Determining origin-destination matrices and optimal multiproduct flows for freight transportation over multimodal networks

We consider a normative transshipment problem for freight flows over a multimodal network. In addition to computing the flows, which minimize a convex cost objective function, an origin/destination matrix which corresponds to the minimal cost flows must be computed as well. The supply is given as totals at origins and the demand as totals at destinations. We formulate the problem and propose an algorithm for its solution. Finally, we describe an application carried out with data for the transportation of coal in Finland.