Guaranteed Hours Versus a Cheaper Part-Timer
A regional bakery staffs one counter 12 hours a day, 7 days a week. Exactly one person must be at the counter at all times, and a second person is required during the 4-hour morning rush, so the base week needs the equivalent of 112 staff-hours. Four full-time employees each have guaranteed 40-hour weeks at $18/hour, and anything past 40 hours is overtime at 1.5×. One part-time employee may work up to 25 hours a week at $15/hour with no overtime premium and no guaranteed hours. The four full-timers are already on payroll and cannot be laid off this quarter, and their guaranteed hours must be paid whether or not the counter needs them. For ten weeks each autumn, demand jumps to 175 staff-hours a week because of holiday orders.
1. How many staff-hours does the base week require? Given the guaranteed-hours rule, how many part-time hours should the manager schedule in the base week, and what does the week cost?
Read the worked answer
Staff-hour requirement: 12 hours/day × 7 days = 84 coverage hours with one person, plus a second body for the 4-hour rush (4 × 7 = 28 extra hours) = 112 staff-hours per week.
The trap: the part-timer looks cheaper ($15 vs $18), so it is tempting to schedule 25 part-time hours and trim full-time hours to match the 112. That saves nothing. Full-time hours are guaranteed: the bakery pays 4 × 40 × $18 = $2,880 whether or not the hours are used. Every part-time hour therefore adds $15 on top of a cost that does not fall.
Cheapest base week: schedule the 112 hours inside the already-paid 160 full-time hours; use 0 part-time hours. Cost = $2,880. Using the part-timer here would raise the bill toward $3,255 for no added coverage.
The real lever is not the schedule but the guarantee itself - renegotiating reduced-hour contracts, or using the 48 surplus full-time hours for prep, cleaning, and training - which is a decision for next quarter's contracts, not this week's roster.
2. During the 10-week autumn peak, demand is 175 staff-hours. Compare covering the 15-hour gap with part-time hours versus overtime, and quantify the difference over the full 10 weeks.
Read the worked answer
The gap: 175 − 160 = 15 hours beyond what the full-timers are already paid for.
Option A - part-timer: 15 × $15 = $225/week. Check the cap: 15 ≤ 25, so the part-timer can absorb all of it.
Option B - overtime: 15 × $18 × 1.5 = $405/week.
Part-time saves $405 − $225 = $180 per week, or $1,800 across the 10 weeks. Weekly cost under Option A is $2,880 + $225 = $3,105.
The reasoning to write down: overtime costs 1.5 × $18 = $27/hour against $15/hour for the part-timer, and the part-timer has 10 spare hours of headroom under the cap. Overtime only becomes the right answer once the part-timer's 25-hour cap is exhausted.
3. Suppose the autumn peak instead requires 200 staff-hours a week. Compute the cheapest weekly cost, and compare it with paying for the whole gap in overtime.
Read the worked answer
The gap is now 200 − 160 = 40 hours.
Cheapest plan - exhaust the part-timer first, then overtime:
- 25 part-time hours × $15 = $375 (cap reached)
- Remaining 15 hours at overtime 15 × $27 = $405
- Extra cost = $780; total week = $2,880 + $780 = $3,660
All-overtime plan:
- 40 × $27 = $1,080; total week = $3,960
Blended plan saves $300/week ($3,000 over the 10 weeks).
Note the ceiling: once demand passes 160 + 25 = 185 staff-hours, overtime is unavoidable, so the useful planning question is not "part-time or overtime" but "when does a temporary hire at straight time beat both." A temp at, say, $20/hour would cost less than $27 for every hour above the part-timer's cap.