A Bayesian trust-based hybrid truck-drone coalition framework for resilient and sustainable last-mile delivery

Abstract

This study proposes a novel hybrid Truck-Drone-Coalition (TDC) framework to enhance the resilience and sustainability of last-mile urban delivery systems. The model optimizes four conflicting objectives simultaneously: total delivery cost, service time, operational risk, and unmanned aerial vehicles (UAVs, also called drones) energy consumption. To address behavioral uncertainty among coalition partners, we integrate a Bayesian trust update mechanism with a Markov transition process, enabling dynamic adjustment of cooperation levels and automatic activation of fallback outsourcing when trust thresholds are breached. The solution combines an exact Mixed-Integer Linear Programming (MILP) core with a Non-dominated Sorting Genetic Algorithm II (NSGA-II) metaheuristic to ensure feasible routing, coalition stability, and robust Pareto-optimal trade-offs. Validated using real-world urban scenarios (Solomon benchmarks and commercial UAV specifications), the framework demonstrates: (a) 18% fewer delivery disruptions compared to static trust models, (b) 94% on-time delivery rate under high uncertainty (an 11% improvement over the base case), and (c) 9% lower costs and 12% higher energy efficiency through adaptive coalition reconfiguration. Simulation results demonstrate that the Bayesian trust mechanism effectively detects misbehavior, reallocates tasks via third-party outsourcing, and sustains service reliability under coalition instability or UAV breakdowns. Additionally, dynamic Shapley cost-sharing ensures fair cost allocation among coalition members. By integrating trust modeling, cooperative game theory, and risk-aware controls, this research bridges a critical gap in hybrid truck-drone logistics. The findings provide actionable insights for logistics managers seeking cost-effective, flexible, and resilient last-mile solutions. Future work will focus on real-time trust evaluation and dynamic coalition reconfiguration using live operational data.