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The paper investigates the application of some large scale solution techniques to the so called traffic assignment problem, or multicommodity flow problem. As this is a network problem, there are two equivalent formulations. The first is based on the node-arc incidence matrix and is the usual approach. The second is based on an arc-chain matrix and the formulation is an extension of Ford and Fulkerson's multi-commodity work. Decomposition techniques are applied to the first formulation and a minimum chain network approach applied to the second. Then an extension of the arc-chain formulation shows it is equivalent to decomposition theory being applied to a slightly different node- arc formulation.