Valid Inequalities for Problems with Additive Variable Upper Bounds

We study the facial structure of a polyhedron associated with the single node re laxation of network ow problems with additive variable upper bounds This type of structure arises for example in network design expansion problems in production planning problems with setup times We rst derive two classes of valid inequalities for this polyhedron and give the conditions under which they are facet de ning Then we generalize our results through sequence independent lifting of valid inequalities for lower dimensional projections Our com putational experience with large network expansion problems indicates that these inequalities are very e ective in improving the quality of the linear programming relaxations