Mathematical Programming

, Volume 5, Issue 1, pp 255-266

First online:

A bad network problem for the simplex method and other minimum cost flow algorithms

  • Norman ZadehAffiliated withIBM Thomas J. Watson Research Center

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For any integern, a modified transportation problem with 2n + 2 nodes is constructed which requires 2 n + 2 n−2−2 iterations using all but one of the most commonly used minimum cost flow algorithms.

As a result, the Edmonds—Karp Scaling Method [3] becomes the only known “good” (in the sense of Edmonds) algorithm for computing minimum cost flows.