Refueling Throughput: Two Trucks, One Deadline, and a Changed Requirement
The fuel line at a small airfield has two refueling trucks. Truck A delivers 220 gal/min; truck B delivers 180 gal/min. Six aircraft are scheduled, each needing 1,100 gal, and a delivery tanker arrives at 0600 to refill the storage tank. The trucks must be finished before the tanker arrives or the field loses its reserve. Work starts at 0535. Truck B must be taken offline for a 15-minute filter change immediately at the start; truck A runs continuously. Partway through, the crew chief reports that one of the six aircraft actually needs 1,600 gal rather than 1,100 gal.
1. Using the original 1,100 gal requirement, what time do the trucks finish and how much margin remains before 0600?
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Total demand: 6 x 1,100 = 6,600 gal
Phase 1 (first 15 min, B offline): truck A alone moves 15 x 220 = 3,300 gal.
Phase 2: remaining 6,600 - 3,300 = 3,300 gal with both trucks at 220 + 180 = 400 gal/min, so 3,300 / 400 = 8.25 min.
Total time: 15 + 8.25 = 23.25 min, finishing at 0535 + 23:15 = 0558:15.
Margin before the 0600 tanker arrival is only about 1 min 45 s. That is thin: a single unplanned delay of two minutes breaks the plan, so the supervisor's promise to the tanker drivers is not really supported by the numbers.
2. With the one aircraft now needing 1,600 gal, does the 0600 deadline still hold?
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Demand rises by 500 gal to 6,600 + 500 = 7,100 gal.
- Phase 1 unchanged: 3,300 gal during B's 15-minute filter change.
- Phase 2: 7,100 - 3,300 = 3,800 gal at 400 gal/min = 9.5 min.
- Total: 15 + 9.5 = 24.5 min, finishing at 0559:30.
It still works, but the margin collapses from 1 min 45 s to 30 seconds. At that point the plan is technically legal and operationally reckless: any delay at all (a truck repositioning, a slow coupling, a pump that primes poorly) misses the tanker. The correct judgement is to start the extra 500 gal into the lowest-demand aircraft first, or to push the tanker arrival, rather than to rely on a 30-second buffer.
3. The filter change actually takes 20 minutes instead of 15, and the extra 500 gal is still required. What is the outcome, and what is the most useful way to state it?
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Phase 1 (20 min, B offline): 20 x 220 = 4,400 gal. Phase 2: 7,100 - 4,400 = 2,700 gal at 400 gal/min = 6.75 min. Total: 20 + 6.75 = 26.75 min, finishing at 0601:45.
The field misses the tanker by about 1 min 45 s, so the reserve is exposed for that period.
Stating it as a time overrun is more useful than 'we were late', because it shows the overrun equals exactly the 5-minute filter slip minus the 3.25 minutes of extra throughput that B's longer absence removed from the parallel phase. Two levers exist: cut the filter change back toward 15 minutes, or pre-load truck A during the maintenance window with the aircraft that needs 1,600 gal. Either closes a gap of under two minutes; neither can be invented after 0559.