Key points are not available for this paper at this time.
(This article originally appeared in Management Science, October 1958, Volume 5, Number 1, pp. 97–101, published by The Institute of Management Sciences.) A simplex computation for an arc-chain formulation of the maximal multi-commodity network flow problem is proposed. Since the number of variables in this formulation is too large to be dealt with explicitly, the computation treats non-basic variables implicitly by replacing the usual method of determining a vector to enter the basis with several applications of a combinatorial algorithm for finding a shortest chain joining a pair of points in a network.
Ford et al. (2004) studied this question.