Convoy Fuel, Tonnage and the 24-Hour Window
A unit must move 18 tonnes of relief stores from Base to Camp, a road distance of 240 km. Five 3-tonne trucks are held, but one is unserviceable, leaving four. Diesel consumption is 4 km per litre loaded and 6 km per litre empty. Each truck has a 120-litre tank, and standing orders forbid the tank falling below 10 litres. Loading at Base takes 30 minutes; unloading at Camp takes 45 minutes. Average speed is 40 km/h loaded and 50 km/h empty. The only fuel point is at Base, where 500 litres are held in drums. No truck may be left overnight at Camp, so every journey is a round trip. The move must be complete within a 24-hour window that starts when the first truck leaves Base.
1. How many loaded journeys are required, and how much diesel does one round trip consume? Does a single round trip fit inside one tank without breaching the reserve rule?
Read the worked answer
Journeys. Load per truck is 3 t, so 18 t ÷ 3 t = 6 loaded journeys (six round trips, since no truck stays at Camp).
Fuel per round trip.
- Loaded leg: 240 km ÷ 4 km/L = 60 L
- Empty return: 240 km ÷ 6 km/L = 40 L
- Total: 100 L per round trip
Tank check. Usable fuel is 120 L − 10 L reserve = 110 L. A round trip needs 100 L, so the truck arrives back at Base with 120 − 100 = 20 L, which is above the 10 L floor. The trip fits - but with only 10 L of slack.
The judgement point. Because 100 L is so close to the 110 L usable figure, a truck cannot carry fuel for two round trips in one fill; every trip must start from the Base fuel point. That single fact drives the answer to the next task.
2. Is the 500 litres of drum stock sufficient to complete the move? Show the shortfall and one realistic way to close it.
Read the worked answer
Demand. 6 round trips × 100 L = 600 L.
Supply. 500 L at Base.
Shortfall. 600 − 500 = 100 L short. The move cannot be completed on Base stock as it stands.
Judgement. The tempting answer - "fill less at Base and top up somewhere" - fails, because there is no fuel point between Base and Camp and the tank rule already leaves only 10 L of slack per trip.
The workable options are:
- Draw 100 L from Camp's own stock and issue it on arrival (about 17 L per trip, or 50 L on each of two trips). Camp issues, Base does not carry it.
- Obtain 100 L at Base before the move starts, which is the cleanest fix.
- Reduce consumption, not tonnage: a single escorted run of two trucks nose-to-tail does not change litres per km, so this only works if loads are consolidated onto fewer, fuller vehicles - impossible here, since the trucks are already at their 3 t ceiling.
A commander who simply says "not enough fuel" without the shortfall figure and an issue point is giving a complaint, not a plan.
3. Can the move be completed inside the 24-hour window with the four serviceable trucks? Give a clear verdict, the margin, and what it means for the commander.
Read the worked answer
One round trip in time.
- Loaded 240 km ÷ 40 km/h = 6.00 h
- Empty 240 km ÷ 50 km/h = 4.80 h
- Handling 0.50 h loading + 0.75 h unloading = 1.25 h
- Total = 12.05 h per round trip
Trips per truck. Six round trips over four trucks means two trucks do one trip each and two do two trips - there is no way to avoid at least one truck doubling, even if the fifth truck is repaired, because six trips cannot be split five ways without one truck doing two.
Doubled truck. 2 × 12.05 h = 24.1 h = 24 h 6 min.
Verdict. On paper the window is missed - by about six minutes, i.e. 0.4% over. That is inside the estimating error of the speed and handling figures.
What the commander should do. Do not report "possible" on the strength of rounding, and do not cancel the move over six minutes. Report it as marginal, and buy the margin deliberately: pre-load the doubled truck so it leaves first, cut unloading to 40 minutes per turn, and start the doubled truck's second loading while other trucks are still out. Any one of these recovers more than six minutes. The decision is about which margin to buy, not about whether the arithmetic is right.