Network Optimization is a large part of Combinatorial Optimization. The

In this paper a new Network Exterior Point Simplex Algorithm (NEPSA) for the Minimum Cost Network Flow Problem (MCNFP) is analytically presented. NEPSA belongs to a special simplex type category and is a modification of the classical network simplex algorithm. The main idea of the algorithm is to compute two flows. One flow is basic but not always feasible and the other is feasible but not always basic. A complete proof of correctness for the proposed algorithm is also presented. Moreover, the computational behavior of NEPSA is shown by an empirical study carried out for randomly generated sparse instances created by the well known gridgen network problem generator