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

This article deals with the uncapacitated multiple allocation p-hub 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 specially well for relatively large values of p.

► New formulation for the uncapacitated p-hub location problem. ► Integer formulation with O(n2) variables. ► New formulation whose constraints can be added on demand. ► Larger instances than those previously solved in literature are solved. ► Problems with up to 200 nodes for large values of p are solved.