Scheduling theory (ST) is a formal framework which have been used many times over the last decade as starting point to model railway traffic management. Graph theory (GT), mathematical programming (MP) or constraint programming (CP) have also be used as additional steps to scheduling theory. This is illustrated in figure 1. The last step is a solution algorithm that is many times based a complete or partial enumeration procedure (EP) of feasible solutions where large subsets are discarded. This article will focus on the path ST → CP → EP to solve railway management problems. I will first briefly introduce each field, and after applications to the railway traffic management.