  Disruptions in the operational flow of rail traffic can lead to conflicts
between train movements, such that a scheduled timetable can no longer be
realised. This is where dispatching is applied, existing conflicts are resolved
and a dispatching timetable is provided. In the process, train paths are varied
in their spatio-temporal course. This is called the train dispatching problem
(TDP), which consists of selecting conflict-free train paths with minimum
delay. Starting from a path-oriented formulation of the TDP, a binary linear
decision model is introduced. For each possible train path, a binary decision
variable indicates whether the train path is used by the request or not. Such a
train path is constructed from a set of predefined path parts (speed-profiles)
within a time-space network. Instead of modelling pairwise conflicts, stronger
MIP formulation are achieved by a cliques formulated over the complete train
path. The combinatorics of speed-profiles and different departure times results
in a large number of possible train paths, so that the column generation method
is used here. Within the subproblem, the shadow prices of conflict cliques must
be taken into account. When constructing a new train path, it must be
determined whether this train path belongs to a clique or not. This problem is
tackled by a MIP. The methodology is tested on instances from a dispatching
area in Germany. Numerical results show that the presented method achieves
acceptable computation times with good solution quality while meeting the
requirements for real-time dispatching.
