Solving the undirected minimum cost flow problem with arbitrary costs

We address the undirected minimum cost flow problem with arbitrary arcs costs. Any optimal solution for this problem is characterized by the property that the flow of each arc with negative cost must be equal to its capacity. That is, the flow can be nonzero in both directions. This situation implies that the flow can take values that are integer multiple of 1/2. Therefore, this single commodity flow problem does not satisfy the unimodularity property. However, using a reformulation of the original problem, we develop an easy method for solving it using any classical minimum-cost flow problem algorithm.