An Efficient Minimal Cost Flow Algorithm - Bennington, G. E. (Management Science, 1973)
One of the methods of solving the minimal cost flow problem is to find cycles of negative length in a marginal cost network. These negative cycles indicate a change in the flows around the cycle, which will result in a reduction in the total cost. The proposed method finds negative cycles by attempting to find the shortest chains from a fixed node to all other nodes. Results of computational experiments comparing this algorithm with the out-of-kilter algorithm are presented. These results indicate that the proposed method of repetitively detecting negative cycles yields an efficient minimal cost flow algorithm.