A Bi-objective optimization model for the last train timetabling problem

In cities where the urban rail transit (URT) systems do not provide 24-h services, passengers may be able to reach their destinations if last train services have closed by time they arrive at transfer stations. This paper aims seek a well-coordinated timetable that can transport as many possible (referred reachable passengers) and also those who cannot unreachable stations close destinations. A bi-objective mixed-integer linear programming (MILP) model is developed maximize number of minimize total remaining travel distance all passengers. The augmented ε-constraint method applied generate Pareto optimal solutions MILP model. Numerical experiments were implemented in Chengdu URT network. Results indicate compared current-in-use timetable, optimized our methods significantly increased meanwhile reduced average addition, we discussed two strategies improve passengers’ destination reachability, which are encouraging early origin stations, optimizing trains non-last same time.