Clearing the land-record backlog: capacity, cost and the target
The Maripur taluk office has 8 clerks clearing land-record correction files. A clerk's full working day is enough for 30 files at first pass. Quality checks return 20 per cent of completed files for rework, and each rework takes half the time a first-pass file takes. At the start of the month the office holds a backlog of 2,400 files and receives 150 new files every working day. The month has 20 working days. The State cell requires the backlog to be cleared by the end of the month and offers the office a choice: two additional clerks for the month, or overtime of up to 5 extra files per clerk per day. A clerk costs ₹1,800 per day and an overtime file costs ₹60. The office must choose the cheaper option that actually meets the target, and the accounts section wants the arithmetic before sanctioning either.
1. Compute the office's present effective daily output and show whether the target will be met.
Read the worked answer
Work in 'first-pass equivalents'. For every 10 files cleared, 2 come back (20 per cent), each costing half a first-pass file: 2 × 0.5 = 1 unit. So 10 files consume 11 units of capacity.
Gross capacity = 8 clerks × 30 = 240 units per day. Let F be first-pass files: F + (0.2F × 0.5) = 1.1F = 240 → F = 218.2 files per day.
Net clearance = 218.2 − 150 inflow = 68.2 files per day. Over 20 days: 68.2 × 20 = 1,364 files cleared from the backlog. Backlog remaining = 2,400 − 1,364 = 1,036 files. The target is missed by a wide margin, so the present establishment is not a option - one of the two offered measures must be taken.
2. Calculate the capacity actually required, then compare the two options on both adequacy and cost. Make a recommendation.
Read the worked answer
Required capacity. Net needed per day = inflow + (backlog ÷ days) = 150 + (2,400 ÷ 20) = 150 + 120 = 270 files per day. Converting to gross units: 270 × 1.1 = 297 units per day, i.e. 297 ÷ 30 = 9.9 → 10 clerks (2 more).
Option 1 – two extra clerks: 10 × 30 = 300 units → 300 ÷ 1.1 = 272.7 files → net 122.7 per day → 2,454 files over 20 days. Target met (2,400 needed). Cost = 2 × ₹1,800 × 20 = ₹72,000.
Option 2 – overtime only: 5 × 8 = 40 extra units → 40 ÷ 1.1 = 36.4 files → total 218.2 + 36.4 = 254.5 → net 104.5 per day → 2,090 files. Target missed by about 310 files. To reach 270 files net you would need 57 extra gross units, i.e. 7.1 per clerk per day, above the 5-file cap. Maximum overtime cost is 40 × ₹60 × 20 = ₹48,000, but it buys a scheme that fails.
The overtime option is cheaper only because it does less. Recommend the two additional clerks (₹72,000). Note the assumptions in the sanction order: no leave, steady inflow, and rework drawn evenly across the month.
3. The quality cell says it can halve the rework rate within a week at no cost. Would that alone meet the target? What should the office do with this offer?
Read the worked answer
With rework at 10 per cent and half-time rework, the multiplier becomes 1 + (0.1 × 0.5) = 1.05.
Capacity = 240 ÷ 1.05 = 228.6 files per day; net = 228.6 − 150 = 78.6 per day; over 20 days = 1,572 files. Backlog remaining ≈ 828 files. It does not meet the target on its own, though it recovers roughly 208 files compared with doing nothing.
It also arrives 'within a week', so at best 15 of the 20 days benefit - the real gain is smaller still.
Practical judgement: accept the process fix (it is free and permanent), but do not let it substitute for the extra clerks. If the fix is delivered, the clerks' output rises to 300 ÷ 1.05 = 285.7 files, net 135.7 per day, which clears the backlog inside 18 days and builds a small buffer. Report it that way - the fix reduces the risk of the hiring decision, it does not replace it.