A primal partitioning approach for single and non-simultaneous multicommodity flow problems

In the first part of this paper, we study the minimum linear cost multicommodity flow problem where the given traffic demand is satisfied through routes having less than a given maximum number of edges. We propose a simplex-based solution method which uses a refined primal partitioning of the basis matrix. Our program has been tested on some real world instances given by the national French telecommunication operator (France Telecom) and also on randomly generated multicommodity flow problems. The second part of our paper generalizes the techniques described previously to handle additional survivability constraints. Major telecommunication operators want to design multicommodity survivable networks, i.e., which are able to route all traffic demands even if any node or edge is damaged. We present a simple model of this problem based on non-simultaneous multicommodity flows.