First location models were oriented to the private sector where spatial efficiency was essential, and therefore median criteria were used. Later on, problems arising in the public sector would require locating fairly, and therefore centrum criteria were used, oriented to optimizing the situation for the worst served user. Other criteria, such as complete coverage, in which all users are located within an acceptable distance from the service, or multicriteria formulations, which incorporate several objectives in the same model, addressed equality in the services accessibility from different points of view. In fact, the progressive increasing of the public sector in the last years has generated a vast debate about equity in location, both from the conceptual and the strategic point of view (how to characterize it? which is the most appropriate criterium?), from the applied point of view (designing models arising in real situations) and from an algorithmic and computational face.

On the other hand, none of the aforementioned models captures the spatial dispersion of users with respect to the service, which is a relevant issue in order to analyze which is the location that offers the most equitable access for its users. Thus, the incorporation of equity in location has been based on designing a set of specific criteria oriented to evaluating the dispersion of the distance distribution. Those are called Equity Criteria, or more formally, Equality Criteria, in the sense that they integrate the concept of “equity” into that of the “equality” of the relative location of users from services. These criteria are formulated via objective functions that quantify the variability of such a distribution so that it is minimized.

One could say that it was in the paper Equity measurement in facility location analysis: a review and framework (European Journal of Operational Research 74, 1994) where Marsh and Schilling collected these criteria (which came from different scientific areas) and gave them structural and formal elements, thanks to which they were added to Location Theory. In this collection we underline the following criteria: variance, absolute median deviation, absolute maximum deviation, sum of absolute difference pairs, variation coefficient, range and Lorenz (the latter specially differs from the others). The reason for mentioning these criteria is: a) for they are the most used in real applications, and b) for they have been the focuses of the LOGRO group.  Actually, even though they are dispersion measures, and the optimization problems they generate are of minimization, Lorenz criterium (based on the curve of the same name, also called concentration curve) gives rise to a maximization problem. A Lorenz curve example is shown in the picture below. The curve is always below the diagonal, and the corresponding criterium is formulated by quantifying the area between the Lorenz curve and the abscise axis, resulting this way in a maximization model which aims at achieving the Equidistribution.

Within the research line in equity in location, the LOGRO group has incorporated the aforementioned criteria in different models, each of them designed according to its own elements, specially insisting in those that are formulated over a graph like space, which is adequate to model problems whose spatial context is a transport network. The works developed by the group address, from the equity point of view, simple location problems (only one service) and multiple location problems, punctual service locations (which can be considered as a point) and dimensional location problems (structures), with known demand (deterministic) and with uncertain demand hypotheses.