On the equivalence between the Node‐ARC and ARC‐Chain formulations for the multi‐commodity maximal flow problem

The purpose of this article is to formulate the multi‐commodity maximal flow problem into a node‐arc form and to show that when decomposition is applied to this form the resulting master and subproblems become precisely those described by Ford & Fulkerson [3] using the arc‐chain formulation. A generalization to the problem is then considered which can potentially speed its convergence.