A multi-commodity flow problem is defined like this:

https://www.wikiwand.com/en/Multi-commodity_flow_problem

I am considering a optimization problem in which there are no demands on each commodity, but the minimum of (F1,F2,F3...Fn) is maximized. Fi (i=1,2,...,n) is the flow from each commodity.

I want to do this since I hope there will be no shortcoming for my network. The performance of my network is concerned with the minimum flow from the commodities, thus I want to maximize it.

I think it would be a NP-hard problem but I can't fully prove it. Can anyone provide me some advice about how to solve it? I will be really appreciated about it.

https://www.wikiwand.com/en/Multi-commodity_flow_problem

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