A row generation method for the inverse continuous facility location problems

Abstract

In the most single facility location problems, a set of points is given and the goal is to find the optimal location of a new facility with respect to given criteria such as minimizing time, cost, and distances between the clients and facilities. On the other side, the inverse single facility location problems try to modify the parameters of the problem with the minimum cost such that a given point becomes optimal. In this paper, we introduce a novel algorithm for the general case of the inverse single facility location problem with variable weights in the plane. The optimality conditions of the algorithm are presented. Then in the special cases the inverse minisum and minimax single facility location problems are considered and the algorithm is tested on some instances. The results indicate the efficiency of the algorithm on these instances.