Passenger Railway Optimization

We review the main optimization problems that are faced in the planning of a passenger railway system, from the definition of the routes and frequencies of the trains in the railway network to the construction of rosters for drivers and conductors. We present these problems in the order in which they are faced in practice, and for each of them we review the existing literature, discussing the various versions that were studied, and present a (mixed) integer linear programming formulation that was used to solve one of these versions, sometimes providing experimental results on real-world instances.