix, E. M. T., & Pelegrín, B. (2011). On Nash equilibria of a competitive location–design problem. European Journal of Operational Research, 210, 588–593.

    Article  Google Scholar 

  • Santos-Peñate, D., Suárez-Vega, R., & Dorta-González, P. (2007). The leader-follower location model. Networks and Spatial Economics, 7, 45–61.

    Article  Google Scholar 

  • Schulz, N., & Stahl, K. (1996). Do consumers search for the highest price? Oligopoly equilibrium and monopoly optimum in differentiated-products markets. The RAND Journal of Economics, 27(3), 542–562.

    Article  Google Scholar 

  • Serra, D., Marianov, V., & ReVelle, C. (1992). The maximum capture hierarchical location problem. European Journal of Operational Research, 62, 363–371.

    Article  Google Scholar 

  • Serra, D., & ReVelle, C. (1994). Market capture by two competitors: The pre-emptive capture problem. Journal of Regional Science, 34(4), 549–561.

    Article  Google Scholar 

  • Stahl, K. (1982). Differentiated products, consumer search, and locational oligopoly. The Journal of Industrial Economics, 31(1/2), 97–113.

    Article  Google Scholar 

  • Thill, J.-C., & Thomas, I. (1987). Toward conceptualizing trip-chaining behavior: A review. Geographical Analysis, 19(1), 1–17.

    Article  Google Scholar 

  • von Stackelberg, H. (1943). Grundlagen der theoretischen Volkswirtschaftslehre (translated as: The theory of the market economy). London: W. Hodge & Co., Ltd. 1952.

    Google Scholar 

  • WiseGeek. (2014). What was the first fast-food restaurant. http://www.wisegeek.org/what-was-the-first-fast-food-restaurant.htm. Accessed 17 July 2014.

  • Wolinsky, A. (1983). Retail trade concentration due to consumers’ imperfect information. The Bell Journal of Economics, 14(1), 275–282.

    Article  Google Scholar 

  • Yang, N. (2013). March of the chains: Herding in restaurant locations. NET Institute Working Paper No. 11-16, Yale School of Management, August 1, 2013.

  • Younies, H., & Eiselt, H. A. (2011). Sequential location models. In H. A. Eiselt & V. Marianov (Eds.), Foundations of location analysis (pp. 175–192). New York/Dordrecht: Springer.

    Google Scholar 

Download references

Acknowledgments

This research was in part supported by a grant from the Natural Sciences and Engineering Council of Canada under Grant Number 0009160, by Grant FONDECYT 1130265, and by Institute Complex Engineering Systems through Grants ICM P-05-004-F and CONICYT FBO16. This support is gratefully acknowledged. The detailed and insightful comments by two referees are much appreciated.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

    Vladimir Marianov

  2. Faculty of Business Administration, University of New Brunswick, Fredericton, NB, Canada

    H. A. Eiselt

Authors
  1. Vladimir Marianov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. A. Eiselt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Marianov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marianov, V., Eiselt, H.A. On agglomeration in competitive location models. Ann Oper Res 246, 31–55 (2016). https://doi.org/10.1007/s10479-014-1704-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-014-1704-5

Keywords

Search

Navigation