高速铁路列车开行方案与票价票额综合优化

Comprehensive Optimization of Line Planning,Ticket Pricing and Seat Allocation of High-speed Railway

为提升高速铁路的运营组织水平和盈利能力,本文提出高铁列车开行方案与票价票额综合优化方法。首先,构建分时客流需求与票价间弹性需求函数,并分析包括出发时段偏差、乘车耗时及票价的旅客广义出行成本,进而采用多项式Logit模型描述分时弹性客流的列车选择行为。在此基础上,以客票总收入与运营总成本之差最大为目标构建三者综合优化模型。其次,利用OD总收益关于列车票价的偏导构造票价方案搜索策略,使票价邻域解和列车开行方案邻域解相适应,并运用Cplex求解对应的最优票额分配方案,设计模拟退火算法求解模型。最后,基于郑西高速铁路进行算例分析,结果表明:在7个不同弹性系数下进行综合优化,旅客出行成功率和列车平均客座率均在90%以上,优化解的列车开行方案、票价方案及票额分配方案均高度匹配;在5组不同规模算例中,三者综合优化的运营净收益相比于固定票价下的开行方案与票额联合优化和固定开行方案下的票价与票额联合优化,分别提高了4.11%~15.25%和3.17%~13.42%,且人均单位里程出行成本亦分别降低了1.69%~4.96%和0.97%~4.35%,表明综合优化更好地提升了高速铁路的运营收益和旅客服务水平。

In order to improve the organization and profitability of high-speed railway,this paper proposed a comprehensive optimization method of line planning,ticket pricing and seat allocation.First,the elastic demand function of time-dependent passenger demand and ticket pricing was constructed,and the broad travel cost of passengers was analyzed,including departure time deviation,travel time consumption and ticket pricing,so that a polynomial Logit model was built to describe the train choice behavior of time-dependent elastic passenger flow.Then,a comprehensive optimization model was constructed with the goal of maximizing the difference between the total ticket revenue and the operating cost.Second,the search strategy of ticket pricing was constructed by applying the partial derivation of OD revenue with respect to ticket pricing to make the ticket pricing neighborhood solution match the line planning neighborhood solution.In addition,the Cplex was used to solve the optimal seat allocation scheme,and the simulation annealing algorithm was designed to solve the model.Finally,the Zhengxi high-speed railway was used in a numerical experiment.The results show that under 7 different elastic coefficients,the passenger success travel rate and the average passenger load factor of the comprehensive optimization are above 90%,and the line planning,ticket pricing and seat allocation of the optimized solution are highly matched.In numerical experiments under 5 different scales,compared with the joint optimization of line planning and seat allocation under fixed ticket pricing and the joint optimization of ticket pricing and seat allocation under fixed line planning,the optimal net revenue of the three-factor comprehensive optimization increases by 4.11%~15.25%and 3.17%~13.42%,respectively,while the per capita unit mileage travel cost decreases by 1.69%~4.96%and 0.97%~4.35%,respectively.The results indicate that comprehensive optimization will better improve the operating revenue and passenger service level of high-speed railway.