基于Epsilon 约束法的高速铁路客票多目标定价研究

高铁客票定价是多目标定价问题，既要保障旅客福利，又要增加企业合理利润. 以企业利润和旅客福利作为高铁定价目标，考虑旅客差异和不同运距情境下的多种运输方式竞争，研究高铁客票多目标定价. 结合Epsilon约束法构建双层规划模型，根据分层序列思想分解多目标问题，设计松弛算法得到纳什均衡解，由解对应的目标值得到帕累托边界，确定多目标定价最优决策. 计算结果表明，对比量价波动和目标值改进，多目标定价适合票价改革要求，时间敏感型客票和短途客票有较高涨价空间，多种运输方式竞争影响定价实施效果. 将 Epsilon 约束法应用于求解高铁客票定价多目标问题，有利于优化客运企业与旅客利益，为铁路部门提供高铁客票定价思路.

Multi-objective Pricing of High-speed Railway Passenger Tickets Based on Epsilon-constraint Method

High-speed rail (HSR) ticket pricing is a multi-objective pricing problem. It not only ensures passenger welfare, but also increases the operator's reasonable profits. Considering passenger differences and multimode competition in different lengths of haul, this paper took profit and passenger welfare as HSR's objectives and discussed the optimal HSR ticket pricing solutions. It built a bi-level programming model combining with the epsilon-constraint method, extracted the multi-objective problems according to lexicographic techniques and designed a relaxation algorithm to derive the Nash equilibrium. Corresponding target values are used to plot the Pareto frontier and optimal pricing was determined. The results from computational experiments show the following findings: First, multi- objective solutions are more suitable for pricing reform because of their smaller fluctuation in price and quantity of passengers and improvements of performance; Second, short-haul tickets and time-sensitive passenger tickets are likely to increase even higher; Third, the competition of multi-mode transportation affects pricing implementation. The innovation is to apply the epsilon-constraint method to solve the multi-objective HSR ticket pricing. The proposed pricing method helps to optimize the interests of operators and passengers and provides thoughts for HSR ticket pricing for railway operator.