Rats, yuck. It's an ongoing battle here too. The dogs have managed to kill a few, not enough to make a huge difference. They chew right through chicken wire to get into my pens, idk about the rest of y'all. They eat SO MUCH feed it is unbelievable so several measures have been taken around here...not that it totally solves the problem or anything. Hunting them down is wildly entertaining at times but the bigger ones scare me. I'll skip the packrat nest in my shed sob story and keep on topic though, lol. If you don't read any other part of my reply, please do at least take a look at the link I posted for you below.
One of my pens was dug into last year and all my guinea keets except one were killed. Instead of burying wire I dug a trench underneath the perimeter of the pen and filled it with concrete. The trench is about 8 inches deep and only a few inches wide, all the way around the pen. This has discouraged the rodents enough they don't even try to get in that pen anymore. It isn't as cheap as chicken wire but it is a more permanent solution. Here, there is so much iron in the 'soil' the wire will rust out in about 2-3 years anyway. And hey, if you are going to dig up the pen perimeter to bury chicken wire you may as well do a more substantial job. I have found, personally, that chicken wire is good for just that, chickens and other poultry. Keeping anything else in or out with chicken wire I have found to be a no-go, I moved away from using it years ago. If it matters to anyone, I use 2x4 inch welded wire fencing in place of chicken wire and then cover that with that plastic orange or green construction fencing to keep raccoon hands out and chicks in.
Second, feeding area. For the animals you are intentionally feeding, not the rats. A bin is good but rats are impossibly smart about these things. I resorted to metal trash cans, to hold the feed in and rats out. It keeps the rain off too. Plastic trash cans got chewed through just like chicken wire out here, tried those too. Metal is good, wood and plastic not so much. IMO.
Next, your bird feeder(s). Hanging them up helps keep rodents out, I imagine that they are coming into your pen for either food, water or possibly shelter to begin with. Making the food and water inaccessible to rats goes a long way towards rectifying the problem. The shelter issue can be trickier.
These things along with your choice of rodent control should help a bunch. Shoot em, poison them, let your dogs eat em, live trap them and release elsewhere, or donate to folks who own reptiles for snake feed. It matters not to me how the rodent control is accomplished, just that it happens. The economic impact on your farm is simply too great to not take measures.
This particular article on the subject says, that EACH RAT on a farm will eat, spoil or damage approximately $25 worth of grain per year. Other scholarly articles from universities that I have read state this number can actually be much higher.
http://www.thepoultrysite.com/articles/824/rodent-control-in-livestock-and-poultry-facilities/