Valid inequalities for problems with additive variable upper bounds

Abstract

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 network design/expansion problems and in production planning problems with setup times. We first derive two classes of valid inequalities for this polyhedron and give the conditions under which they are facet-defining. Then we generalize our results through sequence independent lifting of valid inequalities for lower-dimensional projections. Our computational experience with large network expansion problems indicates that these inequalities are very effective in improving the quality of the linear programming relaxations.