I've had rat problems before, okay several times.But I have found rats will live close to their food supply in winter. I have had them move into the coop even.
Do you see any holes in the ground around or in your coop?If you do start digging and be ready to chop with your shovel!I one time found a nest about one foot deep with 17 rats that I had been feeding.
I bought a Plastic life like owl and mounted it on a near by post and have not seen any rats this year. I hope this helps.

There are rat proof chicken feeders that will basically dry up the rat's food supply since they can not get in the feeder. Here is a website "thecarpentershop.net " that has a quality, low cost rat proof chicken feeder that I know of.

you can just go and visit this link
http://thecarpentershop.net/mediumplywoodchickenfeeder.html

Sorry to hear that you have rat problems. But if you've got rats, you should be worrying more about stolen eggs, eaten chicks,and chickens being killed while they're roosting, than how much food the chickens have.

I recycled my paint bucket into a rat free chicken feeder using Peckomatic Demand Feeder Kit.