Inverse single facility location problem in the plane with variable coordinates

In traditional facility location problems, a set of points is provided, and the objective is to determine the best location for a new facility based on criteria such as minimizing cost, time, and distances between clients and facilities. Conversely, inverse single facility location problems focus on adjusting the problem's parameters at minimal cost to make a specific point optimal. In this paper, we present an algorithm for the general case of the inverse single facility location problem with variable coordinates in a two-dimensional space. We outline the optimality conditions of this algorithm. Additionally, we examine the specific case namely the inverse minisum single facility location problem and test the algorithm on various instances. The results demonstrate the algorithm's effectiveness in these scenarios.