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

2012 ◽  
Author(s):  
Georgios Geranis
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Minimum Cost ◽  
Network Flow Problem ◽  
Type Algorithm ◽  
Minimum Cost Network Flow

An exterior simplex type algorithm for the Minimum Cost Network Flow Problem

2009 ◽  
Vol 36 (4) ◽  
pp. 1176-1190 ◽  
Author(s):  
Konstantinos Paparrizos ◽  
Nikolaos Samaras ◽  
Angelo Sifaleras
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Minimum Cost ◽  
Network Flow Problem ◽  
Type Algorithm ◽  
Minimum Cost Network Flow

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

2009 ◽  
Vol 19 (1) ◽  
pp. 157-170 ◽  
Author(s):  
George Geranis ◽  
Konstantinos Paparizzos ◽  
Angelo Sifaleras
Keyword(s):  
Network Flow ◽  
Feasible Solution ◽  
Flow Problem ◽  
Minimum Cost ◽  
Simplex Algorithm ◽  
Network Flow Problem ◽  
Basic Point ◽  
Type Algorithm ◽  
Dual Simplex ◽  
Minimum Cost Network Flow

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).

scholarly journals Minimum cost network flows: Problems, algorithms, and software

2013 ◽  
Vol 23 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Angelo Sifaleras
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Network Flows ◽  
Minimum Cost ◽  
Network Flow Problem ◽  
Software Packages ◽  
Wide Range ◽  
Solution Methods ◽  
Minimum Cost Network Flow ◽  
Algorithmic Approaches

We present 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. We also discuss state-of-the-art algorithmic approaches and recent advances in the solution methods for the MCNFP. Finally, optimization software packages for the MCNFP are presented.

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