Optimization Problems in Passenger Railway Systems

This article describes 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 the duties and the rosters for drivers and conductors. These problems are presented in the order in which they are faced in practice, illustrating what they are aimed at, and how they are solved by mathematical programming techniques. The article also briefly illustrates recent advances in producing “robust” (i.e., fault-tolerant) solutions for these problems, and in the application of optimization methods for real-time recovery of railway systems.