Transport Capacity Planning for Shared Passenger--Freight Transportation in High-Speed Rail Systems With Uncertain Demand

Shared passenger–freight transportation in high-speed rail (HSR) systems provides an effective way to improve railway capacity utilization and operational revenue while offering a more sustainable alternative for time-sensitive freight services. This study investigates the train capacity planning problem for shared passenger–freight HSR services under uncertain passenger and freight demand. The problem explicitly considers heterogeneous service requirements, including passengers’ departure-time preferences, freight delivery time windows, train capacity restrictions, transfer feasibility, and the different operational characteristics of passenger train units (PTUs) and freight train units (FTUs). To describe these operations, we construct an extended space–time network that captures passenger movements, freight transportation, loading and unloading, transshipment, and the potential reallocation of underutilized PTUs for freight service. Based on this network, a two-stage stochastic programming model is formulated to determine train composition decisions in the first stage and passenger–freight flow assignment decisions in the second stage, with the objective of maximizing expected operational profit while preserving passenger service quality. The stochastic model is approximated through the Sample Average Approximation (SAA) method and reformulated as a mixed-integer linear programming (MILP) model. To solve the resulting large-scale problem, we develop an improved integer L-shaped (ILS) algorithm with strengthened optimality cuts and acceleration strategies. Numerical experiments based on the Beijing–Shanghai HSR corridor demonstrate the computational efficiency of the proposed ILS algorithm and its applicability to practical-scale instances. The results also show that accounting for demand uncertainty and jointly using PTUs and FTUs under flexible train composition improve solution robustness and operational efficiency.