Joint Optimization of Dynamic Pricing and Flexible Refund Fees for Railway Services

This study explores strategies for dynamic pricing and flexible refund fee setting in railway line services, aiming to optimize ticket sales revenue by integrating refund mechanisms into the revenue management framework. By introducing a consistent concept of opportunity cost applicable to both passengers and railway operators, we propose an integrated approach that combines dynamic pricing with flexible refund fees grounded in the demand-driven opportunity cost of seat resources. A dynamic programming model is constructed to quantify the opportunity cost of seat resources. To address the computational challenges arising from the model’s scale, state and time dimension compression methods are applied to develop an approximate linear programming model with fewer constraints. The proposed model is solved using a turning point search algorithm and a constraint generation algorithm. Numerical experiments and ticket sales simulations are conducted to verify the feasibility of the proposed methods and to explore the application effects of different pricing strategy combinations. The results demonstrate that the integration of dynamic pricing and flexible refund fees can significantly enhance ticket sales revenue, particularly in scenarios of supply shortfall.