If your company has a Complaints Department, abolish it. If you can't, quit. Because complaints are the responsibility of everybody, not just some department. Complaints are not just a hazard of business , they are the most important feedback you get. They need to be understood by everyone in the business, especially top management.
Every complaint is potential lost profit, perhaps for ever.
But it is also a potential loyal customer. Every complaint is a vital message about your business and service , about how your employees are working, about the way the business is being run, about future sales, about what your customers want and expect. Don't just send the complainers a pack of vouchers for something they probably don't want, with a standard letter. Treat each complaint as if the whole future of the business depended on it. In every case I have received what I call a Public Relations letter with meaningless soothing words and unnerving phrases like 'assuring you of our committment to the best service at all times' or 'please do not hesitate to call me'.