Gravity Modeling and its Impacts on Location Analysis

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 155)


Throughout the 20th century, geographers have developed a variety of models that assist public and private entities in locating facilities from factories to emergency services. In the area of retail location analysis, the early gravity models of geographers William J. Reilly and David L. Huff played a pioneering role in delineating retail trade areas and modeling many other kinds of spatial interaction. Their fundamental insight was that customers do not necessarily shop at the closest store, but patronize locations in proportion to the attractiveness of the retail centers and in inverse proportion to their distance. In this chapter, we elucidate the early history, structure, and significance of these models.


  1. Applebaum W (1966) Methods for determining store trade areas, market penetration, and potential sales. J Mark Res 3:127–141CrossRefGoogle Scholar
  2. Beaumont, JR (1980) Spatial interaction models and the location-allocation problem. J Reg Sci 20:37–50CrossRefGoogle Scholar
  3. Bell DR, Ho TH, Tang CS (1998) Determining where to shop: fixed and variable costs of shopping. J Mark Res 35:352–370CrossRefGoogle Scholar
  4. Berkeley G (1713) Three dialogues between Hylas and Philonous. In: Mathias MB (ed). Pearson Longman, New York (2007)Google Scholar
  5. Berman O, Krass D (1998) Flow intercepting spatial interaction model: a new approach to optimal location of competitive facilities. Locat Sci 6:41–65CrossRefGoogle Scholar
  6. Bruno G, Improta G (2008) Using gravity models for the evaluation of new university site locations: a case study. Comput Oper Res 35:434–444CrossRefGoogle Scholar
  7. Bucklin LP (1971) Retail gravity models and consumer choice: a theoretical and empirical critique. Econ Geogr 47:489–497CrossRefGoogle Scholar
  8. Carey HC (1858) Principles of social science. Lippincott, PhiladelphiaGoogle Scholar
  9. Carrothers GAP (1956) A historical review of gravity and potential models of human interaction. J Am Inst Plan 22:94–102CrossRefGoogle Scholar
  10. Colome R, Lourenco HR, Serra D (2003) A new chance-constrained maximum capture location problem. Ann Oper Res 122:121–139CrossRefGoogle Scholar
  11. Converse PD (1949) New laws of retail gravitation. J Mark 14:379–384CrossRefGoogle Scholar
  12. Converse PD (1953) Comment of movement of retail trade in Iowa. J Mark 18:170–171CrossRefGoogle Scholar
  13. Cooper LG, Nakanishi M (1988) Market share analysis: evaluating competitive marketing effectiveness. Kluwer, BostonGoogle Scholar
  14. Douglas E (1949) Measuring the general retail trading area: a case study. J Mark 14:46–60CrossRefGoogle Scholar
  15. Drezner T, Drezner Z (2001) A note on applying the gravity rule to the airline hub problem. J Reg Sci 41:67–73CrossRefGoogle Scholar
  16. Drezner T, Drezner Z (2002) Validating the gravity-based competitive location model using inferred attractiveness. Ann Oper Res 111:227–237CrossRefGoogle Scholar
  17. Drezner T, Drezner Z (2007) The gravity p-median model. Eur J Oper Res 179:1239–1251CrossRefGoogle Scholar
  18. Eppli MJ, Shilling JD (1996) How critical is a good location to a regional shopping center? J Real Estate Res 9:5–32Google Scholar
  19. Fotheringham AS (1981) Spatial structure and distance decay parameters. Ann Assoc Am Geogr 71:425–436Google Scholar
  20. Fotheringham AS, O’Kelly ME (1989) Spatial interaction models: formulations and applications.Kluwer, BostonGoogle Scholar
  21. Gautschi DA (1981) Specification of patronage models for retail center choice. J Mark Res 18:162–174CrossRefGoogle Scholar
  22. Ghosh A, McLafferty S, Craig CS (1995) Multifacility retail networks. In: Drezner Z (ed) Facility location: a survey of applications and methods. Springer, New York, pp 301–330Google Scholar
  23. Hakimi SL (1983) On locating new facilities in a competitive environment. Eur J Oper Res 12:29–35CrossRefGoogle Scholar
  24. Hakimi SL (1990) Locations with spatial interactions: competitive locations and games. In: Francis RL, Mirchandani PB (eds) Discrete location theory. Wiley, New York, pp 439–478Google Scholar
  25. Hodgson MJ (1978) Toward more realistic allocation in location allocation models: an interactionapproach. Environ Plan A 10:1273–1285CrossRefGoogle Scholar
  26. Hodgson MJ (1981) A location-allocation model maximizing consumers’ welfare. Regional Studies 15:493–506CrossRefGoogle Scholar
  27. Huff DL (1962) Determination of intraurban retail trade areas. Division of Research, Graduate School of Business Administration, University of California, Los Angeles, CAGoogle Scholar
  28. Huff DL (1963) A probabilistic analysis of shopping center trade areas. Land Econ 39:81–90CrossRefGoogle Scholar
  29. Huff DL (1964) Defining and estimating a trade area. J Mark 28:34–38CrossRefGoogle Scholar
  30. Huff DL (2003) Parameter estimation in the Huff model. ArcUser 6:34–36Google Scholar
  31. Huff DL, Jenks GF (1968) A graphic interpretation of the friction of distance in gravity models. Ann Assoc Am Geogr 58:814–824CrossRefGoogle Scholar
  32. Jain AK, Mahajan V (1979) Evaluating the competitive environment in retailing using multiplicative competitive interactive models. In: Sheth J (ed) Research in marketing. JAI Press, Greenwich, pp 217–235Google Scholar
  33. Lee ML, Pace RK (2005) Spatial distribution of retail sales. J Real Estate Finance Econ 31:53–69CrossRefGoogle Scholar
  34. Lowe JM, Sen A (1996) Gravity model applications in health planning: analysis of an urban hospital market. J Reg Sci 36:437–461CrossRefGoogle Scholar
  35. Luce RD (1959) Individual choice behavior. Wiley, New YorkGoogle Scholar
  36. McLafferty S (1988) Predicting the effect of hospital closure on hospital utilization patterns. Soc Sci Med 27:255–262CrossRefGoogle Scholar
  37. Nakanishi M, Cooper LG (1974) Parameter estimation for a multiplicative competitive interaction model: least squares approach. J Mark Res 11:303–311CrossRefGoogle Scholar
  38. Okabe A, Kitamura M (1996) A computational method for market area analysis on a network. Geogr Anal 28:330–349CrossRefGoogle Scholar
  39. O’Kelly ME (1983) Multipurpose shopping trips and the size of retail facilities. Ann Assoc Am Geogr 73:231–239CrossRefGoogle Scholar
  40. O’Kelly ME, Miller HJ (1989) A synthesis of some market area delimitation models. Growth Change 20:14–33CrossRefGoogle Scholar
  41. Okunuki K, Okabe A (2002) Solving the Huff-based competitive location model on a network with link-based demand. Ann Oper Res 111:239–252CrossRefGoogle Scholar
  42. Reilly WJ (1929) Methods for the study of retail relationships. Research Monograph 4, Bureau of Business Research, The University of Texas, AustinGoogle Scholar
  43. Reilly WJ (1931) The law of retail gravitation. Knickerbocker Press, New YorkGoogle Scholar
  44. ReVelle C (1986) The maximum capture or “sphere of influence” location problem: Hotelling revisited on a network. J Reg Sci 26:343–358CrossRefGoogle Scholar
  45. Reynolds RB (1953) A test of the law of retail gravitation. J Mark 17:273–277CrossRefGoogle Scholar
  46. Sheppard ES (1978) Theoretical underpinnings of the gravity hypothesis. Geogr Anal 10:386–402CrossRefGoogle Scholar
  47. Thrall GI (2002) Business geography and new real estate market analysis. Oxford University Press, New YorkGoogle Scholar
  48. Wagner WB (1974) An empirical test of Reilly’s law of retail gravitation. Growth Change 5:30–35CrossRefGoogle Scholar
  49. Young WJ (1975) Distance decay values and shopping center size. Prof Geogr 27:304–309CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.School of Geographical Sciences and Urban PlanningArizona State UniversityTempeUSA

Personalised recommendations