  In network design problems capacity constraints are modeled in three
different ways depending on the application and the underlying technology for
installing capacity: directed, bidirected, and undirected. In the literature,
polyhedral investigations for strengthening mixed-integer formulations are done
separately for each model. In this paper, we examine the relationship between
these models to provide a unifying approach and show that one can indeed
translate valid inequalities from one to the others. In particular, we show
that the projections of the undirected and bidirected models onto the capacity
variables are the same. We demonstrate that valid inequalities previously given
for the undirected and bidirected models can be derived as a consequence of the
relationship between these models and the directed model.
