Although you are having a big problem with this Customer Service Representative, the bigger problem is that management is not allowing you to do your job. You are the person who leads the department, and you have an employee who is failing in practically every category. There is not much more that can go wrong in terms of his competence, attitude, professionalism, interpersonal skills, and self-control. Management needs to listen to you.
Step up your documentation of this individual's poor performance, and then give management a very clear picture of the costs, damages, and risks associated with keeping this individual on board. Be sure to note the steps you have been taking to develop this individual, as well as examples of his actions that demonstrate resistance to your efforts.
If management still ignores your input and expects you to continue to try to develop this individual, something else must be going on here. Finding out what it is will help you determine if you want to go on here.
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