Circulation of railway rolling stock: a branch-and-price approach

In this paper, we describe a model and a branch-and-price algorithm to determine an efficient railway rolling stock circulation on a set of interacting train lines, Given the timetable and the passengers' seat demand, the model determines an allocation of rolling stock to the daily trips. In order to efficiently utilize the train units, they can be added to or removed from the trains at some stations along the lines. These changes in train compositions are subject to several constraints, mainly corresponding to the order of the train units within the trains. A solution is evaluated based on three criteria, i.e. (i) the service to the passengers, (ii) the robustness, and (iii) the cost of the circulation.