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

Abstract

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 X ρ ( Z ) = { ( x , z ) ∈ R n × Z | ∑ j = 1 n x j ρ d , 0 ⩽ x j ⩽ u j z j , 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 X ρ ( Z ) for each relation ρ is provided, along with polynomial time separation algorithms. Applications in scheduling and network design are also discussed.