Joint optimization of pricing, seat allocation and overbooking for high-speed railway system under demand uncertainty

This paper examines the integrated optimization of pricing, seat allocation, and overbooking strategies in high-speed railway (HSR) operations. Overbooking helps address inefficiencies arising from empty seats due to passenger no-shows or last-minute cancellations. The complexity of the problem stems from two main factors: (i) the interdependence of pricing, seat allocation, and overbooking decisions, which jointly influence railway system performance; and (ii) the uncertainties associated with passenger demand and no-show behavior. To tackle these complexities, we develop a two-stage stochastic programming model aimed at maximizing expected railway profit. In the first stage, the model determines HSR pricing and seat allocation, including overbooking, while the second stage addresses potential denied boarding due to overbooking, based on the first-stage decisions. To solve the model, we employ a sample average approximation method and introduce a tailored progressive hedging algorithm (PHA). Additionally, we adapt commonly used surrogate-based optimization methods, such as Kriging and radial basis function models, for comparative analysis. Numerical studies on both a small-scale example and a real-world HSR line reveal that the proposed joint optimization significantly boosts railway profit across various demand and no-show scenarios, with the PHA solution approach outperforming surrogate-based methods in terms of both solution quality and computational efficiency.