铁道科学与工程学报2026，Vol.23Issue(2)：551-562,12.DOI:10.19713/j.cnki.43-1423/u.T20250606
面向随机需求的高铁列车开行方案与票额分配综合优化方法
A comprehensive optimization method of high-speed railway line planning and ticket allocation based on stochastic demand
摘要
Abstract
The line planning and ticket allocation jointly determine the capacity supply of High-Speed Railway(HSR)passenger transport market,directly influencing both passenger service quality and operational efficiency.To address the challenges posed by uncertain passenger demand in HSR operation,a comprehensive optimization method of HSR line planning and ticket allocation under stochastic demand was proposed,aiming to enhance the robustness and operability of passenger transport plans.First,discrete scenarios were used to depict the uncertain demand,with the objective of maximizing the expected total revenue of HSR passenger transport.Constraints such as train stops,section capacity and train capacity were comprehensively considered to construct a two-stage stochastic programming model.In the first stage,scenario-independent line plans were determined.In the second stage,the ticket allocation strategy was optimized based on the actual demand level,aiming to achieve a better match between transport resources and passenger demand,thereby improving service quality.The model was then transformed into an equivalent integer linear programming problem via linearization techniques,and a solution method based on Column Generation(CG)was developed.Finally,numerical experiments were conducted for the Beijing-Shanghai HSR to validate the effectiveness of the proposed model and algorithm.The results show that,compared with directly solving by GUROBI,CG can obtain better solutions in less time,with higher computing efficiency and convergence,and is also suitable for the design and optimization of line planning in large-scale HSR network.Compared with the line planning and ticket allocation strategy under certain demand,the target value of that considering stochastic demand is increased by 10.57%,which verifies the significant advantages of the stochastic programming method in improving revenue and adapting to demand fluctuations,and can effectively take into account the benefits and service quality of transportation enterprises.关键词
高速铁路/随机需求/列车开行方案/票额分配/列生成算法Key words
high-speed railway/stochastic demand/line planning/ticket allocation/column generation algorithm分类
交通工程引用本文复制引用
徐光明,朱子琪,钟林环,邓连波..面向随机需求的高铁列车开行方案与票额分配综合优化方法[J].铁道科学与工程学报,2026,23(2):551-562,12.基金项目
中国工程院院地合作重大项目(2024-DFZD-57) （2024-DFZD-57）
国家自然科学基金资助项目(72171236) （72171236）
湖南省自然科学基金资助项目(2025JJ50435,2022JJ30767) （2025JJ50435,2022JJ30767）
中南大学研究生科研创新项目(自主探索类)(1053320232760) （自主探索类）
