Sustainable and Safe Last-Mile Delivery: A Multi-Objective Truck–Drone Matheuristic

Background : The rapid growth of e-commerce has intensified the need for last-mile delivery systems that can navigate urban congestion while minimizing environmental impact. Hybrid truck–drone networks offer a promising solution by combining heavy-duty ground transport with aerial flexibility; however, their deployment faces significant challenges in jointly managing operational risks, energy limits, and regulatory compliance. Methods : This study proposes a hybrid matheuristic framework to solve this multi-objective problem, simultaneously minimizing transportation cost, service time, energy consumption, and operational risk. A two-phase approach combines a metaheuristic for initial truck routing with a Mixed-Integer Linear Programming (MILP) formulation for optimal drone assignment and scheduling. This decomposition strikes a balance between exact optimization and computational scalability. Results : Experiments across various instance sizes (up to 100 customers) and fleet configurations demonstrate that integrating MILP enhances solution diversity and convergence compared to standalone strategies. Sensitivity analyses reveal significant impacts of drone speed and endurance on system efficiency. Conclusions : The proposed framework provides a practical decision-support tool for balancing complex trade-offs in time-sensitive, risk-constrained delivery environments, thereby contributing to more informed urban logistics planning.