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 -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.
"An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective." J. Appl. Math. 2014 (SI08) 1 - 12, 2014. https://doi.org/10.1155/2014/562373