Résumé en anglais

In this paper, we study the k-edge-connected network design problem with bounded paths. We introduce new integer programming formulations for this problem. Then we study the polytopes associated with these formulations and introduce some classes of valid inequalities as well as conditions for these inequalities to define facets. Using these results, we devise Branch-and-Cut and Branch-and-Cut-and-Price algorithms for the problem and give some computational results.