A generic mathematical formulation for two-echelon distribution systems based on mobile depots

Abstract

The negative impacts of urban logistics have fostered the search for new distribution systems in inner city deliveries. In this context, interesting solutions can be developed around two-echelon distribution systems based on mobile depots (2E-MD), where loads arriving from the periphery of the city are directly transferred, at intermediate locations, from larger to smaller vehicles more suited to operate in the city centre. Four types of 2E-MD can be identified, according to the degree of mobility of larger vehicles and their accessibility to customers.In this paper, we propose a generic three-index arc-based mixed integer programming model, for a two-echelon vehicle routing problem, with synchronisation at the satellites and multi-trips at the second echelon. This generic base model is formulated for the most restrictive type of problems, where larger vehicles visit a a single transfer location and do not perform direct deliveries to customers, but it can be easily extended to address the other types of 2E-MD. The paper presents how these extensions account for the characteristics of the different types of 2E-MD.The generic model, its extensions and the impact of a set of valid inequalities are tested using problem instances adapted from the VRP literature. Results show that the proposed extensions do adequately address the specific features of the different types of 2E-MD, including multiple visits to satellites, and direct deliveries to customers. Nevertheless, the resulting models can only tackle rather small instances, even if the formulations can be strengthened by adding the valid inequalities proposed in the paper.