A mathematical programming model for the management of carriages in virtually coupled trains

This work proposes a model for exploiting some possibilities that can derive from the concept of virtual coupling in railways, in which trains can be dynamically grouped to form single convoys. In particular, in the considered scenario, convoys running on a railway line are formed by virtually coupling train carriages, and the capacity of each convoy can change dynamically by leaving or adding carriages at each station. In the paper, an original optimization model based on a mathematical programming formulation is proposed for a passenger railway line, with the aim of determining the optimal time-variant capacity of trains that satisfies the transport demand and avoids trains with unnecessary capacity. More in detail, the proposed system determines, for each link of the line, the optimal number of carriages that is needed, allowing maneuvers like the parking of unused carriages and the exchange of them among the trains. The paper presents also an example with the results derived from the implementation of the model for a simple case, done with the aim of testing and validating the model.