COMPETITIVE LOCATION ON A NETWORK

Consider a network with a given number of customers at fixed locations (vertices) and where each customer will purchase a commodity from the facility closer to his,location more frequently than from a remote on e. As a generalization of the Condorcet concept we define an optimal p oint as a location such that there exists no competitor with higher ex pected value. We show that the set of optimal points consists entirely of vertices. In general we provide polynomial algorithms to answer th e question as to: What is the maximum percentage of customers located on the network prefering some rival point to an existing location? Sub optimal points where the maximal relative rejection by a rival point i s minimal are determined in polynomial time.