Robust train timetabling problem with optimized train stop plan

Simultaneously considering train timetabling problem and stop planning problem with uncertain travel time, this paper proposes a collaborative model, which can be decomposed into two stages. Specifically, in the first stage, the travel time of each train on each link is taken as a stochastic variable, which is the sum of a minimum travel time (a constant variable) and disturbance time (a stochastic variable). Through embedding the train stop planning process into the train timetabling problem, the train stop plan and train timetable under different scenarios can be generated/optimized in the first stage. In the second stage, we treat the travel time of each train on each link as a decision variable, which is restricted to be no less than the minimum travel time. Then, based on the train stop plan and train timetable generated in the first stage, an optimal robust train timetable and train stop plan can be obtained, in which the sum of variance between the robust timetable and each timetable generated in the first stage is minimum. The optimization software GAMS with CPLEX and BARON solvers are used to solve the proposed model and generate approximate optimal solutions. Finally, an experiment is implemented to show the effectiveness and efficiency of our proposed method.