Joint optimization for train operation plan and freight rate discount considering bounded rationality in transport path selection

Existing train operation plans often neglect shippers' bounded rational behavior and lack joint optimization of freight rates and transit time, causing supply–demand mismatches. This paper introduces prospect theory, characterizing reference dependence and loss aversion. A joint optimization model is developed incorporating path selection behavior, operation plans, and freight rate discounts within a bi-level framework: the upper level allocates freight volume based on prospect theory, while the lower level optimizes the operation plan. The upper nonlinear problem is solved by PSO, and the lower integer linear program by CPLEX, forming a PSO-CPLEX hybrid algorithm. Numerical experiments on the Western Land-Sea New Corridor verify feasibility and algorithm superiority. Effectiveness shows that bounded rationality improves freight volume prediction and revenue; coordinated pricing boosts revenue. Sensitivity analysis reveals the effects of loss aversion and risk sensitivity. Model extension indicates differentiated services enable market segmentation, while a high-speed, low-price strategy holds value for long-term competitiveness.