Air and high-speed rail (AH) integration services are gaining ground with the development of the high-speed railway and airline industries. A well-designed feeder train timetable with good synchronization is of great significance in an AH integration service, because it can improve the connectivity at transfer nodes and offer more opportunities for intermodal passengers to travel. In this study, we propose a multi-objective model of a feeder railway timetable problem in an AH integration service to improve synchronization. The aims of the optimization model are to maximize the number of synchronizations and the coverage of synchronized flights, as well as to minimize the transfer penalties of passengers. We focus on a scenario of a partial subnetwork in which one direction of a two-direction railroad line with one transfer station is considered. The model is applied to Shijiazhuang Zhengding International Airport, China. The results illustrate the effectiveness of the approach developed in the paper.

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.

With the continuous improvement in the high-speed railway (HSR) network, passengers’ holiday travel demand and the scale of tourism passenger flow have grown rapidly, placing higher requirements on HSR transportation services. Current train line plans are formulated according to regular daily passenger flow and fail to adapt to the travel demand generated by various holiday tourism products, resulting in poor adaptation to holiday passenger flow characteristics. Different from existing line-planning studies that consider only regular daily passenger flow, this paper is among the first to embed hierarchical holiday tourism products as a structural input of the HSR line planning problem and to explicitly handle asymmetric passenger demand in holiday periods. To address this gap, this paper optimizes HSR line plans based on the travel characteristics of tourism products. An integer programming model is established that allocates asymmetric passenger flows to train flows while minimizing the total operating cost. The model incorporates both conventional HSR passenger demand and the differentiated travel demand corresponding to different tourism products. A real-world experiment based on the HSR network in Jiangxi Province, China demonstrates that the proposed model effectively improves the tourism transportation efficiency and passenger flow distribution of HSR with reliable practicability. Sensitivity analyses further reveal how the tourism demand scale, the tourism sub-product diversity, and the benchmark line requirements affect the feasibility and cost of the line plan. This study provides a valid reference for the optimization of holiday train line plans and the coordinated development of tourism and transportation.