Resolving instability in railway timetabling problems

A growth of the railway transportation demand is forecasted in the next decades which needs an increase of network capacity. Where possible, infrastructure upgrading can release extra capacity, although in some cases this is not enough to satisfy the entire transportation demand unless optimised timetabling is performed. We propose a heuristic approach to develop a stable and timetable which maximise the satisfaction of transportation demand in situations where network capacity is limited. In case the demand cannot be fully satisfied, the model relaxes the given line plan and timetable design parameters. In addition, the aim is to maximize the satisfied demand by keeping as many train services as possible. We develop the mixed integer programming (MIP) model for minimizing cycle time to find an optimal stable timetable for the given line plan. The heuristic iteratively solves the MIP model and applies relaxation measures. We tested the model on the Dutch network. The results showed that the model can generate stable timetables by removing train services from the critical circuit, and also, higher transportation demand can be satisfied by additionally relaxing timetable design parameters.