Fixed or variable demand? Does it matter when locating a facility?

In most competitive location models available in the literature, it is assumed that the demand is fixed independently of market conditions. However, demand may vary depending on prices, distances to the facilities, etc., especially when the goods are not essential. Taking variable demand into consideration increases the complexity of the problem and, therefore, the computational effort needed to solve it, but it may make the model more realistic. In this paper, a new planar competitive location and design problem with variable demand is presented. By using it, it is shown numerically for the first time in the literature that the assumption of fixed demand influences the location decision very much, and therefore the selection of the type of demand (fixed or variable) must be made with care when modeling location problems. Finally, two methods are presented to cope with the new model, an exact interval branch-and-bound method and an evolutionary algorithm called UEGO (Universal Evolutionary Global Optimizer).