Journal of Operational Research and Its Applications ( Applied Mathematics ) - Lahijan Azad University

In this paper, we investigate the backup undesirable -center location models on tree graphs. The aim is to obtain the best locations on the vertex set of the underlying tree for establishing two undesirable servers so that the expected value of the closest distance from the existing customers to the functioning facilities is maximized under the assumption that any facility may fail with a given probability and in this case the other active server must serve all the customers. The exact combinatorial algorithms with  and time complexities are developed for obtaining the optimal solutions of two certain models, where is the number of the vertices in the given tree graph.