In this chapter we study a class of linear programs called network flow problems. These problems are important for several reasons. Many important applications give rise to linear programming models where all, or a large portion, of the constraints have a network flow structure. The constraint matrix of a network flow linear program has a structure that enables these linear programs to be optimized very quickly. In addition, the associated polyhedron is integer which means that no enumeration is required in order to find integer solutions. Thus, not only can the linear programming relaxation of a network problem be solved quickly, no enumeration is necessary.