Locating a desirable facility with an equity criterion

A possible equity criterion for locating a facility is the minimization of the variance of the vector of distances separating the facility and the users. However, such criterion may yield locations which, although rather equitable, are unreliable in practice due to the extremely high transportation costs associated with them. In this note we address the problem of locating a desirable facility in a continuous space when demand is distributed following an N-variate random vector. As performance measure, equity and efficiency criteria are combined into a single objective following a weighing approach, leading to a parametric global-optimization problem, which can be tackled by standard techniques such as the BSSS method.