Algorithm for Max Network Flow with lower bounds and its complexity I have built a max network flow graph that carries certain amount of people from a source to a destination. Now, I'd like to attach a lower bound $l_(e_)$ constraint to each edge $e$. But I don't know what algorithm to use and how to analyze its complexity. Here's the graph:
http://jeffe.cs.illinois.edu/teaching/algorithms/notes/25-maxflowext.pdf

There's a very simple reduction from that problem to the maximum flow problem. This is simply called "maximum flow with edge demands".