A Set Partitioning Approach to Shunting

The Vehicle Positioning Problem (VPP), also know as the shunting problem, is a classical combinatorial optimization problem in public transport planning. It has been investigated using several models and approaches, which work well for small instances, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation approach for the VPP and for a multiperiod generalization. The model provides a tight linear description of the problem and can, in particular, produce non-trivial lower bounds. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time, for some versions of the problem. Computational results for large-scale instances are reported.