The Doughnut Line That Cannot Keep Up
A regional bakery produces 4,000 doughnuts per 8-hour shift on a single line. Demand has risen to 5,200 per day, and the owner is weighing two options. Option A: add a second 6-hour evening shift using the same line, but the line needs 45 minutes of cleaning between shifts and evening labour costs 1.4 times the day rate. Option B: buy a second automated fryer for $180,000, which raises capacity to 5,600 per shift but adds $9,000 per year in maintenance and requires one extra technician at $62,000 per year. Current defect rate is 2.1% and rising because the fryer runs above its rated temperature during peak output. Customers have begun complaining about inconsistent texture. The owner has $200,000 in retained earnings and wants payback within three years.
1. Calculate the effective daily output of Option A and assess whether it solves the capacity problem. Show your working.
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Working. Nominal evening shift output: 6 hours × (4,000 ÷ 8) = 3,000 units. Deduct the 45-minute cleaning changeover, which produces nothing: effective evening run time = 6h − 0.75h = 5.25h. Effective evening output = 5.25 × 500 = 2,625 units. Combined daily capacity = 4,000 + 2,625 = 6,625 units, which exceeds the 5,200 demand.
Judgement. Option A technically covers demand with roughly 1,425 units of headroom. However, the changeover eats 12.5% of the evening shift, and the same single line is still being pushed at peak temperature, so the 2.1% defect rate is not addressed. The candidate who only computes 3,000 and declares success has missed the changeover constraint; the stronger answer notes that capacity is solved but quality is not.
2. Evaluate which option the owner should choose, using payback and the quality evidence.
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Option A payback. Evening labour cost depends on wage data not given in dollar terms, so payback cannot be computed precisely - but the capital outlay is effectively zero, meaning payback is immediate and the $200,000 is preserved. The trade-off is higher variable cost per unit (1.4× labour) and no fix to defects.
Option B payback. Annual cost = $9,000 maintenance + $62,000 technician = $71,000. Against $180,000 capital, simple payback is 180,000 ÷ 71,000 ≈ 2.5 years, inside the three-year target. But this ignores the revenue effect of quality: at 5,200 units and 2.1% defects, about 109 units per day are lost or reworked. If defects fall to, say, 0.5%, roughly 83 units per day are recovered - at a $1.20 margin that is about $100/day, or $30,000+ per year, shortening payback to roughly 1.8 years.
Recommendation. Option B is the stronger judgement because it addresses both capacity and the rising defect rate, and its payback fits the owner's constraint. Option A is the lower-risk cash choice if demand is uncertain, but it leaves the quality problem to compound. A defensible answer must weigh the quality evidence, not just the arithmetic.