A Multi-objective Optimization Model for Robust Skip-Stop Scheduling with Earliness and Tardiness Penalties

Inefficient transport systems impose extra travel time for travelers, cause dissatisfaction and reduce service levels. In this study, the demand-oriented train scheduling problem is addressed using a robust skip-stop method under uncertain arrival rates during peak hours. This paper presents alternative mathematical models, including a two-stage scenario-based stochastic programming model and two robust optimization models, to minimize the total travel time of passengers and their waiting time at stations. The modeling framework accounts for the design and implementation of robust skip-stop schedules with earliness and tardiness penalties. As a case study, each of the developed models is implemented on line No. 5 of the Tehran metro, and the results are compared. To validate the skip-stop schedules, the values of the stochastic solution and the expected value of perfect information are calculated. In addition, a sensitivity analysis is conducted to test the performance of the model under different scenarios. According to the obtained results, having perfect information can reduce up to 16% of the value of the weighted objective function. The proposed skip-stop method has been shown to save about 5% in total travel time and 49% in weighted objective function, which is a summation of travel times and waiting times as against regular all-stop service. The value of stochastic solutions is about 21% of the value of the weighted objective function, which shows that the stochastic model demonstrates better performance than the deterministic model.