Relaxed equidistant function and its axiomatic characterization on complete graphs and complete bipartite graphs

Classical location problems such as center and median deal with identifying locations that minimise the maximum distance to the customers or the average distance to the customers, respectively. This paper presents a novel location function termed as the relaxed equidistant function, aimed at reducing the disparity between the farthest and nearest distances of a facility from its customers. Using axioms that already exist in the literature for location functions along with an axiom specific to relaxed equidistant function, we provide an axiomatic characterization of this function on some important graph classes such as complete graphs and complete bipartite graphs. This function is essential in locating emergency facilities, where reducing inequality in accessing services is as important as lowering the worst-case (maximum) distance.