Despite everything you can think, especially since the recession started in 2008, discount stores are not stealing your customers.
Nielsen research shows that 73% of the spend that shifted to the bargain stores came from the four largest supermarkets.
So unless you are one of the four largest supermarkets or unless your competitors are the big supermarkets, you have not a lot to fear from discount stores.
Stop worrying about them and focus on what you are doing better.