Valid inequalities for problems with additive variable upper bounds

We study the facial structure of a polyhedron associated with the single node relaxation of network flow problems with additive variable upper bounds. This type of structure arises, for example, in production planning problems with setup times and in network certain expansion problems. We derive several classes of valid inequalities for this polyhedron and give conditions under which they are facet-defining. Our computational experience with large network expansion problems indicates that these inequalities are very effective in improving the quality of the linear programming relaxations.