In the minimization of the number of subtours made by the insertion head of an SMD placement machine a variant of the network flow problem arose. In a network with $n$ vertices and $m$ arcs a set $F$ of arcs (parametrized arcs) is given. The task is to find a flow of a given size such that the maximum of flow values along the arcs from $F$ is minimized. This problem can be solved by a sequence of maximum flow computations in modified networks where the capacities of the parametrized arcs are successively...