Physical Internet Hub-Integrated Drone Logistics Model: Optimizing Cost and Energy Efficiency for Urban Delivery Systems

Drones are revolutionizing urban logistics by enhancing last-mile delivery efficiency and speed. This study focuses on integrating drones within the Physical Internet (PI) framework, a paradigm aimed at optimizing goods movement, through the development of the Physical Internet Hub-Integrated Drone Logistics (PI-HI-DL) model. The model minimizes operational costs by optimizing delivery routes and is formulated as a Mixed-Integer Linear Programming (MILP) problem. To address the computational complexity of the model, a tailored Hybrid Genetic Algorithm (HGA) is introduced. The HGA features two novel components: the Adaptive Insertion and Allocation (AIA) heuristic and the Hybrid Heuristic Crossover (HHX) operator. The AIA heuristic enables real-time synchronization of drone routes, energy consumption, and the dynamic positioning of open urban hubs (OUH) and open recharge stations (ORS), ensuring adaptability to changing conditions. The HHX operator incorporates problem-specific knowledge to improve solution quality during crossover operations, enhancing the algorithm's efficiency and scalability. The study compares two scenarios: a drone-only model and the PI-HI-DL model. Results demonstrate the PI-HI-DL model's superior performance, particularly in solving both small and large problem instances. A comparative analysis between the exact MILP approach and the HGA-based metaheuristic highlights the trade-offs between computational efficiency and solution quality. Further, results from a real-world case instance reveal that the PI-HI-DL model achieves up to 9% energy cost savings compared to the drone-only scenario. These findings underscore the potential of integrating drones within PI networks to enhance cost-effectiveness and energy efficiency, advancing sustainable and resilient urban logistics systems.