A dual exterior point simplex type algorithm for the minimum cost network flow problem

A new dual simplex type algorithm for the Minimum Cost Network Flow Problem (MCNFP) is presented. The proposed algorithm belongs to a special 'exterior- point simplex type' category. Similarly to the classical network dual simplex algorithm (NDSA), this algorithm starts with a dual feasible tree-solution and reduces the primal infeasibility, iteration by iteration. However, contrary to the NDSA, the new algorithm does not always maintain a dual feasible solution. Instead, the new algorithm might reach a basic point (tree-solution) outside the dual feasible area (exterior point - dual infeasible tree)

An Efficient Extension of Network Simplex Algorithm

In this paper, an efficient extension of network simplex algorithm is presented. In static scheduling problem, where there is no change in situation, the challenge is that the large problems can be solved in a short time. In this paper, the Static Scheduling problem of Automated Guided Vehicles in container terminal is solved by Network Simplex Algorithm (NSA) and NSA+, which extended the standard NSA. The algorithms are based on graph model and their performances are at least 100 times faster than traditional simplex algorithm for Linear Programs. Many random data are generated and fed to the model for 50 vehicles. We compared results of NSA and NSA+ for the static automated vehicle scheduling problem. The results show that NSA+ is significantly more efficient than NSA. It is found that, in practice, NSA and NSA+ take polynomial time to solve problems in this application

Clustering for Faster Network Simplex Pivots

We show how to use tree clustering techniques to improve the time bounds for optimal pivot selection in the primal network simplex algorithm for minimum cost flow, and for pivot execution in the dual network simplex algorithm for the same problem, from O(m)toO( # m) per pivot. Our techniques can also speed up network simplex algorithms for generalized flow, shortest paths with negative edges, maximum flow, the assignment problem, and the transshipment problem

Clustering for faster network simplex pivots

We show how to use tree clustering techniques to improve the time bounds for optimal pivot selection in the primal network simplex algorithm for minimum cost flow, and for pivot execution in the dual network simplex algorithm for the same problem, from O(m) to O([square root of]m) per pivot. Our techniques can also speed up network simplex algorithms for generalized flow, shortest paths with negative edges, maximum flow, the assignment problem, and the transshipment problem