Group for Research in Decision Analysis

G-92-02

An Impossibility Result in Axiomatic Location Theory

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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.

, 36 pages

This cahier was revised in July 1992