Analysis of multimedian problems on time dependent networks

Time dependency arises in transportation and computer-communication networks due to factors such as time varying demand, traffic intensity, and road conditions. This necessitates a locational decision to be based on an analysis involving a time horizon. In this study, we analyze multi-median problems with linear demand functions on both tree and cyclic networks in a continuous time domain. The trajectory of the optimal solution is a piecewise linear concave function. We develop an algorithm that constructs the trajectory by solving 0{q) static problems, where q is the number of linear pieces in the trajectory. The properties of the optimal solution over the time horizon are also analyzed for various randomly generated problem instances.