Locating the two-median of a tree network with continuous link demands

Typical formulations of the p-median problem on a network assume discrete nodal demands. However, for many problems, demands are better represented by continuous functions along the links, in addition to nodal demands. For such problems, optimal server locations need not occur at nodes, so that algorithms of the kind developed for the discrete demand case can not be used. In this paper we show how the 2-median of a tree network with continuous link demands can be found using an algorithm based on sequential location and allocation. We show that the algorithm will converge to a local minimum and then present a procedure for finding the global minimum solution.