No studies that I know of, because to do so you would have to define "effective" and we haven't done that.
It IS easy enough to map out the costs of various options, with Excel and a little arithmetic. It's totally a local exercise, however, because the cost of benefits (including retirement, vacation, sick leave, insurance, etc.) is all dependent on what the individual agency provides.
If you have a very expensive benefits package, it has sometimes been found to be cheaper to pay the overtime rather than add another employee. You just have to do the arithmetic and see where the lines on the graph cross.
At least as important is the willingness of people to work the schedule. Many EMSers hold down two or more jobs to make ends meet. If you start making them work 5 days a week on an 8hr 5d schedule, and they used to work 3x12 or 4x12, you may cause them to look for work elsewhere.
A good compromise between working days and overtime is the average 42 hour work week provided by the 12 hour shift schedule that has employees working 3 days one week and 4 days the next, with a 3-day weekend every other week.
This is a small rural service that has a HR person that doesn't like to see the scheduled overtime on the budget. The director has tried to explain the differences between schedules. I thought there might be a something out there he could use for a little outside information he feels kind of hand cuffed because it is going to affect his schedule as well.
There is a big difference between scheduled, budgeted overtime (good, it's part of your system) un-budgeted overtime (bad, things are out of control).
The trick is getting the right amount budgeted - you have to cover sick leave, vacation, etc., as well as the regularly designed schedule. And few EMS agencies are large enough to make effective use of scheduled float personnel.
My part-time job schedules 12 hour shifts 6 days per week, and uses 8 hour shifts on Mondays to cut scheduled OT. This does require part-time staff to be used every week, or in a pinch ovetime. I like it as a PRN employee, because it means there will be at least a little bit of time open evey week, for periods when people don't take vacation.