  This paper deals with the facility location problems with balancing on
allocation clients to servers. Two bi-objective models are considered, in which
one objective is the traditional p-median or p-maxian objective and the second
is to minimize the maximum demand volume allocated to any facility. An edge
deletion method with time complexity O(n^2) is presented for the balanced
$2$-median problem on a tree. For the balanced 2-maxian problem, it is shown
the optimal solution is two end vertices of the diameter of the tree, which can
be obtained in a linear time.
