The pig "huts" were just pieces of old tin propped up on sticks. By the time we got around to cleaning up the pig pens, the sticks had fallen down and the tin was just on the ground, perfect homes for rats.
The guys working for us invented the game "Bat the Rat" - they'd flip over a piece of tin and see how many rats they could whack before the rats found a new shelter. We had a part Labrador dog named Bud that took a few tries to learn the game. First time, he grabbed a rat and carried it away to finish off. Then he watched what the guys had been doing. About the third piece of tin, Bud had the idea - kill all the rats he could and deal with the remains later.
Although Bud was too big to be as quick as the dogs in the video, he got pretty good at finishing off the rates. By the time we started loading up pieces of tin to haul off, there were few rats left in that area. The survivors moved into the fields which were unpicked corn. I'd go out, start at the edges and mow the fields, spiraling into the middle. By the time I was down that last swath of corn stalks, the red tailed hawks were hovering overhead and would stoop on any rodents (rats and rabbits) that had sheltered in that last strip of shelter.
We no longer have the big cotton rats that were here. We still have mice but the barn cats keep them under control.