A column generation method for the (r, p)-centroid problem

Much effort in the discrete location theory has aimed at developing insights concerning the classical models with one decision maker only. In this paper, we study a competitive model with two noncooperative decision makers: the leader and the follower. They compete to attract clients from the given market and wish to maximize their own profits. In fact, this is the noncooperative Stackelberg game. Following Hakimi [2], we call it the (r, p)-centroid problem. It is known that the problem is ∑p 2-complete [3]. So, it is a more difficult problem than any decision problem in the class NP.