<p>From my experience benchmarking MCF in an industry setting, there are three publicly available implementations that are competitive,</p>
<ol>
<li>Andrew V Goldberg's cost scaling <a href="https://github.com/iveney/cs2" rel="nofollow noreferrer">implementation</a>.</li>
<li>Coin-OR's Lemon library cost scaling <a href="http://lemon.cs.elte.hu/pub/doc/latest/a00102.html" rel="nofollow noreferrer">implementation</a>.</li>
<li>Coin-OR's Network Simplex <a href="http://lemon.cs.elte.hu/pub/doc/latest/a00269.html" rel="nofollow noreferrer">implementation</a>.</li>
</ol>
<p>I would try those in that order if you are limited for time. Other honorable mentions are,</p>
<ol>
<li>Google-OR's cost scaling <a href="https://github.com/google/or-tools/blob/stable/ortools/graph/min_cost_flow.cc" rel="nofollow noreferrer">implementation</a>. I haven't benchmarked this, but I'd expect it to be competitive with those above.</li>
<li>MCFClass has several <a href="http://groups.di.unipi.it/optimize/Software/MCF.html" rel="nofollow noreferrer">implementations</a> listed under various restricted licenses for commercial use. RelaxIV is very competitive but restrictive.</li>
</ol>
<p>In terms of studying literature and a survey of competitive algorithms, the work of <a href="https://arxiv.org/pdf/1207.6381.pdf" rel="nofollow noreferrer">Kirarly and Kovacs</a> are an excellent starting point.</p>
Best Algorithm for Minimum Cost Maximum Flow?
<p>Can someone tell me which is the best algorithm for minimum cost maximum flow (and easy to implement) and from where to read will be helpful? I searched online and got names of many algorithms and unable to decide which one to study.</p>