Minimum cost flow and Ford-Fulkerson I have a question concerning the use of the Ford-Fulkerson algorithm. Since a minimum cost flow problem is a linear programming problem, it has a dual problem. That dual would be to maximize a certain function. Considering this, is it possible to apply the Ford-Fulkerson algorithm to that dual in order to solve the minimum cost flow problem?
No.  Ford-Fulkerson cannot be used to solve arbitrary linear programming instances.  It can only solve instances that are in the form of &quot;max flow in this flow graph&quot;.  The dual doesn't have that form.
The dual is to find the minimum cut.  A standard way to find the minimum cut is by finding the max flow, and then using the max-flow min-cut theorem.