The most common problems studied in network location theory are the p-median and the p-center models. The p-median problem on a network is concerned with the location of p points (medians) on the network, such that the total (weighted) distance of all the nodes to their respective nearest points is minimized. The p-center problem is concerned with the location of p-points (centers) on the network, such that the maximum (weighted) distance of all the nodes to their respective nearest points is minimized. To capture more real-world problems and obtain a good way to trade-off minisum (efficiency) and minimax (equity) approaches, Halpern introduced the centdian model, where the objective is to minimize a convex combination of the objective functions of the center and the median problems. In this paper, we studied the p-centdian problem on tree networks and present the first polynomial time algorithm for this problem.
