基于偏好序的高铁票价与售票时间窗联合优化

Joint Optimization of Ticket Price and Ticket Time Window for High-speed Railway Based on Preference Order Choice

采用形式灵活且适用性好的偏好序模型刻画旅客购票选择行为,拓展现有高速铁路动态定价与售票控制策略联合优化的研究方法。按照票价变动范围划分客票等级,结合偏好序模型的特点,通过决策各等级客票售票时间窗进行售票控制,同时,在一定范围内优化各客票等级的票价,实现票价与售票控制的联合决策。本文在分析弹性客流的基础上,采用偏好序选择概率、到达率和时间窗长度测算客票销售量。根据运营需要设定客票产品排序,以各客票产品停售时间和票价作为决策变量,建立以期望总收益最大为目标的非线性规划模型,并且将粒子群算法与线性规划精确求解嵌套求解模型。以京沪高铁为背景进行数值实验,结果表明:与固定各等级票价只优化售票时间窗的方案相比,联合优化方案可提升期望总收益约4.54%;不同需求水平下,联合优化方案的期望总收益均高于固定票价方案;期望总收益随着转移购买概率增加而增加,且不同转移概率取值下联合优化方案的期望总收益均高于固定票价方案。所提方案可为高铁列车动态定价和制定售票控制策略提供决策支持。

This paper proposes a preference order model with flexible form and good applicability to describe passengers’ticket choice behavior and expands the research method of joint optimization of existing high-speed railway dynamic pricing and ticketing control strategies.The study defines the ticket classes based on the price change range.With the preference order model,the ticket sales control is carried out by optimizing the ticket time window,while the ticket price is also optimized within a certain range to realize the joint optimization of ticket prices and time windows.Based on the analysis of elastic passenger flow,this paper uses the preference order choice probability,arrival rate and time window length to calculate the ticket sales.The study also sets the ticket ranking according to the operation needs,take the ticket time window and ticket price of each class as the decision variables,and establishes a nonlinear programming model to maximize the expected ticket revenue.The particle swarm algorithm and linear programming are precisely nested to solve the model.The results from the Beijing-Shanghai High-speed Railway case study show that the joint optimization scheme improves the total expected revenue of high-speed railway tickets by about 4.54%compared with the scheme of fixing the fare of each class and only optimizing the time window.The expected total revenue of the joint optimization scheme under different demand levels is higher than that of the fixed fare scheme.The expected total revenue increases as the probability of transfer purchases increases,and the expected total revenue of the joint optimization scheme under different transition probability values is higher than that of the fixed fare scheme.The proposed method can provide decision support for the dynamic pricing of high-speed railway trains and the formulation of sales control strategy.