Clearing a Registration Backlog in Five Days
A registration unit has four clerks and must clear a backlog of 1,860 applications within five working days. Each clerk works a 7-hour day and processes 18 applications an hour. On Wednesday and Friday afternoons, all four clerks lose three hours each to mandatory training. Separately, about 1 in 10 applications is returned by the checker and needs 5 minutes of corrective work; this rework is done by the same clerks and comes out of the same processing hours. No application is returned twice. A fifth clerk could be borrowed from another team for one full 7-hour day, but would need two hours of induction before processing at the normal rate.
1. Using the figures given, will the unit clear the 1,860 applications within the five days? Show your working.
Read the worked answer
No - the unit is about 2.8 hours (roughly 51 applications) short.
- Gross hours: 4 clerks x 7 hours x 5 days = 140 hours.
- Training lost: 4 clerks x 2 afternoons x 3 hours = 24 hours. Net capacity = 140 - 24 = 116 hours.
- Base processing: 1,860 / 18 applications per hour = 103.33 hours.
- Rework: 10% of 1,860 = 186 applications; at 5 minutes each = 930 minutes = 15.5 hours.
- Total hours needed: 103.33 + 15.5 = 118.83 hours.
- Shortfall: 118.83 - 116 = 2.83 hours, which is about 51 applications at 18 per hour.
Note the assumption: reworked applications are not returned a second time (the setup says so), otherwise the gap would be larger.
2. What is the minimum extra clerk capacity needed to hit the target, and how would you express that to a manager in one sentence?
Read the worked answer
Minimum extra capacity: 2.83 hours - practically, 3 clerk-hours.
Any answer below 2.83 hours leaves the backlog unfinished. Because work is organised in whole shifts in practice, the safest phrasing is "three additional clerk-hours, or the equivalent of 51 extra applications processed".
One-sentence version for a manager: "At current rates we need about 119 clerk-hours and have 116, so we are roughly three hours - around 50 applications - short of the five-day target."
A common error to avoid is quoting the shortfall as 51 hours rather than 51 applications, or forgetting that rework consumes the same processing capacity as first-pass work.
3. The manager offers two options: (i) move all training to the following week, freeing 24 clerk-hours; or (ii) borrow a fifth clerk for one full day. Which do you recommend, and under what condition would you switch?
Read the worked answer
Recommend option (i) if the training can lawfully and practically be deferred; otherwise option (ii).
Reasoning:
- Option (i) frees 24 hours against a 2.83-hour shortfall - far more headroom, and the team keeps its familiar workflow. Risk: training may be mandatory with its own compliance deadline, and deferring it may breach that deadline or push the loss into a week with no slack.
- Option (ii) adds 7 hours, which also clears the 2.83-hour gap, but only if the borrowed clerk actually reaches 18 applications per hour. The two-hour induction means 5 productive hours, i.e. about 90 applications - still enough, but with less margin. There is also supervision and access-approval cost.
Switch condition: if the training is statutory or cannot be rescheduled without a compliance breach, take option (ii) - or split it, rescheduling only the Friday session (12 hours freed, still ample). Correct reasoning rests on margin of safety, not just on which number is bigger.