# Multi-type max-flow

Suppose you have $m$ sources $s_i$ and $n$ sinks $t_j$, but every source produces a certain type of flow, out of $k$ types, and every sink demands a certain type as well. We would like to know if it is possible to satisfy all demands given the constraints in the network. Assume different flows types all have a certain weight, which is used to compare against edge capacities, and also to check for satisfying the demands.

Is there a formulation of this to a regular max-flow algorithm?

• Perhaps there is. What have you tried and where did you get stuck? – Discrete lizard Feb 24 '18 at 11:59
• The title you have chosen is not well suited to representing your question. Please take some time to improve it; we have collected some advice here. Thank you! – Raphael Feb 24 '18 at 21:46