Maximal Covering Location Problem with Price Decision for Revenue Maximization in a Competitive Environment ∗ Frank Plastria & Lieselot Vanhaverbeke MOSI - Dept. of Math. , O.R. , Stat. and Inf. Syst. for Management, Vrije Universiteit Brussel Pleinlaan 2, B-1050 Brussels, Belgium e-mail: {Frank.Plastria, Lieselot.Vanhaverbeke}@vub.ac.be May 13, 2008 Abstract In this paper we extend the classical maximal covering model in a competitive envi- ronment 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 Cov- ering Problem, Mixed Integer Programming. 1 Introduction A new firm wants to enter a market where other players are already active. Location and price are to be decided upon. Given that we consider a homogeneous product, we assume that it is impossible to differentiate on that aspect. The firm’s goal is to maximize its revenue in this competitive environment. Models for competitive location including price decisions are rather rare. The first analytical competitive location study was done by Hotelling in his seminal paper ‘Stability in Competi- tion’ Hotelling H. (1929). He described the strategies of two competitors in a linear market with respect to price and location and he studied equilibrium questions. Several authors replied to Hotelling’s work and extended its assumptions in the years after the first publica- tion, for an overview see Eiselt, H.A., Laporte, G., Thisse, J.-F. (1993). Later, Hotelling’s “Principle of Minimum Differentation” was criticized by d’Aspremont et al. d’Aspremont, C., Gabszewicz, J., Thisse, J.-F. (1979). In the seventies of the 20th century, a myriad of ∗ This research was partially supported by the projects OZR1067 and SEJ2005-06273ECON. 1