A multi-objective matheuristic framework for sustainable truck-UAV last-mile delivery in smart urban built environments

Purpose – This study addresses the escalating challenges of last-mile logistics driven by e-commerce growth and sustainability requirements. Despite recent advances in truck-UAV delivery models, existing studies often treat cost, energy and risk objectives in isolation or rely on purely heuristic or purely exact solution methods. This study explores the integration of hybrid truck-UAV delivery systems as an innovative component of sustainable urban infrastructure, with a focus on jointly balancing cost, service time, energy consumption and safety risk. Design/methodology/approach – A hybrid multi-objective matheuristic framework is proposed, combining a metaheuristic-based truck routing phase with a mixed-integer linear programming (MILP)-based UAV assignment and scheduling phase. This integration leverages the scalability of heuristics with the precision of mathematical programming to generate efficient Pareto-optimal solutions. Computational experiments were conducted on benchmark instances of up to 100 customers. Findings – Results show that MILP-guided initialization accelerates convergence and improves solution diversity compared to purely heuristic approaches. Sensitivity analyses highlight that configurations with two UAVs per truck and moderate endurance achieve the most balanced performance across sustainability objectives, significantly reducing energy use and delivery risk. Practical implications – The framework provides a scalable decision-support tool for logistics operators, urban planners and policymakers to design safe, efficient and climate-responsive last-mile delivery networks that align with sustainable urban development strategies. Social implications – By incorporating sustainability and safety risk into the optimization process, the framework supports the transition towards resilient, inclusive and environmentally responsible delivery systems, directly contributing to the achievement of the United Nations sustainable development goals (SDGs). Originality/value – To the best of the authors' knowledge, this study is among the first to develop a multi-objective matheuristic that integrates exact and heuristic optimization methods for truck-UAV coordination in sustainable last-mile logistics. It advances both methodological innovation and practical relevance for the built environment, bridging operations research with urban sustainability.