Journal of Operational Research and Its Applications ( Applied Mathematics ) - Lahijan Azad University

Today, with the rapid development of rail transport systems, passenger demands and the potential for risks in this industry are increasing. These conditions create uncertainty in passenger demand, create negative consequences for the occurrence of risks, and make accurate programming difficult. Therefore, robust optimization of train scheduling problem in the presence of risk is required to deal with uncertainties and reduce risks negative effects. In this study, we propose a two-stage mixed integer programming model. In the first stage, the nominal problem objective is to minimize the total train travel time. In the second stage, a robust optimization model is developed to minimize unsatisfied passenger demand. Additionally, the presence of primary and secondary risks is programming at both stages. To verify the effectiveness and compare the proposed models, a data envelopment analysis approach is used and a practical example is presented. The results show that under conditions of uncertainty, robust solutions can significantly and effectively minimize unsatisfied demand by a slightly rise in the travel time and the number of stops obtained from the nominal problem. Furthermore, the results demonstrate that secondary risk plays a significant role in the process of optimal response actions selection.