This paper reports on a comparative study of alternative algorithmic approaches for the decomposition and solution of large multicommodity network flow problems. Three specific algorithms are considered: (1) a smooth penalty function algorithm, (2) a coercion function algorithm, and (3) a row-action iterative algorithm. Qualitative comparisons are based on the applicability, ease of implementation and robustness of each algorithm. Quantitative comparisons are based on the performance of the algorithms when applied to a common set of test problems. Special attention is given to the suitability of the algorithms for parallel computations. Direct comparisons with an interior point code, OBI, are also included.