New Valid Inequalities for the Two-Echelon Capacitated Vehicle Routing Problem

Multi-echelon distribution systems are quite common in supply-chain and logistic management. They are used by public administrations in their transportation and traffic planning strategies as well as by companies to model their distribution systems. In the literature, most studies address issues related to the movement of flows throughout the system from the origins to their final destinations. In this paper we consider the Two- Echelon Capacitated Vehicle Routing Problem (2E-CVRP), the two-echelon variant of the well known Capacitated Vehicle Routing Problem, where the delivery from one depot to the customers is managed by routing and consolidating freight through intermediate depots, called satellites. The main goal of this paper is the definition of new classes of valid inequalities for strengthening the linear formulation of the 2E-CVRP. More in detail, valid inequalities based on the TSP and CVRP, the network flow formulation, and the connectivity of the transportation system graph are presented. These valid inequalities are tested through a branch-and-cut algorithm and extensive computational results on instances with up to 50 customers and 5 satellites are reported.