A method and apparatus for grooming traffic demands according to mileage based tariffs. An Integer Linear Program (ILP) that captures the traffic grooming problem is defined, and such a linear program can in principle be solved by conventional linear program application systems which are fully familiar to those of ordinary skill in the art. However, the time required to solve such an ILP is fairly large, even for the moderately sized networks we are interested in. That is, there are many possible routes to consider, and hence many integer variables in the ILP. Therefore, further in accordance with the principles of the present invention, the ILP is advantageously run on the Delaunay Triangulation of the network rather than on the completely connected network graph.