A row generation method for the general case of inverse continuous facility location problem Jafar Fathali ∗ Abstract 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 crite- ria such as minimizing time, cost and distances between the clients and facilities. On the other side, the inverse models try to modify the pa- rameters 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 vari- able 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. Keywords: continuous facility location; row generation; inverse facility location; variable weights 1 Introduction The single facility location problem is well known in operations research literature and plays an important role in practice. The continuous version of this problem asks for finding the location of a facility in the plane, such that the cost of servicing clients by the facility is minimized. In the classical version of facility location problems, a set of points, represent the location of clients, are given and a weight is assigned to each point. Two basic ob- jective functions in the facility location problems are minimizing the sum of weighted distances and the maximum weighted distances between clients and the facility, which called minisum and minimax single facility location * Faculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, Iran, E-mail: fathali@shahroodut.ac.ir. 1 arXiv:2008.00704v1 [math.OC] 3 Aug 2020