Inverse and reverse balanced facility location problems with variable edge lengths on trees

Abstract

This paper deals with 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.