Incarceration? Well, we know how expensive that is -- even if the government decided to use the incarcerated illegals in chain gangs that just happened to be part of construction crews and produce picking crews. And again, Mexico would protest. It could even decide to divert oil to China (nice of us to have built the Panama Canal).
To date, the cheapest solution is repatriation, usually by bus.
The one form of punishment that actually generates income is to fine the businesses that knowingly use illegal labor. But as already discussed on this thread, it's all a game.
There's a free-market solution, and it's actually quite simple: privatize all land in the United States. The land-owner has the right to shoot trespassers. After that, whose property is the body? Obviously, the original owner no longer can claim it; therefore unless a will clearly bequeathes it to somebody, it is abandoned property.
The land-owner has first dibs, since its on his land, and can do what he wants with it. Presumably, a market for these raw materials will exist; perhaps a fertilizer or animal-feed company. Soylent green, maybe. Instead of a state-centric disposal problem, we have a free-market solution that produces benefits and generates wealth.
the cheapest solution is repatriation
Don't forget the need for a deterrent. Repatriation after public flogging, maybe. Sure, that's fine with me as well.