Handbook of Optimization in the Railway Industry by Ralf Borndörfer Torsten Klug Leonardo Lamorgese Carlo Mannino Markus Reuther & Thomas Schlechte

Author:Ralf Borndörfer, Torsten Klug, Leonardo Lamorgese, Carlo Mannino, Markus Reuther & Thomas Schlechte
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

One major disadvantage of time expanded models is their enormous size if the number of time steps increases, e. g., due to a finer discretization. In track allocation the time horizon typically consists of several hours up to several days and the discretization step is often 1 min or less. Hence, the time expanded network of a single train can have many thousands nodes and arcs, which leads to large memory requirements.

In practice there are often conditions that allow reducing the size of these networks. For instance, often a train may not be shifted arbitrarily in time but its schedule may only deviate from an “ideal” schedule by a few minutes. However, this is not always the case and further techniques are required to handle these huge models.

Dynamic Graph Generation, see [11, 13] , is a technique developed for the case where the train schedules may deviate arbitrarily from some ideal timetable, but the general objective is to have all trains run as early as possible. This is a reasonable goal in many applications, because a train running late implies a high delay in the train’s schedule, which should typically be avoided. In particular, the algorithm focuses on the solution of the shortest path subproblems

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