Integer knapsack and flow covers with divisible coefficients: Polyhedra, optimization and separation

Three regions arising as surrogates in certain network design problems are the knapsack set , the simple capacitated flow set and the set where the capacity is an integer multiple for all j. The authors present algorithms for optimization over the sets X and Y as well as different descriptions of the convex hulls and fast combinatorial algorithms for separation. Some partial results are given for the set Z and another extension.