Staffing a Seven-Day Annex Detail Inside a Fixed Budget
You are scheduling a seven-day security detail for a courthouse annex. Each day requires three coverage blocks: a lobby post staffed by two officers for eight hours each (16 officer-hours), a sallyport post staffed by one officer for twelve hours (12 officer-hours), and a rover for four hours during the 10 a.m. to 2 p.m. peak (4 officer-hours). You have five officers, each of whom may work up to 40 regular hours in the week; hours beyond 40 are overtime at 1.5 times the base rate of $31.50 per hour. The approved labor budget is $7,500 for the week. Overtime must be approved in advance, and no officer may exceed 52 total hours in the week.
1. Compute the total officer-hours the detail requires for the week, and the minimum number of overtime hours needed with five officers.
Read the worked answer
Per day: lobby 2 x 8 = 16; sallyport 1 x 12 = 12; rover 4. Total = 32 officer-hours per day.
Per week: 32 x 7 = 224 officer-hours.
Regular capacity: 5 officers x 40 hours = 200 hours. Minimum overtime = 224 - 200 = 24 hours.
Cap check: 224 hours spread over five officers averages 44.8 hours each, so the 52-hour ceiling is not breached.
2. Compute the total labor cost for the week and determine whether it fits the budget.
Read the worked answer
Regular: 200 x $31.50 = $6,300. Overtime rate: $31.50 x 1.5 = $47.25. Overtime cost: 24 x $47.25 = $1,134. Total: $6,300 + $1,134 = $7,434.
The detail fits the $7,500 budget with $66 to spare. That is thin: a single unplanned eight-hour absence would erase the margin, so the schedule should be treated as having no cushion.
3. One officer now takes eight hours of approved leave on Thursday. Recompute the cost, and propose the lowest-cost fix that still keeps the mandated posts covered.
Read the worked answer
Leave removes 8 hours of regular capacity: 192 regular hours. Overtime becomes 224 - 192 = 32 hours.
Cost: 192 x $31.50 = $6,048; 32 x $47.25 = $1,512; total $7,560. That is $60 over budget.
The lobby and sallyport are mandated coverage and cannot be cut. The rover is peak-period support. Dropping two rover hours on each of two days removes 4 officer-hours, all of which come out of overtime: 28 overtime hours instead of 32.
New cost: $6,048 + (28 x $47.25 = $1,323) = $7,371, which is $129 under budget. Cutting mandated post hours would save more money but is not a compliant option, so it is not the answer.