Exploring similarities in discrete facility location models with equality measures

There has been a number of discrete facility location models that deal with the use of some equality measures of the distances between the facility and the users. They have been used in order to guarantee a similar level of equity among the users that may be affected in a positive or in a good way from a facility. These models have been formulated trying to adapt equality measures taken from context different from the location one. This way, every measure is very specific to the particular application and it is not highlighted why a measure should be selected and what is the contribution to the equity distribution among the users that can provide. In this paper, we propose a Facility Location Problem (FLP) in which we have to locate a given number of facilities among a set of potential facilities, optimizing an equality measure. We propose a computational study in order to test the similarity and the differences of a good number of measures with more than a single facility to locate and we point out which measures produce similar results and how they depend on each other.