Abstract
We present a network simplex method for the maximum balanced flow problem, i.e., the problem of finding a maximum flow in a source-to-sink network such that each arc-flow value does not exceed a fixed propor-tion of the total flow value from the source to the sink. We generalize the notion of strong feasibility in the network simplex method for the maximum flow problem to give a finiteness proof for the new algorithm. We also consider the maximum balanced integral flow problem, and show that the problem can be solved in polynomial-time for a special case when the balancing rate function is constant.
