中文摘要：

旅客列车开行方案直接影响着铁路旅客出行费用，从而导致铁路旅客运输需求的变化。通过分析与旅客列车开行方案相关的铁路旅客运输需求影响因素，构造旅客运输弹性需求函数关系，将旅客换乘方案的选择归结为弹性需求下的用户平衡分配问题，进而利用铁路企业与旅客之间的Stackelberg博弈关系，建立了基于弹性需求的旅客列车开行方案的双层规划模型，并设计了基于模拟退火算法求解的优化算法。算例分析表明，基于弹性需求的旅客列车开行方案优化模型和算法能够更好地优化旅客列车开行方案，使之与铁路旅客运输需求相吻合，从而产生更大的社会与经济效益。

英文摘要：

The passenger train plan directly influences the railway passenger travel cost, thus it affects railway passenger transport demand. In this paper, analyzing the influence factors of railway passenger transport demand, establishing the railway passenger transport elastic demand function and concluding passenger train choice behavior as the distribution problem of user equilibrium with elastic demands, the bi-level programming model for making the passenger train plan with elastic demands is set up by utilizing the Stackelberg game relation between railway enterprise and passengers, and the optimal algorithm based on the simulated annealing algorithm is designed. A numerical example illustrates that the model and algorithm for making the passenger train plan with elastic demands can effectively optimize the passenger train plan, make it coincide with passenger transport demand and bring more social and economic benefit.