Multi-objective optimization of a truck–drone delivery system for fair and efficient humanitarian logistics under disruption and disinformation

Humanitarian logistics systems face significant challenges due to infrastructure damage, accessibility constraints, and the need for equitable and timely aid delivery. This paper introduces the Multi-Truck and UAV Routing Problem (MTURP), a novel bi-objective optimization model that coordinates trucks and drones to support last-mile delivery under disrupted conditions. The two objectives are to minimize the delivery time gap to improve fairness and reduce total travel distance to enhance efficiency. Unlike existing truck–drone routing models that optimize latency or cost alone, our formulation introduces a fairness objective based on a minimax criterion, minimizing the temporal gap between the earliest and latest deliveries to ensure equitable service. The model also incorporates socially informed prioritization using community vulnerability data (SVI) as equity weights, linking operational optimization with social resilience considerations. Given the problem's NP-hard nature, we develop a solution approach based on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and benchmark its performance against an ϵ-constraint exact method using Gurobi. Results demonstrate that NSGA-II can achieve near-optimal solutions within 3%–10% of the Pareto front while significantly reducing computational time, especially for larger instances. Two case studies validate the framework: (i) an urban flood in Hoboken, NJ, and (ii) a rural disaster in Hopkins County, KY, where SVI-based weights are used solely to prioritize aid equitably across communities under uncertain information conditions. This approach emphasizes fairness without excluding any demand nodes or inferring disinformation, aligning with humanitarian principles of inclusive and needs-based allocation. Overall, the proposed framework highlights the practical value of integrating collaborative truck–drone operations with multi-objective optimization for scalable, fair, and disruption-resilient humanitarian logistics.