An approximation algorithm for the facility location problem with lexicographic minimax objective

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. © 2014 ľuboš buzna et al.