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)∈Rn×Z|∑j=1nxjρd,0⩽xj⩽ujzj,j=1,…,n}, where ρρ is one of ⩽⩽, == or ⩾⩾, and Z⊂{0,1}nZ⊂{0,1}n consists of the allowed configurations. We consider the case when ZZ consists of affinely independent vectors. Under this assumption, a characterization of the non-trivial facets of the convex hull of Xρ(Z)Xρ(Z) for each relation ρρ is provided, along with polynomial time separation algorithms. Applications in scheduling and network design are also discussed.