中文摘要：

针对高铁和航空共存的客运枢纽网络，考虑枢纽机场容量，建立了求解多模式枢纽网络中高铁和航空的最优票价问题的双层规划模型，其中上层最大化航空和高铁各自的利润，下层是竞争市场中的随机用户均衡．为求解该模型，设计了基于灵敏度分析的启发式算法．最后，利用实际枢纽网络的算例验证了模型和算法的有效性．结果表明，当枢纽机场容量限制增强时，利润贡献最大市场的票价变化幅度最小，所以枢纽容量应优先满足该市场需求．

英文摘要：

In view of the passenger transport hub network with both the railway and the airline, considering the capacity constraint of the hub airport, a bi-level programming model is established to solve the price optimization problem of high-speed rail （HSR） and airline in a multi-modal hub network, in which the upper level is to maximize the operators＇ profits and the lower level is a stochastic user equilibrium of the competitive market. A heuristic algorithm based on sensitivity analysis is designed to solve the model. Finally, the validity of the model and algorithm is by an example of an actual hub network. The results show that when the hub airport capacity constraint is enhanced, the fare of the market with the largest profit reaches the smallest change scale, thus the hub airport capacity should satisfy the demand of this market at first.