The sum of absolute differences on a network: Algorithm and comparison with other equality measures

In this work, we address a double objective. In the first place, we study the problem of locating a single facility on a network N(V,E) which minimizes the sum of absolute difference between all pairs of weighted travel distances from the users to the facility, and we propose an O(E//V[²]log/V/) algorithm for solving it. Likewise, we present a computational experience in which we compare the behavior of several equality measures by means of the placement of their respective optimal locations. To this end, we define a measure of relative proximity between two optima, and we analyse the results obtained by considering several setting models of the network.