Integrating electric vehicles into the pickup and delivery problem with crossdock and time window constraints

Pickup and delivery operations with cross-docking play a critical role in urban freight logistics by enabling rapid consolidation and synchronization of goods flows. The increasing adoption of electric vehicles in such systems is motivated by environmental targets but introduces operational challenges related to limited driving range, battery charge feasibility, and charging constraints under strict time-window requirements. This study investigates whether crossdock-based pickup and delivery systems can be operated feasibly and efficiently when vehicle routing decisions must also satisfy battery-related constraints. To address this question, a mixed-integer linear programming model is developed that integrates battery charge dynamics and opportunistic recharging directly into the crossdock handling process, ensuring energy feasibility across multiple routing phases. Numerical experiments show that, while the use of electric vehicles leads to moderately higher operating costs compared to conventional fleets, feasible and operationally consistent solutions can be achieved without additional routing detours. Overall, the proposed formulation provides an optimization framework for assessing the trade-offs between energy constraints, synchronization requirements, and routing efficiency in sustainable urban logistics systems.