Periodic timetabling with flexibility based on a mesoscopic topology

Many railway companies operate with periodic schedules. The periodic event scheduling problem (PESP) was investigated by many different authors and was applied to real word instances. It has proven is practicability in different case studies. The Swiss Railway Company (SBB) seeks in the project Smart Rail 4.0 a coordination of the railway value chain (e.g. line planning, timetabling and vehicle scheduling, etc.). In the context of an applied research project together with SBB, we have developed an extension of the PESP model. On one hand the extension is based on using a finer resolution of the track infrastructure, the so-called mesoscopic topology. The mesoscopic topology uses in addition to the operation points and their connections, the concrete number of tracks and the allowed track switches. The mesoscopic topology allows creating timetables with train lines assigned to track paths. On the other hand, we use a known, flexible PESP formulation (FPESP), i.e. we calculate time intervals instead of time points for the arrival resp. departures times at operating points. Both extensions (mesoscopic topology and flexibility) should enhance feasibility of the timetables on the microscopic infrastructure. We will call our model therefore track-choice, flexible PESP model (TCFPESP). A preliminary version of this model was shown last year at the OR 2018 conference in Brussel. In the presentation, we will show the embedding of the model TCFPESP briefly in the overall context of the research project. Then, we discuss the mathematical formulation of TCFPESP as mixed integer linear program in detail and show numerical results of a small case study