Energy-Aware Time-Dependent Routing of Electric Vehicles for Multi-Depot Pickup and Delivery with Time Windows

The rapid expansion of e-commerce and on-demand logistics has intensified the need for cost-effective and reliable urban distribution systems. This paper investigates an energy-aware routing problem for electric vehicle fleets operating from multiple depots under time-varying traffic conditions. We propose a novel multi-depot vehicle routing model that jointly incorporates time-dependent travel speeds, simultaneous pickup and delivery operations, and time window constraints. The model explicitly captures key operational realities, including battery capacity limitations, load- and speed-dependent energy consumption, synchronized pickup-delivery requirements, and soft time windows. The objective is to minimize total operational cost by simultaneously optimizing depot assignments, vehicle routes, and service schedules. Given the NP-hard nature of the problem, we develop a two-stage heuristic solution framework. In the first stage, a spatio-temporal clustering strategy is employed to assign customers to depots efficiently. In the second stage, route construction and improvement are performed using an enhanced Adaptive Large Neighborhood Search (ALNS) algorithm equipped with problem-specific destroy and repair operators. Computational experiments on adapted benchmark instances demonstrate that the proposed approach consistently produces high-quality solutions and exhibits robust convergence behavior. In addition, sensitivity analyses provide managerial insights, revealing an optimal range of vehicle energy capacity and an economically efficient speed band that balances travel time and energy consumption.