New formulation and a branch-and-cut algorithm for the multiple allocation p-hub median problem

New formulation and a branch-and-cut algorithm for the multiple allocation p-hub median problem Sergio García, Mercedes Landete and Alfredo Marín Septiembre 2011 ISSN 1576-7264 Depósito legal A-646-2000 Abstract This article deals with the uncapacitated multiple allocation phub median problem, where p facilities (hubs) must be located among n available sites in order to minimize the transportation cost of sending a product between all pairs of sites. Each path between an origin and a destination can traverse any pair of hubs. For the first time in the literature, an Integer Programming formulation with O(n2) variables has been devised to approach this problem. Based on this formulation, a branch-and-cut algorithm has been developed which allows to solve larger instances than those previously solved in the literature. The proposed algorithm performs especially well for relatively large values of $p$.