Short-sightedness usually wins. A 12-hour shift schedule invariably requires scheduled OT. Averaging weeks is not legal for non-exempt employees in the private sector. So, somebody somewhere is going to have to work more than 40 hours in a week to cover a 12 hour rotation.
But an 8 hour rotation simply cannot be done with fewer than six shifts. You can write one on paper that uses five shifts without overtime, but it won't work in the real world. You need six at least.
Naturally, a little built-in OT is much cheaper than increasing your full-time workforce by 20%. BUT, OT gets tracked and managers get hammered for it, while a bloated staff on straight time doesn't draw the same negative attention.
Here's a sample of an 8 hour rotation that assumes no scheduled overtime, and a pay week of Mon-Sun. If your pay week is different, you can adjust by starting your pay week where I have Monday.
Legend: 1=midnight to 8 am, 2 = 8 am to 4 pm, 3 = 4pm to midnight, A = first rest day (an off day that pays time and a half if you work it) B= second rest day (an off day that pays double time if you work) R=Relief shift(any shift may be worked that day, or work on days but not part of op shift) T= Training (which would be nice if you did 4-10's that week to get a 5 day weekend before starting the shift rotation)
Day MTWTFSS|MTWTFSS|MTWTFSS|MTWTFSS|MTWTFSS|MTWTFSS|
Shift - 1 AB33333 |33AB111 |1111AB2 |22222AB|ARRRR2B |TTTTTAB |
Shift - 2 TTTTTAB |AB33333 |33AB111 |1111AB2|22222AB |ARRRR2B|
Shift - 3 ARRRR2B|TTTTTAB |AB33333 |33AB111 |1111AB2 |22222AB|
Shift - 4 22222AB |ARRRR2B |TTTTTAB |AB33333 |33AB111 |1111AB2|
Shift - 5 1111AB2 |22222AB |ARRRR2B|TTTTTAB |AB33333 |33AB111|
Shift - 6 33AB111 |1111AB2 |22222AB |ARRRR2B|TTTTTAB |AB33333|
BTW, the math isn't new. It has been established long ago that you need a certain number of employees for each position to cover vacations, personal days, etc.. If you are covering 7 days a week, the factor is 1.7. So, add it up. You have 1 SM per shift. There are three shifts per day So, there are 3 SM's total per day. 3x1.7 = 5.1 Rounding off and adding 1 for Training means that you need at least 6 full shifts to cover the week.
For 12 hour shifts the math is the same. You just have 2 shifts per day instead of 3. So, the minimum number of shifts goes from 6 to 4.4. Practically speaking, since you can't hire 0.4 shift managers, you really need 5 or there will be schedule problems.
Bottom line: 12's are better for everybody.