Joint Scheduling and Route Optimization for Bus–Heterogeneous Drone Collaborative Delivery Systems Under Spatiotemporal Synchronization Constraints

Rural logistics faces persistent challenges such as high distribution costs, dispersed demand, and limited transport infrastructure, which hinder efficient last-mile delivery. To address these issues, this study proposes a bus–heterogeneous drone collaborative delivery system that integrates the fixed-route coverage of rural buses with the flexibility of multiple types of drones. The proposed system enables synchronized operations between buses and drones, where buses serve as mobile depots for drone launching and recovery along predefined routes. A mixed-integer programming (MIP) model is developed to jointly optimize bus schedules and drone routing under spatiotemporal synchronization constraints, considering drone endurance, payload capacity, energy consumption, and bus departure times. Due to the NP-hard nature of the problem, an Improved Genetic Algorithm (IGA) is designed, incorporating a three-layer encoding scheme, adaptive crossover and mutation operators, and a local search repair mechanism to enhance convergence and solution feasibility. A real-world case study from Baihe County, Shaanxi Province, China, is conducted to evaluate the performance of the proposed model and algorithm. Comparative experiments under the reported case-study setting show that the proposed bus–heterogeneous drone system achieves notable cost reduction and improved overall delivery performance. Sensitivity analyses further confirm the robustness of the model with respect to drone endurance, drone payload capacity, and bus stop quantity. This research contributes to the literature by bridging the methodological gap between truck–drone coordination and bus-based collaborative delivery, offering an innovative framework for sustainable rural logistics and multi-modal last-mile optimization.