Minimizing the number of vehicles and the total time travelled in order to visit each delivery points, is a challenging task studied within the Vehicle Routing Problems and applied to several domains. In this paper, we introduce a multi-vehicle and multi-depot pickup and delivery problem with time constraints considering the capacities of both vehicles and logistic nodes. Our solution, structured on three-layer architecture, integrates information about sorting nodes and delivery nodes, travel distances, and demands (items to be delivered daily) allowing us to simulate arrival times at each destination points. We apply our model to a real-world scenario in the postal and logistics domain and we provide computational experiments to demonstrate the value of our approach. The model allows logistic designers to assess the impact of volumes and capacity changes on overall delivery times.