Polyhedral results on single node variable upper-bound flow models with allowed configurations

In this paper we investigate the convex hull of single node variable upper-bound flow models with allowed configurations. Such a model is defined by a set Xρ(Z) = {(x,z) ∈ ℝ^N × Z|∑ⁿj=ixjpd, 0⩽xj⩽ujzj, j=1,…,n}, where ρ is one of ⩽, = or ⩾, and Z ⊂ {0,1}ⁿ consists of the allowed configurations. We consider the case when Z consists of affinely independent vectors. Under this assumption, a characterization of the non-trivial facets of the convex hull of Xρ(Z) for each relation ρ is provided, along with polynomial time separation algorithms. Applications in scheduling and network design are also discussed.