A robust branch-cut-and-price algorithm for the heterogeneous fleet vehicle routing problem

This paper presents a robust branch-cut-and-price algorithm for the Heterogeneous Fleet Vehicle Routing Problem (HFVRP), vehicles may have various capacities and fixed costs. The columns in the formulation are associated to q-routes, a relaxation of capacitated elementary routes that makes the pricing problem solvable in pseudo-polynomial time. Powerful new families of cuts are also proposed, which are expressed over a very large set of variables. Those cuts do not increase the complexity of the pricing subproblem. Experiments are reported where instances up to 75 vertices were solved to optimality, a major improvement with respect to previous algorithms.