The inverse 1-median problem on a tree with transferring the weight of vertices

In this paper, we investigate a case of the inverse 1-median problem on a tree by transferring the weights of vertices which has not been raised so far. This problem considers modifying the weights of vertices via transferring weights of the vertices with the minimum cost such that a given vertex of the tree becomes the 1-median with respect to the new weights. A linear programming model is proposed for this problem. The applicability and efficiency of the presented model are shown in numerical examples and a real-life problem dealing with transferring users in a social network.