Call Centre Staffing Shortfall
A municipal call centre handles 62,000 calls a month. The average handling time is 6.5 minutes, including after-call work. Staff have 22 working days a month and 7.5 paid hours a day. The service target is 78% occupancy, defined as time on calls divided by available time after shrinkage. Shrinkage - leave, training, meetings and absence - is 18% of paid time. The centre currently employs 38 full-time equivalents (FTE). An agency can supply up to 10 temporary staff in three weeks at 1.35 times the internal hourly cost. Overtime is available at 1.5 times cost but is capped at 8 hours per person per week. The finance director will fund only one of these options for the next quarter. Twelve percent of calls are currently misrouted to the wrong team and take an average of 2.1 minutes before transfer; a new directory is expected to remove most of these calls. A union agreement requires consultation before temporary staff are used.
1. Calculate the FTE required to meet the 78% occupancy target. Show the formula and the staffing gap.
Read the worked answer
Step 1: daily calls = 62,000 ÷ 22 = 2,818.2.
Step 2: daily workload = 2,818.2 × 6.5 = 18,318 minutes = 305.3 hours.
Step 3: paid hours per FTE per day = 7.5. After 18% shrinkage: 7.5 × 0.82 = 6.15 available hours.
Step 4: at 78% occupancy, productive hours per FTE = 6.15 × 0.78 = 4.797.
Step 5: required FTE = 305.3 ÷ 4.797 = 63.6, so 64 FTE.
Gap = 64 − 38 = 26 FTE.
Do not round down: 63 FTE would leave the centre slightly short, and the 0.6 FTE represents about 2.9 productive hours per day - roughly 27 calls - so rounding up is the safe planning choice. The result also assumes the 78% target is applied after shrinkage; if occupancy were defined before shrinkage, the answer would change.
2. The finance director will fund either 10 agency staff or the capped overtime, but not both. Evaluate both options against the target and recommend one, with conditions.
Read the worked answer
Agency: adds 10 FTE, so 48 FTE. Available after shrinkage = 48 × 6.15 = 295.2 hours a day; at the 78% target, capacity = 48 × 4.797 = 230.3 hours a day. Workload is 305.3 hours a day, so the centre would be 75.0 hours a day short of the target; even at 100% occupancy it would be 10.1 hours a day short. The target would be missed. The 10 staff cost 1.35 times and need three weeks, but add sustainable capacity.
Overtime: 38 × 8 = 304 hours a week, or 60.8 hours a day. To reach the target from 38 FTE, the centre needs 305.3 minus 182.3 = 123.0 extra productive hours a day. Overtime covers about half, at 1.5 times cost, with fatigue and error risk.
Recommendation: neither option alone meets the target. Fund the agency staff, use limited overtime for peak days, and fix the 12% misrouting; consult the union before temps. If only one option is funded, choose agency staff for sustainable capacity, but tell the director plainly that the 78% target will still be missed.