Time Dependent Truck–Drone Green Vehicle Routing Problem with Pickup and Delivery in Large Cities

Recognizing the limitations of traditional vehicle routing models in urban environments, this work presents the Time-Dependent Truck-Drone Green Vehicle Routing Problem with Pickup and Delivery (TDTDGVRPPD) to simultaneously optimize environmental impact and operational efficiency. We first develop a truck fuel consumption and carbon emission model that accounts for the effects of time-varying speeds and real-time loads during delivery. A nonlinear energy consumption model is then proposed for drones, considering payload weight. Based on these models, a mathematical formulation is developed to minimize the total operational cost, including truck and drone usage costs, truck fuel and carbon emission costs, drone energy consumption costs, truck–drone coordination time costs, and time-window violation penalties. The model also incorporates truck no-entry zones, time-varying speeds, and customers’ simultaneous pickup and delivery demands. An Improved Whale Optimization Algorithm (IWOA) hybridized with Variable Neighborhood Search (VNS) is developed to solve the problem. Simulation results show that the proposed model and algorithm effectively optimize truck departure times to avoid traffic congestion, reduce truck–drone coordination time, and lower total logistics costs and energy consumption, thereby contributing to energy conservation and emission reduction in logistics operations.