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OA
A comprehensive optimization method of high-speed railway line planning and ticket allocation based on stochastic demand
列车开行方案与票额分配计划共同决定高铁客运市场的运输能力供给,直接影响旅客服务质量和企业运营效益.针对高铁客运系统中旅客需求不确定性对动车组运营组织带来的挑战,研究随机需求下列车开行方案与票额分配综合优化方法,旨在提升客运计划的鲁棒性与可操作性.首先,采用离散场景法刻画旅客需求的不确定性特征,以最大化高铁客运的期望总收益为目标,综合考虑列车停站方案、区间通过能力以及列车容量限制等约束条件,构建两阶段随机规划模型.第1阶段决策与场景无关的列车开行方案;第2阶段依据实际客流水平,决策实际执行的票额分配计划,寻求运输资源与旅客需求的良好匹配,提高旅客服务质量.其次,通过线性化技术将模型转化为等价线性规划问题,并设计基于列生成算法(column generation,CG)的求解方法.最后,以京沪高铁为案例进行数值实验,验证所提出的模型与算法的有效性.实验结果表明:与直接调用GUROBI进行求解相比,CG算法能够在更短时间内获得更优解,具有较高的运算效率和收敛性,适用于大规模高铁网络列车开行方案的设计和优化;相较于基于确定需求获取的列车开行方案和票额分配计划,考虑随机需求的目标值提高了10.57%,验证了随机规划方法在提升收益和适应需求波动方面的显著优势,能够有效兼顾运输企业效益和服务质量.
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.
徐光明;朱子琪;钟林环;邓连波
中南大学 交通运输工程学院,湖南 长沙 410075中南大学 交通运输工程学院,湖南 长沙 410075中南大学 交通运输工程学院,湖南 长沙 410075中南大学 交通运输工程学院,湖南 长沙 410075
交通工程
高速铁路随机需求列车开行方案票额分配列生成算法
high-speed railwaystochastic demandline planningticket allocationcolumn generation algorithm
《铁道科学与工程学报》 2026 (2)
551-562,12
中国工程院院地合作重大项目(2024-DFZD-57)国家自然科学基金资助项目(72171236)湖南省自然科学基金资助项目(2025JJ50435,2022JJ30767)中南大学研究生科研创新项目(自主探索类)(1053320232760)
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