An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective

Abstract EN

We present a new approximation algorithm to the discrete facility location problem providing solutions that are close to the lexicographic minimax optimum.

The lexicographic minimax optimum is a concept that allows to find equitable location of facilities serving a large number of customers.

The algorithm is independent of general purpose solvers and instead uses algorithms originally designed to solve the p-median problem.

By numerical experiments, we demonstrate that our algorithm allows increasing the size of solvable problems and provides high-quality solutions.

The algorithm found an optimal solution for all tested instances where we could compare the results with the exact algorithm.