We discuss the optimal choice of traffic lines with periodic timetable
s on a railway system. A chosen line system has to offer sufficient ca
pacity in order to serve the known amount of traffic on the system. Th
e line optimization problem aims at the construction of a feasible lin
e system optimizing certain objectives, We introduce a mixed integer l
inear programming formulation. For real world data we succeed in solvi
ng the model by means of suitable relaxations and sufficiently strong
cutting planes with the commercial LP solver CPLEX 3.0.