Trade-off between efficiency and fairness in timetabling on a single urban rail transit line under time-dependent demand condition

When minimizing the total waiting time of all passengers during timetabling, a small number of passengers would have to endure a very long waiting time. This suggests that fairness issue exists in timetabling. This study analyzes this problem by taking an urban railway timetable as a case. Two fairness criteria are analyzed, namely min–max fairness and α-fairness. A mixed-integer programming model is developed to optimize the timetable by considering the trade-off between efficiency and fairness. A simulated annealing-based adaptive large neighborhood search metaheuristic algorithm is applied to solve the problem. A real-world experiment is conducted to demonstrate the effectiveness of the proposed model. It finds that an ‘efficient’ timetable does not always perform well from the perspective of fairness. Moreover, there is a trade-off between the fairness and efficiency. The proposed model can effectively optimize the rail timetable by keeping its efficiency while simultaneously improving fairness