An Axiomatic Approach to Location on Networks

The problem under consideration is that of locating a facility on a tree-network, given data specifying the locations of the users on the network. The approach taken is to formulate axioms that require consistent response of the solution to variations in the users' location data. It is shown that three independent axioms determine together a unique solution, located at the point that minimizes the sum of the squares of the distances to the users.