On the Computational Behavior of a Dual Network Exterior Point Simplex Algorithm for the Minimum Cost Network Flow Problem

The Minimum Cost Network Flow Problem (MCNFP) constitutes a wide category of network flow problems. A Dual Network Exterior Point Simplex Algorithm (DNEPSA) for the MCNFP is presented here, together with some computational results. Similarly to the classical Dual Network Simplex Algorithm (DNSA), the new algorithm starts with a dual feasible tree-solution and, after a number of iterations, it produces an optimal solution. However, contrary to DNSA, our algorithm does not always maintain a dual feasible solution. Instead, it produces tree-solutions that can be infeasible for both, the dual and the primal problem. This family of algorithms is believed to be more efficient than the classical Simplex-type algorithms. They can cross over the infeasible region of the dual problem and find an optimal solution reducing the number of iterations needed. In this paper, we describe the algorithm and, for the first time, we present its computational behavior compared to the Dual Network Simplex Algorithm.