The centdian problem [2,3] seeks P points that minimize a convex combination of the median (average) and center (maximum) distance objectives. In this paper we outline an approach to finding all non-dominated points on the tradeoff between these two objectives, including those that are contained in the duality gap region (i.e., those that could not be found by minimizing a convex combination of two other solutions). We solve the problem assuming that facilities must be located on the nodes of the network. We first solve the P-center problem yielding the smallest maximum distance within which all demands can be served by P facilities. We then solve the P-median problem yielding the smallest average distance. The largest distance, Dc , for the P-median solution is computed. A suitably large endogenously determined constant is added to all distances greater than or equal to Dc. The solution to a new P-median problem with the modified distance matrix will utilize new facility locations and will have a maximum assigned distance strictly less than Dc, and a larger average distance. We then compute the maximum distance for the new solution and repeat the process until the maximum distance for the last solution found equals the objective function value for the P-center problem. The algorithm was tested on problems ranging in size from 49 nodes to 200 nodes and for values of P=5, 10, 15, 20
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