he algorithm proposed by Shigeno et al.(2000) is a scaling method to solve the minimum cost-flow problem. In each phase, they applied the most positive cut canceling idea. In this paper, we present a new approach to solve the problem, which uses the scaling method of Shigeno et al.(2000); but, in each phase, we apply the out-of-kilter idea instead of the most positive cut canceling idea. Our algorithm is inspired by Ghiyasvand (2012). The algorithm gives a geometrical explanation for the optimality concept.
