Demand-oriented timetable design for urban rail transit under stochastic demand

In the context of public transportation system, improving the service quality and robustness through minimizing the average passengers waiting time is a real challenge. This study provides robust stochastic programming models for train timetabling problem in urban rail transit systems. The objective is minimization of the weighted summation of the expected cost of passenger waiting time, its variance and the penalty function including the capacity violation due to overcrowding. In the proposed formulations, the dynamic and uncertain travel demand is represented by the scenario-based multi-period arrival rates of passenger. Two versions of the robust stochastic programming models are developed and a comparative analysis is conducted to testify the tractability of the models. The effectiveness of the proposed stochastic programming model was demonstrated through the application to Tehran underground urban railway. The outcomes show the reductions in expected passenger waiting time of 22%, and cost variance drop of 60% compared with the baseline plans using the proposed robust optimization approach.