Mathematical Formulations And Results Regarding Two Echelon Electric Vehicle Routing Problems
Mehmet Anıl Akbay, Christian Blum
TL;DR
The paper addresses the Two-Echelon Electric Vehicle Routing Problem (2E-EVRP) and its extensions by formulating robust MILP models that couple a first-echelon truck fleet with a second-echelon EV fleet. It extends the baseline model to incorporate time windows with satellite synchronization, simultaneous pickup and delivery, and partial deliveries, and evaluates solution approaches including CPLEX, Clarke-Wright variants, CMSA, and VNS. Across small to large instances, the study demonstrates the effectiveness and scalability of a hybrid approach, with exact methods excelling on small problems and CMSA (often with Clarke-Wright seeding) delivering strong performance on larger ones. The findings highlight the practical potential of 2E-EVRP formulations for sustainable urban logistics, showing how multi-echelon, battery-constrained routing can be solved efficiently with a mix of exact and heuristic strategies. The work also provides a publicly available dataset and a clear roadmap for future enhancements in routing under charging, time-window, and partial-delivery constraints.
Abstract
The growing need for sustainable logistics solutions has led to the evolution of vehicle routing problems (VRPs) into more complex variants that address modern challenges. Among these, the Two-Echelon Electric Vehicle Routing Problem (2E-EVRP) has emerged as a significant problem variant, integrating electric vehicles (EVs) into a multi-echelon distribution system. This problem considers environmental and operational constraints such as limited battery range, charging infrastructure, and urban logistics complexities. In this report, we present a comprehensive mathematical formulation for the 2E-EVRP and its variants, which include constraints like time windows, simultaneous pickup and delivery, and partial deliveries. These formulations aim to provide a robust framework for optimizing multi-tiered distribution networks using sustainable practices. Computational experiments demonstrate the effectiveness of the proposed methods.