For a general Min Cost Max Flow problem cost C associated to an edge having flow F results in C*F .

Thus Objective is to minimize Sigma Ci * Fi, where Fi <= Capacity of ith Edge and giving maximum flow.

0-1 Version

If we have a variation that with a flow F <= Capacity is flowing through an edge only Ci cost should be considered NOT Ci*Fi.

i.e. If edge allows flows its going to cost C or else its going to cost 0.

I am not sure, How can I proceed for it. The optimal cost flow is not required.