Twelve-Day Production Plan on Two Finishing Lines
A currency press runs two finishing lines. Line A is rated at 1,20,000 note impressions an hour and Line B at 90,000. Both lines are available for 20 productive hours a day; the remaining 4 hours go to maintenance and changeover. Historical wastage - sheets rejected for register, ink smudges and numbering faults - is 0.5 per cent of gross impressions on Line A and 1.2 per cent on Line B. The production plan for the next 12 days must deliver 5,00,00,000 (5 crore) good notes. Paper costs Rs 3.60 a sheet and each sheet yields 40 note impressions; ink, numbering foil and other variable consumables come to Rs 0.45 per gross impression. Also on the table is a vendor proposal to calibrate Line B at a one-time cost of Rs 1,80,000, which is expected to bring its wastage down to 0.8 per cent.
1. Calculate the good notes the two lines will deliver across the 12-day window and state whether the 5 crore target is met.
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Step 1 - gross and net output per day.
| Line | Gross per day | Wastage | Good notes per day |
|---|---|---|---|
| A | 1,20,000 × 20 = 24,00,000 | 0.5% | 24,00,000 × 0.995 = 23,88,000 |
| B | 90,000 × 20 = 18,00,000 | 1.2% | 18,00,000 × 0.988 = 17,78,400 |
Step 2 - combine and extend to 12 days.
Combined good notes per day = 23,88,000 + 17,78,400 = 41,66,400. Over 12 days = 41,66,400 × 12 = 4,99,96,800.
Conclusion: the plan falls short of 5,00,00,000 by 3,200 notes. The percentage gap is tiny (about 0.006 per cent), but a supply commitment cannot be met by a short-packed consignment, so the gap has to be closed by extra run time rather than dismissed as rounding.
2. How much additional running time, and on which line, would close the gap?
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Work in good-note terms, because extra hours only count if the output survives wastage.
- Line A: 1,20,000 × 0.995 = 1,19,400 good notes an hour.
- Line B: 90,000 × 0.988 = 88,920 good notes an hour.
Time needed for 3,200 notes:
- On B: 3,200 ÷ 88,920 = 0.036 hour ≈ 2.2 minutes.
- On A: 3,200 ÷ 1,19,400 = 0.027 hour ≈ 1.6 minutes.
Either line closes the gap inside a single shift. The better operational choice is to trim about 3 minutes from one day's changeover window on Line A (faster, and lower wastage) and record the change in the production log, rather than schedule a part shift that would add start-up waste. Note the direction of the decision: because B wastes more than twice as much as A per impression, any extra hour is always worth more on A.
3. Should the plant approve the Rs 1,80,000 calibration of Line B on the strength of this 12-day run alone? Support the answer with numbers.
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Compare the value of the notes saved against the cost of the calibration.
Extra good notes from the calibration (Line B, 12 days). Gross on B over 12 days = 90,000 × 20 × 12 = 2,16,00,000. At 1.2% wastage: 2,13,40,800 good notes. At 0.8% wastage: 2,14,27,200 good notes. Gain = 86,400 notes.
What one good note costs to produce. Paper per impression = 3.60 ÷ 40 = Rs 0.09. Add consumables Rs 0.45 → Rs 0.54 per gross impression. Cost per good note on B = 0.54 ÷ 0.988 ≈ Rs 0.547.
Value of the gain = 86,400 × 0.547 ≈ Rs 47,200.
Judgement: Rs 47,200 of avoided production cost against a one-time spend of Rs 1,80,000 does not pay back within this run - the plant would need roughly four runs of similar volume before the calibration broke even. On a 12-day horizon the honest recommendation is to decline or defer, and to close the 3,200-note gap with minutes of extra Line A running time instead. The calibration becomes defensible only as a multi-run capital decision, which is a different approval route.