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The Train Timetabling Problem (TTP) consists in nding a train schedule on a railway network that satises some operational con- straints and maximizes a prot function which counts for the eciency of the infrastructure usage. In practical cases, however, the maximization of the objective function is not enough and one calls for a robust solution that is capable of absorbing as much as possible delays/disturbances on the network. In this paper we propose and analyze computationally four dierent methods to nd robust TTP solutions for the aperiodic (non cyclic) case, that combine Mixed Integer Programming (MIP) and ad-hoc Stochastic Programming/Robust Optimization techniques. We compare computationally the eectiveness and practical applicability of the four techniques under investigation on real-world test cases from the Italian railway company (Trenitalia). The outcome is that two of the proposed techniques are very fast and provide robust solutions of comparable qual- ity with respect to the standard (but very time consuming) Stochastic Programming approach.

10. Fast Approaches to Robust Railway Timetabling