The value of integrating loading and routing

Location-routing, inventory-routing, multi-echelon routing, routing problems with loading constraints are classes of problems that are receiving increasing attention in the scientific community. Problems in these classes generalize classical vehicle routing problems enlarging the decision space to optimize a broader system. The resulting problems are computationally harder to solve but offer opportunities to achieve remarkable additional savings. In this paper, we address the issue of quantifying the potential benefit deriving from tackling directly such complex problems instead of solving the individual problems in a not integrated manner. To this aim, we consider as a proof of concept the Capacitated Vehicle Routing Problem (CVRP) with Two-dimensional Loading constraints (2L-CVRP), a variant of the CVRP where rectangular-shaped items have to be delivered to customers and loading constraints have to be satisfied. We consider the 2L-CVRP in an integrated manner and compare the solutions with those obtained from three not integrated approaches based on addressing separately the routing and the loading problems. The importance of an integrated approach for the 2L-CVRP is validated through the study of the worst-case performance of the not integrated approaches, and conducting computational experiments on benchmark and new instances.