Branch and Price for Large-Scale Capacitated Hub Location Problems with Single Assignment

This paper presents a branch-and-price algorithm for the capacitated hub location problem with single assignment, in which Lagrangean relaxation is used to obtain tight lower bounds of the restricted master problem. A lower bound that is valid at any stage of the column generation algorithm is proposed. The process to obtain this valid lower bound is combined with a constrained stabilization method that results in a considerable improvement on the overall efficiency of the solution algorithm. Numerical results on a battery of benchmark instances of up to 200 nodes are reported. These seem to be the largest instances that have been solved to optimality for this problem.