Branch-and-Cut for a 2-Commodity Flow Relocation Model with Time Constraints.

We deal here with a general 2-commodity flow model designed for the management of shared mobility systems which operate on a given transit network. The model involves an integral flow which represents carriers together with an integral flow which represents the objects transported by those carriers. It may be viewed as the projection on the transit network of a flow model formulated on a time expanded network which simultaneously copes with temporal and resource issues, but does not fit practical computation. In order to make this projected model compatible with the time expanded network model, we introduce specific constraints whose handling involves a separation process. We prove that this separation process can be performed in polynomial time, discuss the experimental behaviour of the related Branch-and-Cut algorithm and briefly address the lift issue to turn an optimal solution of our projected model into a solution of the original problem.