  In this paper, we concentrate on generating cutting planes for the
unsplittable capacitated network design problem. We use the unsplittable flow
arc-set polyhedron of the considered problem as a substructure and generate
cutting planes by solving the separation problem over it. To relieve the
computational burden, we show that, in some special cases, a closed form of the
separation problem can be derived. For the general case, a brute-force
algorithm, called exact separation algorithm, is employed in solving the
separation problem of the considered polyhedron such that the constructed
inequality guarantees to be facet-defining. Furthermore, a new technique is
presented to accelerate the exact separation algorithm, which significantly
decreases the number of iterations in the algorithm. Finally, a comprehensive
computational study on the unsplittable capacitated network design problem is
presented to demonstrate the effectiveness of the proposed algorithm.
