While the minimum cost flow (MCF) problems have been well documented in many publications, due to its broad applications, little or no effort have been devoted to explaining the algorithms for identifying loop formation and computing the value needed to solve MCF network problems. This paper proposes efficient algorithms, and MATLAB computer implementation, for solving MCF problems. Several academic and real-life network problems have been solved to validate the proposed algorithms; the numerical results obtained by the developed MCF code have been compared and matched with the built-in MATLAB function Linprog() (Simplex algorithm) for further validation
