A new formulation and an exact approach for the many-to-many hub location-routing problem

An important problem of the freight industry is the parcel delivery network design, where several facilities are responsible for assembling flows from several origins, re-routing them to other facilities where the flows are disassembled and the packages delivered to their final destinations. In order to provide this service, local tours are established for the vehicles assigned to each of the processing facilities, which are then responsible for the pickup and delivery tasks. This application gives rise to the many-to-many hub location routing problem that is the combination of two well known problems: the vehicle routing problem and the single assignment hub location problem. In this work, a new formulation for this important problem is proposed and solved by a specially tailored Benders decomposition algorithm. The proposed method is robust enough to solve instances up to 100 nodes having 4 million integer variables.