Optimization of cooperative passenger-freight-postal operation for urban-rural public transport with time window constraints

The integrated passenger-freight-post (PFP) cooperative model, as an important innovation in urban-rural integrated development in the new era, provides a novel solution to the "last-mile" logistics challenge in rural areas and opens new avenues for the transformation and upgrading of urban-rural bus operations. This study addresses the bus scheduling optimization problem under the PFP integrated model by constructing a multi-objective collaborative optimization model considering time window constraints, aiming to improve the utilization of urban-rural bus capacity, reduce rural logistics costs, and ensure public transportation accessibility while balancing the interests of passengers, bus operators, and logistics companies. Based on operational data from a county-level urban-rural bus line in Shanxi Province, China, the study establishes a multi-objective optimization model for PFP-coordinated bus scheduling, with bus dispatch intervals and vehicle configurations as decision variables. The optimization objectives include minimizing passenger travel time, maximizing bus operator revenue, and maximizing logistics company profit. A time-sensitive penalty cost function is introduced to quantify the impact of delivery timeliness on logistics service quality. The non-dominated sorting genetic algorithm- II (NSGA-II) is employed to solve the Pareto optimal solution set, and the technique for order preference by similarity to ideal solution(TOPSIS) method is applied for multi-criteria decision analysis to determine the optimal scheduling scheme. The results demonstrate that the optimized scheme significantly reduces passenger travel costs (by 15.4%) while improving economic benefits for both bus operators (15.5% profit increase) and logistics companies (29.9% costs reduce), validating the model's effectiveness and practicality. This research not only provides an innovative solution to the inefficiencies and conflicting interests in traditional urban-rural bus operations but also offers empirical support for the wider application of the PFP cooperative model. The findings hold substantial theoretical and practical significance for promoting integrated urban-rural transportation development.