Choosing a tea factory site under perishability and flood constraints
A tea growers’ cooperative must choose one of three sites for a new factory handling 8,000 kg of green leaf per day at peak. Garden A is 9 km from Site X on a national highway, 22 km from Site Y (18 km fair-weather road plus 4 km highway) and 30 km from Site Z on a road closed for about 20 days each monsoon. Garden B is 12 km from X, 10 km from Y and 15 km from Z. Leaf must be processed within four hours of plucking to avoid quality loss. Site X land costs three times Site Y and four times Site Z; Y is 0.5 km from a river, X is 1.5 km and Z is 3 km. Power supply is reliable at X and Y but fails often at Z. Assume 25 km/h on fair-weather roads and 40 km/h on highways.
1. Calculate the road travel time from Garden A to each site under the stated speeds. Show your working.
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Use time = distance ÷ speed × 60 minutes.
- Site X: 9 km ÷ 40 km/h × 60 = 13.5 minutes.
- Site Y: 18 km ÷ 25 km/h × 60 = 43.2 minutes on the fair-weather road, plus 4 km ÷ 40 km/h × 60 = 6 minutes on the highway. Total = 49.2 minutes.
- Site Z: 30 km ÷ 40 km/h × 60 = 45 minutes.
All three are within the four-hour processing limit in normal weather. The calculation does not settle the choice, because Site Y’s time is weather-dependent and Site Z’s road is closed for about 20 days each monsoon, when the effective travel time becomes indefinite.
2. Recommend a site using at least four criteria, including perishability and flood risk.
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A simple weighted judgement can be shown. Suppose quality/reliability is weighted 40%, land cost 20%, water access 20% and power 20%, scoring 1–5.
- X: quality 5, cost 1, water 3, power 5 → 0.4(5)+0.2(1)+0.2(3)+0.2(5)=3.8.
- Y: quality 3, cost 3, water 5, power 5 → 1.2+0.6+1.0+1.0=3.8.
- Z: quality 1, cost 5, water 2, power 2 → 0.4+1.0+0.4+0.4=2.2.
X and Y tie, so judgement matters. X is better for perishability and monsoon reliability, but land is expensive. Y is cheaper, has the best water access and is still under four hours in dry weather, but 49 minutes leaves little margin on wet days. Z is cheapest but the 20-day closure and power failures are unacceptable for green leaf. Recommend X if capital is available; otherwise Y with collection sheds, a road upgrade and a leaf-quality protocol.
3. Explain how the monsoon closure at Site Z changes the factory’s effective capacity and leaf quality.
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The closure is not a small transport cost; it breaks the processing chain. For about 20 days the factory cannot receive 8,000 kg per day unless a long detour exists. Green leaf cannot be stored, so it either spoils in the field or must be diverted to another factory, reducing the cooperative’s throughput. The factory’s effective annual capacity falls, labour is idle and fixed costs are spread over fewer processing days. Quality loss is also non-linear: leaf held for more than four hours begins to deteriorate, and wet, compacted leaf in a truck deteriorates faster. Cheap land at Z therefore carries a hidden reliability penalty that can outweigh the saving.