Abstarct: In ‎this ‎thesis, ‎we ‎combine ‎inverse ‎location ‎and ‎balanced ‎location ‎problem.‎‏ ‎in a‎ ‎model‎ the inverse and reverse balanced facility location problems with considering the variable edge lengths. The aim of the inverse problem is modifying the length of edges with minimum cost, such that the difference between the maximum and minimum weights of clients, allocated to the given facilities is minimized. On the other hand, the reverse case of the balanced facility location problem considers the modifying the lengths of edges with a given budget constraint, such that the difference between the maximum and minimum weights of vertices, allocated to the given facilities is reduced as much as possible. Two algorithms with time complexity O(nlogn)are presented for the inverse and reverse balanced 2-facility location problems.‏‎ in‎ addition, ‎we introduce a case of inverse single facility location problem on a tree‏ ‎and ‎we ‎want ‎to ‎modify in the length of edges with minimum cost, such that the difference of distances between the farthest and nearest clients to a given facility is minimized. Two cases are considered: bounded and unbounded nonnegative edge lengths. In the unbounded case, we show the problem can be reduced to solve the problem on a star graph. Then an ‎O(nlogn)‎ algorithm is developed to find the optimal solution. For the bounded edge lengths case an algorithm with time complexity O(n^2)is presented. ‎