Solving Single-Track Railway Scheduling Problem Using Constraint Programming

The Single Track Railway Scheduling Problem can be modelled as a special case of the Job-Shop Scheduling Problem. This can be achieved by considering the train trips as jobs, which will be scheduled on tracks regarded as resources. A train trip may have many tasks that consist of traversing from one point to another on a track. Each of these distinct points can be a station or a signal placed along the track. Conflicts may occur when the desired timetable would result in two trains occupying the same section of the track at the same time.

The mapping of the problem we have proposed in this thesis is a more realistic approach when modelling the physical representation of a track railway. This is because we take into account the actual signals placed along the track delimiting each track segment, avoiding thus the possibility of trains running into each other. Previous authors adopted an approximation to what is found in practice by adding minimum headway constraints between trains into their model.

Two strategies for resolving the conflicts in a desired timetable are presented. The two strategies have their applicability in practice. For instance, resolving a conflict in the first strategy stems from the observed practice of train operators: in the first strategy a conflict is resolved by re-timing one of the trips at its departure time up to the point the conflict is resolved. Train operating companies do not typically want to plan for passenger trains being delayed after their departure.

On the other hand, the second strategy resolves a conflict by delaying only the conflicting piece of one of the two trips (and subsequent pieces of that trip). In this way, the section of the trip before the conflicting point does not need to be re-timed. This procedure yields solutions with lower total delay. Moreover, with this second strategy, we can also handle the usual practice with passenger trains of not delaying them after their departure, as well as situations in which a train may be delayed along a trip in order to reslove a conflict.

Furthermore, we present a group of practical constraints, incorporated into our software to solve the problem, that arise in real-life problems to which little attention has been paid.

Using the algorithms developed in this thesis, we are able to solve 21 real-life single-track railway scheduling instances of problems, 19 of them to optimality.