On Parametric Medians of Trees

In this paper we consider the optimal location of a single facility with respect to a set of demand points on a tree network. The demands of the points to be served are dynamic and our model takes into account predictable changes in these demands. We study problems with both linear and nonlinear demand functions. We make use of the analytical properties of tree networks and sensitivity analysis, and devise efficient algorithms to construct the optimal trajectory of the parametric location problem. We also give theory that exploits the network topology.