Urban rail planning is extremely complex, mainly because it is a decision problem under different uncertainties. In practice, travel demand is generally uncertain, and therefore, the timetabling decisions must be based on accurate estimation. This research addresses the optimization of train timetable at public transit terminals of an urban rail in a stochastic setting. To cope with stochastic fluctuation of arrival rates, a two-stage stochastic programming model is developed. The objective is to construct a daily train schedule that minimizes the expected waiting time of passengers. Due to the high computational cost of evaluating the expected value objective, the sample average approximation method is applied. The method provided statistical estimations of the optimality gap as well as lower and upper bounds and the associated confidence intervals. Numerical experiments are performed to evaluate the performance of the proposed model and the solution method.
Shakibayifar, Masoud, Erfan Hassannayebi, Hossein Jafary, and Arman Sajedinejad. 2017. Stochastic optimization of an urban rail timetable under time-dependent and uncertain demand. Applied Stochastic Modeles In Business And Industry ۳۳ (۶): ۶۴۰-۶۶۱.