Abstract: Passengers’ selection of the train number when they travel by railway is associated with both the trains’ conditions and passengers’ actual demand. Analyzing uncertain factors referring to selecting trains and multiple objects passengers seeking, introducing stochastic decision making optimization theory, a stochastic chance constrained objective programming model of railway passengers selecting trains is developed, which is subject to passengers demand for actual arriving time, traveling cost, probability of buying tickets successfully, and traveling comfort level. Train delay time arriving at the terminal station and remaining tickets amount when buying tickets are two important factors influencing passengers’ train selection, which are also stochastic variables. According to their distribution functions and passengers correlative demand, the stochastic chance constrained objective programming model is transformed into a certain model, and implicit enumeration is applied in a calculation example. The calculating result shows that the model can give passengers reasonable suggestions on train selection.

Key words: railway transportation, stochastic chance constrained programming, objective programming, railway passenger train, model, implicit enumeration

摘要： 旅客乘坐铁路列车出行时，需选择列车车次，这与各次列车的情况和旅客的出行要求均相关. 分析旅客选择列车时的不确定因素和追求的多重目标，引入随机决策优化理论，在旅客对列车实际到达时刻、出行费用、购票成功概率、旅行舒适度等要求的约束下构建了选择列车的随机机会约束目标规划模型. 列车到站时的晚点时间与购票时的剩余票额是影响旅客选择列车的两个重要的不确定因素，且是随机变量. 根据其分布函数和旅客出行的相关要求将含有不确定约束的模型转化为确定模型，并用隐枚举法进行了算例求解. 结果表明，模型能够明确地给出旅客选择列车的合理建议.

关键词: 铁路运输, 随机机会约束规划, 目标规划, 旅客列车, 模型, 隐枚举