Facility location and the mean function: A study of centrality measures in facility location with an emphasis on the mean function

This paper presents the well known center and median functions on graphs in the context of determining a facility location for a profile of customers. This differs somewhat from the customary approach where the center and median are studied on entire graphs rather than a select profile of vertices. This paper often presents properties of the center and median that have been proven to hold true in the customary approach, and extends them to include profiles where appropriate.;This paper also presents a less known function identified as the mean. Included are some original results on properties of the mean function on profiles in a tree. We conclude with a presentation of the axiomatic approach to facility location, within which the mean is shown to satisfy several meaningful axioms.