We show that certain reasonable axioms for an optimal solution to the problem of locating a facility on a network, i.e., axioms of distance determination, Pareto optimality, existence, and anonymity, and a weak Lipschitz condition, can be self-contradictory. In particular, we show that they fail for any network that has a cycle. It follows that under the axioms of distance determination, Pareto optimality, existence, and anonymity, choice of optimal location may be very sensitive to changes in the locations of the users.
Published January 1992 , 36 pages
This cahier was revised in July 1992