Periodic network optimization with different arc frequencies Original Research Article

For a fixed time interal served railway system we consider the problem to find a timetable such that for a selected class of change possibilities the arising waiting time is minimal. As a mathematical model to deal with such problems, we introduce “perioidic networks”. The general discussion of this concept allows to give formulas for network caused waiting times at all junctions. Based on this results we formulate the optimization task to find timetables which minimize a global objective depending on all local waiting times. In general, these “periodic programs” are NP-hard. We present a branch and bound approach. As shown by computational results for the case of a linear objective, the use of the Hermite normal form considerably improves the performance of the algorithm. For unconstrained problems we give a polynomially working method to find the lexicographic best solution.