Water planning for a 60-hour patrol: when the arithmetic forces a command decision
Twelve soldiers must patrol for 60 hours in a hot, dry area with no water source on the route. The planning figure is 5 L of drinking water per person per day, and a 10% reserve is mandatory. Water is carried in 20 L jerry cans; each empty can weighs 1.2 kg. Only four soldiers can be released from radio, medical and command duties to carry water, and each may carry at most 25 kg in addition to personal kit. A vehicle can meet the patrol at any point between 20 and 40 hours in, provided a written resupply request is submitted 6 hours in advance. Reassigning a fifth carrier is possible but strips another specialist task.
1. Compute the total water requirement and the number of cans needed, then test the plan against carrying capacity. Show every rounding decision.
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Requirement:
- 60 hours = 2.5 days.
- 12 soldiers × 5 L × 2.5 days = 150 L.
- Reserve 10% = 15 L → 165 L of water to be carried.
Cans: 165 ÷ 20 = 8.25. Round up to 9 cans, because you cannot carry a quarter of a can and the reserve has to be real water, not a number on a planning sheet. That is 180 L.
Weight: water 9 × 20 = 180 kg; cans 9 × 1.2 = 10.8 kg; total 190.8 kg.
Capacity: 4 carriers × 25 kg = 100 kg available.
Conclusion: the plan is infeasible - it needs about 1.9 times the carrying capacity available. The rounding matters: rounding 8.25 down to 8 cans would hide the deficit by pretending the reserve need not be carried, and would still be infeasible. Something structural must change: duration, headcount, number of carriers, or resupply.
2. The vehicle is offered at the 30-hour mark. Work out whether four carriers can reach it with the mandated reserve, and state the cleanest fix with numbers.
Read the worked answer
Maximum with four carriers: 100 kg ÷ 21.2 kg per can (20 kg water + 1.2 kg can) = 4.7 → 4 cans, weighing 84.8 kg, giving 80 L of water at 21.2 kg per soldier.
Endurance on 80 L: 80 ÷ (12 × 5) = 1.33 days = 32 hours with no reserve. With the 10% reserve set aside, usable water is 80 ÷ 1.1 = 72.7 L → 1.21 days ≈ 29 hours.
30 hours is therefore out of reach with four carriers and a legal reserve - the shortfall is small but real.
Options, costed:
- Five cans and five carriers: needed water for 30 h with reserve = 12 × 5 × 1.25 × 1.1 = 82.5 L, so 5 cans (100 L) at 106 kg total. Five carriers give 125 kg capacity, 21.2 kg each - feasible, but costs a specialist from radio or medical duty.
- Move the meet to 24 hours with four carriers: requirement = 12 × 5 × 1.0 × 1.1 = 66 L, which 4 cans (80 L, 84.8 kg, 21.2 kg each) cover comfortably. Keeps all specialists in place.
Cleanest fix: request the meet at 24 hours. It solves the problem without degrading a specialist function, and it leaves a margin of 14 L against the plan. The decision has to be made before departure, not at hour 24, because the request needs 6 hours' notice.
3. Name the two assumptions in this plan most likely to fail in the field, and how you would build margin against them.
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Assumption 1 - that the patrol lasts exactly 60 hours and that consumption stays at 5 L per person per day. Contact with the enemy, a casualty evacuation, broken ground or a hotter than forecast day all extend time and raise demand; a casualty can double individual consumption. Margin: plan on 6 L per person per day, fix a hard turnaround time, and treat the reserve as untouchable until the meet has actually happened.
Assumption 2 - that every can arrives full and that four carriers stay fit. Spillage, leaking cans, cans opened for washing, and one carrier going down with heat illness all destroy the arithmetic. Margin: carry the emergency water in one designated can that is never opened for routine issue, inspect can seals before departure, and rehearse redistribution - if one carrier falls out, the remaining three cannot absorb his load, so the patrol must slow or dump non-essential weight.
The reasoning being assessed is that a logistics answer is only as good as its weakest assumption, and that rounding, reserves and notice periods are all places where plans silently fail.