In my opinion, separated employees should not be approving timesheet after they have been fired or quit - there is just too much potential for employees who are unhappy with you to fudge their numbers a bit. Instead, have a supervisor override function that allows supervisors or the payroll department to approve the hours instead.
We don't have employees approve their timesheets because we found it was a redundant extra step. In our policies, we basically state that employees are responsible for the accuracy of their time cards and/or PTO information, and falsifying time or vacation records is an offense that will likely result in termination. We feel that's a good enough deterrent. However, we do have the supervisors approve timesheets instead. The supervisor is in the best position to know whether their employees worked those hours, or correctly entered PTO for sick days, vacation time, etc. Our software provides a mass-transaction editor that allows them to approve timesheets in one click, so it works for us without too much intrusion on a supervisor's duties.
For our timekeeping system, we used to use TimeClock Plus, which was so antiquated that we had to get rid of it. In early 2009 we went to Paychex Time & Labor Online, and while clocking in/out or submitting a PTO request is very easy, the administration side of it is a bit cumbersome. I can't say in all honesty that I'd recommend them, but for the time being, it suffices for our needs.
Best of luck!
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