A Capacitated, Balanced, 2-Median Problem on a Tree Network with a Continuum of Link Demands

This note considers the problem of locating an absolute 2-median on an undirected tree network having discrete nodal demands as well as a continuum of link demands. The service facilities are assumed to have known finite capacities which sum to the total demand on the network. For this capacitated, balanced case, we derive certain necessary optimality conditions which admit useful localization results. These results permit us to identify and characterize a reduced, finite set of candidate solutions which may be compared to obtain an optimal 2-median for the problem.