  In a single facility location problem, a set of points is given and the goal
is finding the optimal location of new facility respect to given criteria such
as minimizing time, cost and distances between the clients and facilities. On
the other side, the inverse models 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 convergence
and 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 tested on some instances. The results indicate the
efficiency of the algorithm on these instances.
