A tutorial on non-periodic train timetabling and platforming problems

Non-cyclic train timetabling and comparability graphs

We consider the customary formulation of non-cyclic train timetabling, calling for a maximumprofit collection of compatible paths in a suitable graph. The associated ILP models look for a maximum-weight clique in a(n exponentially-large) compatibility graph. By taking a close look at the structure of this graph, we analyze the existing ILP models and propose some new stronger ones, all having t...

Solution of Real-World Train Timetabling Problems

Solution of the Train Platforming Problem

In this paper we study a general formulation of the train platforming problem, which contains as special cases all the versions previously considered in the literature as well as a case study from the Italian Infrastructure manager that we addressed. In particular, motivated by our case study, we consider a general quadratic objective function, and propose a new way to linearize it by using a s...

Ordering Constraints in Time Expanded Networks for Train Timetabling Problems

The task of the train timetabling problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. This kind of problem has proven to be very challenging and numerous solution approaches have been proposed. One of the most successful approaches is based on time discretized network models. However, one of the major weaknesses of these models is that fra...

A column generation approach to train timetabling on a corridor

We propose heuristic and exact algorithms for the (periodic and non-periodic) train timetabling problem on a corridor that are based on the solution of the LP relaxation of an ILP formulation in which each variable corresponds to a full timetable for a train. This is in contrast with previous approaches to the same problem, which were based on ILP formulations in which each variable is associat...