No, the mayor is correct. You can staff a 24/7 call center with six shifts, easily. With eight hour shifts and 40 hour work weeks, you have four days covered with three shifts, and the other three days covered with three more shifts, which would only work 32 hours per week. With 68 full time positions, that allows assignment of over eleven people per shift for those six shifts. If you allow for eighty hours of vacation, and average of around four sick days per year per employee, you should still be able to perform minimum staffing of 8.
This is an issue of mismanagement of resources, not lack of resources. The dispatch center supervisor needs to be replaced. Anyone who allows staffing to fall to four with the number of personnel he has available is incompetent, and allowing 3/4 of the staff to be on break when below minimum staffing levels is inexcusable.