Most payroll companies have an HRIS product that is typically offered as an add-on to the current system and should be reasonably affordable. I know that ADP has such a system that performs the tasks you mention and also has some functions for performance management as well. Rather than going with a separate solution, it may make financial and logical sense to check with your payroll provider to see what they offer.
Sorry I should have mentioned. Payroll is handled in-house. Thanks!
Accounting / Contracts
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