Anti-cent-dian on networks

This paper deals with the problem of locating an undesirable facility on a network using the anti-cent-dian criterion. The objective is the maximization of a convex combination of the average and the minimum distance to the population. The model is formulated and its main properties are studied. Two problems are considered: to find the optimal location given the weights of the convex combination, and to provide the set of optimal locations for all convex combinations. A finite dominant set of points is identified for both problems, and for the first a heuristic algorithm is proposed to reduce the number of computations. Some computational results on randomly generated networks are given.