The two-echelon capacitated vehicle routing problem

Multi-echelon distribution systems are quite common in supply-chain and logistic systems. They are used by public administrations in their transportation and traffic planning strategies as well as by companies to model their distribution systems. Unfortunately, the literature on com- binatorial optimization methods for multi-echelon distribution systems is very poor. The aim of this paper is twofold. Firstly, it introduces the family of Multi-Echelon Vehicle Routing Problems. Second, the Two-Echelon Capacitated Vehicle Routing Problem, is presented. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) is an extension of the classical VRP where the delivery passes through intermediate depots (called satellites). As in the classical VRP, the goal is to deliver goods to customers with known demands, minimizing the total delivery cost while considering vehicle and satellites capacity constraints. A mathematical model for 2E-CVRP is presented and some valid in- equalities given, which are able to significantly improve the results on benchmark tests up to 50 customers and 5 satellites. Computational re- sults under different realistic scenarios are presented.