A Branch-and-Cut-and-Price Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem

In this paper, we introduce a branch-and-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem. The algorithm relies on a reformulation based on q-routes that combines two important features. First, it overcomes symmetry issues observed in a formulation coming from a previous study of the problem. Second, it is strengthened with several classes of valid inequalities. As a result, the branch-and-cut-and-price implementation compares favorably with previous exact solution approaches for the problem—namely, two branch-and-price algorithms and a branch-and-cut method. Overall, 10 new optimality certificates and 8 new best upper bounds are provided in this study. New best lower bounds are also presented for all instances in the hardest test set from the literature.