Solution of real-world train timetabling problems

The train timetabling problem (TTP) aims at determining a timetable for a set of trains which does not violate track capacities and which satisfies some operational constraints. We concentrate on the problem of a single, one-way track linking two major stations, with a number of intermediate stations in between. In this paper, we describe the design of a train timetabling system that takes into account several additional constraints that arise in real-world applications. In particular, we address the following: (1) automatic and manual signalling of the presence of a train on a track segment between two consecutive stations; (2) station capacities, i.e. the maximum number of trains that can be present at a station at the same time; (3) a prescribed timetable for a subset of the trains, which is imposed when some of the trains are already scheduled and additional trains are to be inserted; (4) maintenance operations, which keep a track segment occupied for a given period; and (5) periodic trains, e.g. families of trains that should have the same timetable, modulo a given time interval, say one hour. Due to capacity constraints, however, the timetable may be slightly changed within the family. We present computational results on real-world instances from Ferrovie dello Stato SpA, the Italian railway company.