A row generation method for inverse continuous facility location problem

TL;DR

This paper introduces a new row generation algorithm for the inverse single facility location problem with variable weights, demonstrating its effectiveness through theoretical analysis and computational experiments.

Contribution

It presents a novel row generation method for the inverse continuous facility location problem, including convergence and optimality analysis, and applies it to special cases with promising results.

Findings

Algorithm is efficient on tested instances

Convergence and optimality conditions are established

Effective for inverse minisum and minimax problems

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 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.