Minimum cost network flows: Problems, algorithms, and software

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.