The track formulation for the Train Dispatching problem

With few exceptions, train movements are still controlled by human operators, the dispatchers. They establish routes and precedence between trains in real-time in order to cope with normal operations but also to recover from deviations from the timetable, and minimize overall delays. Implicitly they tackle and solve repeatedly a hard optimization problem, the Train Dispatching Problem. We recently developed a decomposition approach which allowed us to solve real-life instances to optimality or near optimality in times acceptable for dispatchers. We present here some new ideas which appear to significantly reduce computational times while solving to optimality even large instances.