Persistent Homology applied to location problems

Different approaches to solve location problems in transport and logistics have been developed in the literature. This article introduces a new approach using the concept of persistent homology which has been proved to be an efficient method in topological data analysis; and has been served as an alternative new tool in many and various research areas such as image processing, material science and biological systems. Precisely, inspired by the notions of the first homology groups and the persistent homology which mainly describe the behaviour of connectivity relation between elements during a filtration of specific topological spaces; we develop a new method and approach for the treatment of facility location–network design problems.