Two-echelon vehicle routing problem with direct deliveries and access time windows

Nowadays, heavy-duty trucks are usually restricted from entering urban areas due to emission and congestion problems in most cities. So, a two-echelon distribution system becomes vastly applicable, in which satellites transfer cargo and avoid heavy-duty trucks entering urban areas. However, with the development of new energy vehicles and access policies and regulations, some environmentally friendly trucks are accessible to urban areas within specific time windows of daytime directly. In light of this, we introduce a two-echelon vehicle routing problem with direct deliveries and access time windows (2E-VRPDDATW) arising in city logistics. In this problem, customers are served by the two-echelon distribution systems within their required time windows and are allowed to be directly delivered by the first echelon vehicles within access time windows, which provides more flexible routing schemes. A novel mixed integer linear programming (MILP) model for the above problem is presented, and the corresponding adaptive large neighborhood algorithm is developed. The computational experiments are provided to verify the validity of the proposed model and the effectiveness of the algorithm. Finally, the sensitivity analysis shows some interesting findings about the number of two-echelon vehicles and the assignment of customers. Moreover, we conclude that direct deliveries are advantageous in transportation costs when the proportion of the end time of access time window to the last end time of customers is greater than 0.25.