Flow pack facets of the single node fixed-charge flow polytope

i∈N yi ≤ b, yi ≤ uixi ∀i ∈ N}, where variable yi is the flow on arc i with capacity ui, xi is a binary variable that indicates whether arc i is open or closed, and N = N ∪N. The single node fixed–charge flow model is interesting not only because it is a relaxation of the fixed–charge network flow problem, but also because it is possible to derive relaxations of the form S of a general MBIP problem. Therefore, valid inequalities for S can be used as cutting planes in branch–and–cut algorithms to solve MBIP problems. General purpose mixed–integer programming software packages, such as CPLEX, MINTO [8] and bc–opt [4] use cutting planes derived from S among others. We refer the reader to [13] for a detailed discussion on using S and related structures as relaxations in mixed–integer programming. Valid inequalities for S have also been instrumental in developing strong cutting planes for a variety of problems, including lot–sizing problems [3, 10] and facility location problems [1]. The study of the polyhedral structure of the convex hull of S is initiated by Padberg et al. [9] for the case with N = ∅. They introduce the flow cover inequalities, which are generalized by Van Roy and Wolsey [12]. Gu et al. [5] strengthen these inequalities through sequence independent lifting for S.