Timetables determine the service quality for passengers and the energy consumption of trains in metro systems. In metro networks, a timetable can be made by optimizing train departure frequencies for different periods of the day. Typically, the optimization problem that arises from optimizing train departure frequencies in metro networks involves integer variables, which can cause the problem to be computationally too complex for real-time applications. The main objective of this thesis is to reduce the computational complexity of optimizing train departure frequencies in metro networks while maintaining a relatively accurate solution.

In this thesis, we first apply classical Benders decomposition to optimize train departure frequencies in a metro network considering time-varying passenger demands. Subsequently, we apply an $\epsilon$-optimal Benders decomposition approach to reduce the computational complexity further. A simulation-based case study using a grid metro network illustrates the performance of the two Benders decomposition-based approaches.

The simulation results show that the classical Benders decomposition approach significantly reduces the computational burden of optimizing train departure frequencies in metro networks. Moreover, the $\epsilon$-optimal Benders decomposition approach can further reduce the computation time when the problem size increases of the optimization problem when compared to the classical Benders decomposition approach while maintaining an acceptable level of performance.

Railway networks are subjected to disruptions on a daily basis, which may make the timetable unimplementable, which in its turn may significantly influence passenger satisfaction. In practice, train dispatchers are responsible for mitigating the influence of disruptions, such as delays of trains, train cancellations, and overcrowdedness at stations. The solutions they propose are highly dependent on their experience, often resulting in low quality solutions. In addition, the disruptions must be solved in a matter of minutes, which is challenging because of the problem scale and computational complexity. Effective models and solution approaches are required to mitigate the influence of disruptions.

In recent decades, railway rescheduling models have been developed to support train dispatchers and to improve rail services. A recent and promising model is the event-activity network model, which is a graph-based formulation that supports a wide variety of rescheduling measures. This thesis extends the event-activity network model by including rolling stock circulation with depot entry and exit operations to increase the practicability of the operator-centric model. In addition, a passenger-centric model is proposed by embedding detailed passenger-related factors into the operator-centric model, where the train capacity is included, and the detailed number of passengers in the railway network is calculated. Therefore, the effect of delays on passengers can be handled properly. The passenger-centric model can help minimize the number of waiting passengers on platforms to avoid overcrowding and to improve passenger satisfaction. In practice, the resulting passenger-centric mixed-integer linear programming (MILP) problem is hard to solve due to the introduction of binary variables for train orders, which are important for calculating the detailed number of passengers. An adaptive large neighborhood search (ALNS) algorithm is introduced to address the complexity due to train orders and to improve the computational efficiency of the passenger-centric method. With properly designed destroy and repair operators, the ALNS algorithm can explore the solution space efficiently. Therefore, a balanced trade-off between solution time and quality can be made.

Case studies are conducted based on the train lines operating between the stations of Utrecht and 's-Hertogenbosch in the Netherlands. The simulation results show that the developed model can explicitly include the number of passengers while considering the rolling stock circulation plan. Compared to directly solving an MILP problem using a commercial solver, ALNS can calculate solutions more efficiently while maintaining a high level of solution quality.