Skip to main content
SpringerLink
Log in

A refinement of the gravity model for competitive facility location

  • Original Paper
  • Published:
Computational Management Science Aims and scope Submit manuscript

Abstract

Most competitive location models assume that as the distance increases, the patronage of a facility declines at the same rate regardless of the facility attractiveness. We observed that the rate at which patronage declines is slower for more attractive facilities. Customers are willing to drive long distances to patronize an attractive facility. Less attractive facilities hardly attract customers from long distances. We propose to modify the effect of attractiveness on the appeal of the facility to customers. Many methods for estimating the market share captured by a facility can be modified to incorporate such property. We implemented the new modification on the gravity model and tested it on a real data set of shopping malls in Orange County, California. The approach was statistically validated and is computationally straightforward to implement with existing software such as R. Further, new facility location decisions are expected to be more accurate due to the improved market share estimates by the proposed model.

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
Fig. 5

Similar content being viewed by others

Notes

  1. Data is available up on request from the authors.

  2. We have seen earlier that the marginal distribution of \(\textrm{Y}_{ij}\) has an over-dispersion value of \({\hat{\theta }}=0.2813\). Although model (21) manages to push \({\hat{\theta }}\) higher to 1.320, a substantial over-dispersion still remains.

  3. Note that imposing \(\beta =0\) in (21) or (22) leads to the basic gravity model.

References

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Aboolian R, Berman O, Krass D (2009) Efficient solution approaches for discrete multi-facility competitive interaction model. Ann Oper Res 167:297–306

    Article  Google Scholar 

  • Bell D, Ho T, Tang C (1998) Determining where to shop: fixed and variable costs of shopping. J Mark Res 35(3):352–369

    Article  Google Scholar 

  • Christaller W (1966) Central places in Southern Germany. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Drezner T (2022) Competitive location problems. In: Salhi S, Boylan JE (eds.), The Palgrave handbook of operations research, pp 209–236. Palgrave, London. ISBN: 978-3-030-96034-9

  • Drezner Z (1982) Competitive location strategies for two facilities. Reg Sci Urban Econ 12:485–493

    Article  Google Scholar 

  • Drezner T (1994) Locating a single new facility among existing unequally attractive facilities. J Reg Sci 34:237–252

    Article  Google Scholar 

  • Drezner T (1994) Optimal continuous location of a retail facility, facility attractiveness, and market share: an interactive model. J Retail 70:49–64

    Article  Google Scholar 

  • Drezner T (1995) Competitive facility location in the plane. In: Drezner Z (ed) Facility location: a survey of applications and methods. Springer, New York, NY, pp 285–300

    Chapter  Google Scholar 

  • Drezner T (2006) Derived attractiveness of shopping malls. IMA J Manag Math 17:349–358

    Google Scholar 

  • Drezner Z (2007) A general global optimization approach for solving location problems in the plane. J Glob Optim 37:305–319

    Article  Google Scholar 

  • Drezner T, Drezner Z (1996) Competitive facilities: market share and location with random utility. J Reg Sci 36:1–15

    Article  Google Scholar 

  • Drezner T, Drezner Z (2002) Validating the gravity-based competitive location model using inferred attractiveness. Ann Oper Res 111:227–237

    Article  Google Scholar 

  • Drezner T, Drezner Z (2004a) Finding the optimal solution to the Huff competitive location model. Comput Manag Sci 1:193–208

    Article  Google Scholar 

  • Drezner Z, Suzuki A (2004b) The big triangle small triangle method for the solution of non-convex facility location problems. Oper Res 52:128–135

    Article  Google Scholar 

  • Drezner T, Drezner Z, Salhi S (2002) Solving the multiple competitive facilities location problem. Eur J Oper Res 142:138–151

    Article  Google Scholar 

  • Drezner T, Drezner Z, Kalczynski P (2011) A cover-based competitive location model. J Oper Res Soc 62:100–113

    Article  Google Scholar 

  • Drezner T, Drezner Z, Kalczynski P (2012) Strategic competitive location: improving existing and establishing new facilities. J Oper Res Soc 63:1720–1730

    Article  Google Scholar 

  • Drezner T, Drezner Z, Kalczynski P (2020) A gradual cover competitive facility location model. OR Spectr 42:333–354

    Article  Google Scholar 

  • Drezner T, Marcoulides GA, Drezner Z (1998) A procedure for estimating the attractiveness of shopping malls. In: Proceedings of 29th annual DSI meeting, Vol. II, pp 1090–1092, Las Vegas, NV

  • Fernández J, Hendrix EM (2013) Recent insights in huff-like competitive facility location and design. Eur J Oper Res 227:581–584

    Article  Google Scholar 

  • Fernández J, Pelegrin B, Plastria F, Toth B (2007) Solving a Huff-like competitive location and design model for profit maximization in the plane. Eur J Oper Res 179:1274–1287

    Article  Google Scholar 

  • Fetter FA (1924) The economic law of market areas. Q J Econ 38:520–529

    Article  Google Scholar 

  • Ghosh A, Rushton G (1987) Spatial analysis and location-allocation models. Van Nostrand Reinhold Company, New York, NY

    Google Scholar 

  • Glover F, Laguna M (1997) Tabu Search. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

  • Goldberg DE (2006) Genetic algorithms. Pearson Education, Delhi, India

    Google Scholar 

  • Hakimi SL (1981) On locating new facilities in a competitive environment. Presented at the ISOLDE II Conference, Skodsborg, Denmark

  • Hakimi SL (1983) On locating new facilities in a competitive environment. Eur J Oper Res 12:29–35

    Article  Google Scholar 

  • Hakimi SL (1986) \(p\)-Median theorems for competitive location. Ann Oper Res 6:77–98

    Article  Google Scholar 

  • Hakimi SL (1990) Locations with spatial interactions: competitive locations and games. In: Mirchandani PB, Francis RL (eds) Discret Locat Theory. Wiley-Interscience, New York, NY, pp 439–478

    Google Scholar 

  • Hansen P, Mladenović N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130:449–467

    Article  Google Scholar 

  • Hansen P, Peeters D, Thisse J-F (1981) On the location of an obnoxious facility. Sistemi Urbani 3:299–317

    Google Scholar 

  • Hodgson MJ (1981) A location-allocation model maximizing consumers’ welfare. Reg Stud 15:493–506

    Article  Google Scholar 

  • Hotelling H (1929) Stability in competition. Econ J 39:41–57

    Article  Google Scholar 

  • Huff DL (1964) Defining and estimating a trade area. J Mark 28:34–38

    Article  Google Scholar 

  • Huff DL (1966) A programmed solution for approximating an optimum retail location. Land Econ 42:293–303

    Article  Google Scholar 

  • Kirkpatrick S, Gelat CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  Google Scholar 

  • Launhardt W (1885) Mathematische Begründung der Volkswirthschaftslehre. W. Engelmann

  • Leonardi G, Tadei R (1984) Random utility demand models and service location. Reg Sci Urban Econ 14:399–431

    Article  Google Scholar 

  • Lösch A (1954) The economics of location. Yale University Press, New Haven, CT

    Google Scholar 

  • McCullagh P, Nelder JA (2019) Generalized linear models. Routledge

    Book  Google Scholar 

  • Nakanishi M, Cooper LG (1974) Parameter estimate for multiplicative interactive choice model: least squares approach. J Mark Res 11:303–311

    Google Scholar 

  • Raykov T, Marcoulides GA (2012) A first course in structural equation modeling. Routledge

  • Reilly WJ (1931) The law of retail gravitation. Knickerbocker Press, New York, NY

    Google Scholar 

  • ReVelle C (1986) The maximum capture or sphere of influence problem: hotelling revisited on a network. J Reg Sci 26:343–357

    Article  Google Scholar 

  • Schöbel A, Scholz D (2010) The big cube small cube solution method for multidimensional facility location problems. Comput Oper Res 37:115–122

    Article  Google Scholar 

  • Serra D, ReVelle C (1995) Competitive location in discrete space. In: Drezner Z (ed) Facility location: a survey of applications and methods. Springer, New York, NY, pp 367–386

    Chapter  Google Scholar 

  • Venables WN, Ripley BD (2013) Modern applied statistics with S-PLUS. Springer Science & Business Media

  • Wolpert J (1976) Regressive siting of public facilities. Nat Resour J 16:103–115

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Business and Economics, California State University-Fullerton, Fullerton, CA, 92834, USA

    Zvi Drezner & Dawit Zerom

Authors
  1. Zvi Drezner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dawit Zerom
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zvi Drezner.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Drezner, Z., Zerom, D. A refinement of the gravity model for competitive facility location. Comput Manag Sci 21, 2 (2024). https://doi.org/10.1007/s10287-023-00484-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10287-023-00484-w

Keywords

Search

Navigation