Research on the Optimization of Urban–Rural Passenger and Postal Integration Operation Scheduling Based on Uncertainty Theory

The integration of postal and passenger transport is an effective measure to enhance the utilization efficiency of passenger and freight transportation resources and to promote the sustainable development of urban–rural transit and logistics. This paper considers the uncertainty in passenger and freight demand as well as transit operation times, constructing an optimization model for integrated urban–rural transit and postal services based on uncertainty theory. Passenger and freight demand, along with the inverse uncertain distribution of events, serve as constraints, while minimizing passenger travel time and the cost for passenger transport companies are the optimization objectives. Taking into account the uncertainty of urban–rural bus travel time, the scheduling model is transformed into a robust form for scenarios involving single and multiple origin stations. The model is solved using an improved NSGA-II (Nondominated Sorting Genetic Algorithm II) to achieve effective coordinated scheduling of both passenger and freight services. Through a case study in Lotus County, Jiangxi Province, vehicle routing plans with varying levels of conservativeness were obtained. Comparing the results from different scenarios, it was found that when the total vehicle operating mileage increased from 1.96% to 62.26%, passenger transport costs rose from 2.95% to 62.66%, while the total passenger travel time decreased from 55.99% to 172.31%. In terms of optimizing costs and improving passenger travel efficiency, operations involving multiple starting stations for a single vehicle demonstrated greater advantages. Meanwhile, at a moderate level of robustness, it was easier to achieve a balance between operational costs and passenger travel time. The research findings provide theoretical support for improving travel conditions and resource utilization in rural areas, which not only helps enhance the operational efficiency of urban–rural transit but also contributes positively to promoting balanced urban–rural sustainable development and narrowing the urban–rural gap.