Clearing a claim backlog before a regional deadline
A divisional office begins July with 9,600 pending claim files. The branch has 8 clerks, each clearing 30 files on a working day, and the office works 22 days a month. In July, two clerks are deputed for 15 working days each to a training programme, and no replacement is provided. From August, fresh claims arrive at a steady 120 per working day, and the office continues to have 22 working days a month. The branch manager has promised the regional office that the entire backlog plus all August arrivals will be cleared by 31 August. Additional clerks can be recruited, but each must be productive from day one and clears 30 files a day. Alternatively, the existing staff can work two hours of overtime daily for all 22 working days; each clerk clears 4 files an hour during overtime, and fatigue is assumed not to reduce normal output. The manager must decide the cheapest credible way to keep the promise.
1. How many files will still be pending on 31 July, and what is the total workload that August must absorb?
Read the worked answer
July capacity. Full strength would give 8 clerks × 22 days × 30 files = 5,280 files. The training deputation removes 2 clerks × 15 days × 30 files = 900 files of capacity. Net July output = 5,280 − 900 = 4,380 files.
Closing backlog on 31 July = 9,600 − 4,380 = 5,220 files.
August arrivals = 120 files × 22 working days = 2,640 files.
August workload = 5,220 + 2,640 = 7,860 files.
Note the trap: a careless reading would use 120 × 30 or count 20 instead of 22 working days. The inflow must be computed on working days only, because claims arrive on days the office is open. The July shortfall (5,220 against a normal monthly capacity of 5,280) is almost exactly one month's work, so August has to deliver roughly one and a half months of output in one month.
2. With the existing 8 clerks, what is the minimum number of additional clerks needed in August? Show the working.
Read the worked answer
August capacity at present strength = 8 × 22 × 30 = 5,280 files.
Shortfall = 7,860 − 5,280 = 2,580 files.
Contribution of one additional clerk = 22 days × 30 files = 660 files in the month.
Clerks required = 2,580 ÷ 660 = 3.91, which must be rounded up to 4, because a clerk cannot be hired as 0.91 of a person and the promise allows no shortfall.
Check: 5,280 + (4 × 660) = 5,280 + 2,640 = 7,920 files, which clears 7,860 with 60 files to spare - under one day's cushion for eight people, so realistic only if attendance is near perfect.
Rounding down to 3 would give 5,280 + 1,980 = 7,260, leaving 600 files pending on 31 August and breaking the commitment. Three-and-a-half clerks is not an option available to a branch.
3. Evaluate the overtime alternative against the recruitment option and recommend one.
Read the worked answer
Overtime arithmetic. Two hours at 4 files an hour adds 8 files per clerk per day. Over 22 days with 8 clerks: 8 × 22 × 8 = 1,408 extra files.
- Overtime alone: 5,280 + 1,408 = 6,688 files, short by 1,172. Not sufficient.
- 2 extra clerks alone: 5,280 + 1,320 = 6,600, short by 1,260. Not sufficient.
- 2 extra clerks + overtime: 6,600 + 1,408 = 8,008 files, clearing 7,860 with 148 spare.
Comparison. Four recruits alone meet the target with a 60-file cushion and no extra hours. Two recruits plus overtime meet it with a 148-file cushion and a lighter recruitment burden, but every clerk works a longer day for a whole month, which the model assumes away fatigue - an assumption a real branch cannot rely on, since error rates in claim processing rise with long shifts, and rework would eat the cushion.
Recommendation: recruit 4 clerks as the primary plan, and hold one week of limited overtime as contingency for the last week of August rather than running it for all 22 days.