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

Abstract

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)

JAVENGA: JAva‐based Visualization Environment for Network and Graph Algorithms

“…The visualization of more algorithms is another plan. More specifically, we intend to visualize algorithms for the maximum flow, the transportation, and the assignment problems as well as exterior point simplex algorithms for the minimum cost network flow problem [48,49]. In doing so, JAVENGA will be converted into a general-purpose system [36] covering a wide range of graph and network algorithms.…”

On a dual network exterior point simplex type algorithm and its computational behavior

“…A primal exterior point simplex-type algorithm for the MCNFP has been recently reported in [27]. A preliminary geometrical interpretation of DNEPSA was described in [12], while in this paper we show for the first time (i) the algorithm's mathematical proof of correctness, (ii) an encouraging comparative computational study of DNEPSA and DNSA, (iii) a statistical analysis of the experimental results, and finally (iv) some new results on the empirical complexity of DNEPSA.…”

Solving Minimum Cost Multi-Commodity Network Flow Problem Using Lexicographic Goal Programming Approach

“…the Braess's Paradox, which shows that adding capacity to a network can sometimes actually slow down the traffic. Also, Sifaleras (2013) presented a wide range of problems concerning minimum cost network flows, and give an overview of the classic linear single-commodity Minimum Cost Network Flow Problem (MCNFP) and some other closely related problems, either tractable or intractable; Geranis, et al (2009) Tamiz andJones, 2010 andSchniederjans, 1984 described Goal Programming as a Multi-Objective Decision Making (MODM) technique that allocates scarce resources (road capacity) to competing needs (vehicles) in an optimal manner when the decision maker has multiple objectives (minimize travel time, maximize speed and maximize the number of vehicles that a route can carry), so long as the problem can be expressed by an objective function and linear inequality constraints.…”