Exploring Similarities in Discrete Facility Location Models with Equality Measures

There have 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 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 contexts 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 article, we propose a facility location problem 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 to test the similarities 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.