Water Point Allocation
A provincial water authority has 3 tanker trucks to serve 5 villages during a dry spell lasting 10 days. Each truck can make 2 trips per day and carries 5,000 litres per trip. Daily minimum need per village is estimated as: Village A 3,000 L, B 2,500 L, C 2,000 L, D 1,500 L, E 1,000 L. Total daily supply capacity is therefore 3 × 2 × 5,000 = 30,000 litres, but road conditions mean each truck can realistically complete only 1.5 trips per day on average, reducing effective supply. Village C has a clinic; Village E is the furthest and costs one full trip to reach. The authority must decide an allocation rule and justify it to the provincial council.
1. Compute the realistic daily supply and assess whether total minimum need can be met. Show your reasoning.
Read the worked answer
Step 1 – Realistic supply. 3 trucks × 1.5 trips/day × 5,000 L = 22,500 L/day.
Step 2 – Total minimum need. 3,000 + 2,500 + 2,000 + 1,500 + 1,000 = 10,000 L/day.
Step 3 – Compare. 22,500 L > 10,000 L, so aggregate need is comfortably met - supply is more than twice the minimum.
Step 4 – The real constraint is not volume but distribution. The binding limits are trips and distance, not litres. E costs a full trip for only 1,000 L, so trip-efficiency matters more than litre-efficiency.
Conclusion: the authority cannot claim a shortage in aggregate. Any shortfall would be a logistics failure (trip allocation, routing), not a supply failure. The allocation rule must therefore be justified on trip cost and vulnerability, not on scarcity.
2. Propose an allocation rule that a council would find defensible, given the clinic in C and the distance to E.
Read the worked answer
A defensible rule combines need, vulnerability, and trip cost.
- Protect the clinic first. Village C's 2,000 L baseline is guaranteed and, if the clinic serves surrounding villages, allocated a buffer. Health infrastructure is a non-negotiable floor.
- Meet minimum need everywhere before surplus. Since aggregate supply exceeds need, every village should receive at least its stated minimum. Surplus (≈12,500 L) is then distributed by population or demonstrated demand.
- Consolidate trips to E. Because E costs a full trip for 1,000 L, schedule E deliveries on a fixed rotation (e.g., every second day with a larger load) rather than daily small drops. This raises trip efficiency.
- Publish the rule in advance. A council accepts an allocation it can predict and audit; it resists ad hoc decisions.
Judgement point: the strongest justification is transparency plus a protected floor for the clinic, not a claim of scarcity that the numbers contradict.