Best Practice: Who should schedule concurrent request?

We are facing an issue that is starting to require IT intervention more and more.  At one time, using departments scheduled their own concurrent requests.  Ex.  The Payables area scheduled their Create Accounting process. The General Accounting are  scheduled their Create Accounting process.  Due to departmental employee turnover, the Create Accounting processes would have to be re-scheduled by someone else in the area.  To alleviate that problem, the IT department started scheduling some of the more important processes under user = SYSADMIN.
Now, the IT department is "needed" whenever someone wants to change anything with their respective processes.  We would like to turn the scheduling of important concurrent processes back over to the departments.