An aggregation approach to solving the network p-median problem with link demands

This paper considers the p-median problem on a general network with link demands. We construct the network in such a way that only transportation intersections are taken to be nodes and, therefore, both continuous and discrete link demands are allowed in our model. For such a model, we show that a nodal solution can be used to approximate the true optimal solution and an error bound which involves only the demands on a single link is given for the error caused by such an approximation. Based on nodal solutions, we demonstrate that a model with continuous link demands can be transformed into an equivalent discrete link demand model. Further, we propose a method to aggregate demands on each link in solving the p-median problem on a general network without introducing any aggregation errors to the problem solution. The implementation of the proposed approach with some heuristics is discussed.