OR Spectrum

, Volume 31, Issue 3, pp 555–571 | Cite as

Maximal covering location problem with price decision for revenue maximization in a competitive environment

Regular Article

Abstract

In this article, we extend the classical maximal covering model in a competitive environment by including a price decision. We formulate a revenue maximization model and propose two procedures to solve it. By a careful examination of the relationships between the maximal covering problems for different prices, we reveal interesting properties of the deduced revenue maximization model, leading to a full enumeration solution approach. With the help of two more properties we develop a second, more intelligent solution procedure. Computational experiments show promising results for a small, medium and large case study.

Keywords

Competitive location Spatial pricing Revenue maximization Maximal covering problem Mixed integer programming 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Church R, ReVelle C (1974) The maximal covering location problem. Pap Reg Sci 32(1): 101–118CrossRefGoogle Scholar
  2. d’Aspremont C, Gabszewicz J, Thisse J-F (1979) On Hotelling’s “Stability in Competition”. Econometrica 47(5): 1145–1150CrossRefGoogle Scholar
  3. Eiselt HA (1992) Hotelling’s duopoly on a tree. Ann Oper Res 40(1): 195–207CrossRefGoogle Scholar
  4. Eiselt HA, Laporte G (1993) The existence of equilibria in the 3-facility Hotelling model in a tree. Transport Sci 27(1): 39–43CrossRefGoogle Scholar
  5. Eiselt HA, Laporte G, Thisse J-F (1993) Competitive location models: a framework and bibliography. Transport Sci 27(1): 44–54CrossRefGoogle Scholar
  6. Hakimi S (1986) p-median theorems for competitive locations. Ann Oper Res 6(4): 75–98CrossRefGoogle Scholar
  7. Hotelling H (1929) Stability in competition. Econ J 39(153): 41–57CrossRefGoogle Scholar
  8. Labbé M, Hakimi S (1991) Market and location equilibrium for two competitors. Oper Res 39(5): 749–756CrossRefGoogle Scholar
  9. Lederer P, Thisse J (1990) Competitive location on networks under delivered pricing. Oper Res Lett 9(3): 147–153CrossRefGoogle Scholar
  10. Plastria F (2001) Static competitive facility location: an overview of optimisation approaches. Eur J Oper Res 129(3): 461–470CrossRefGoogle Scholar
  11. Plastria F, Vanhaverbeke L (2007) Aggregation without loss of optimality in competitive location models. Netw Spat Econ 7(1): 3–18CrossRefGoogle Scholar
  12. Serra D, ReVelle C (1995) Competitive location in discrete space. In: Drezner Z (ed) Facility location. Springer, Berlin, pp 337–356Google Scholar
  13. Serra D, Revelle C (1999) Competitive location and pricing on networks. Geogr Anal 31: 109–129Google Scholar
  14. Wendell R, McKelvey R (1981) New perspectives in competitive location theory. Eur J Oper Res 6(2): 174–182CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.MOSI, Department of Mathematics, O.R., Stat. and Inf. Syst. for ManagementVrije Universiteit BrusselBrusselsBelgium

Personalised recommendations