A Biobjective Multifacility Minimax Location Problem on a Tree Network

In this paper we consider a biobjective multifacility minimax location problem on a tree network, which involves as objectives the maximum of the weighted distances between specified pairs of new and existing facilities, and the maximum of the weighted distances between specified pairs of new facilities. We establish necessary and sufficient conditions for a location vector to be efficient. We also give an algorithm for finding the efficient frontier of the problem, and provide an example illustrating the use of the algorithm. In addition, we consider a broad class of multiobjective location problems and give general necessary and sufficient conditions for a location vector to be efficient.