Problemas de localización competitiva. El modelo de Huff

Abstract

The ability of a firm to produce goods and/or services and market them effectively depends largely on the location of its facilities. Location theory deals with the modelling, formulation and solution of mathematical problems related to sitting facilities in a given space. In this text, we focus on competitive location models. The root of competitive location models is Hotelling’s seminal article ‘Stability in Competition’ in 1929. Frank Plastria defines a location model as competitive “ when it explicitly incorporates the fact that other facilities are already - or will be - present in the market and that the new facility or facilities will have to compete with them for its or their market share". This work starts with a short introduction to competitive location models, including a brief description of the elements of these models. Next, we address Huff’s model in the continuous space, exposing two different techniques to solve this problem, the generalized Weiszfeld algorithm and a standard branch and bound algorithm. Then, we develop a discrete competitive location model. Resolution methods are described. Computational experiments are reported both for the continuous and the discrete model. The remainder of the text contains the codes of R and AMPL used for solving the posed problems.