If you have a customer service department, it might mean that you don’t understand what customer service means.
The principles of customer service belong to every department, every employee and every door along the management corridor. Customer service must be deep in the psyche of your business, not written in a box on the organisation chart.
The trouble with having a customer service ‘department’ is that it can encourage everybody else in the business to dump their problem customers and customer problems onto someone else, abdicating responsibility. Customers hate this almost as much as the people who work in the customer service department.