Asana is good at tracking and approving, of course, so if you’re already using Aasna that’s a natural.
I recommend one of the Asana solutions I outlined here:
The same task in a PTO project could be multihomed to such a private project, optionally with the employee granted collaborator access to their task only.
Subsequent to that are formula fields if more calculation is required, but I don’t think that’s necessary.