The Supply Drop Window
You command a four-vehicle resupply convoy moving to a forward position 90 km away. Vehicles must travel in convoy at 30 km/h on the only route, which passes through a single-lane bridge. The bridge can take one vehicle at a time and each crossing takes 4 minutes, with a minimum 2-minute gap between vehicles to avoid overloading. One vehicle develops a fuel leak and can only safely cover 60 km before repair; a repair kit is at the bridge checkpoint and takes 25 minutes to apply. You must have all four vehicles at the forward position within 5 hours of departure. A radio message warns that the route beyond the bridge may be closed for 40 minutes at some point for engineering work.
1. Calculate the earliest time all four vehicles can arrive, assuming the engineering closure occurs and you repair the leaking vehicle at the checkpoint.
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Drive to bridge: Assume the bridge is reached after some distance; the convoy travels at 30 km/h. The critical path is driving plus crossing plus repair plus closure.
- Total driving time for 90 km at 30 km/h = 3 hours (180 min).
- Bridge crossing: 4 vehicles x 4 min = 16 min, plus 3 gaps x 2 min = 6 min, total 22 min.
- Repair at checkpoint: 25 min.
- Engineering closure: 40 min.
If repair and closure overlap, add only the larger delay. Worst case they do not overlap: 180 + 22 + 25 + 40 = 267 min = 4 h 27 min. This is within the 5-hour limit, but only by 33 minutes.
Key judgement: the margin is thin, so any additional delay (e.g. the leak worsening) breaches the deadline. You should radio ahead to confirm whether the closure can be delayed or whether the repaired vehicle can proceed separately.
2. The repair takes longer than expected (45 minutes). What do you do, and what is your reasoning?
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Recompute: 180 + 22 + 45 + 40 = 287 min = 4 h 47 min - still inside 5 hours, but with only 13 minutes of slack.
Decision: proceed, but take mitigating action:
- Send the three healthy vehicles ahead immediately so they are not exposed to the closure; they arrive earlier and can begin unloading.
- Keep the repaired vehicle with a escort/safety margin and confirm the route beyond the bridge is clear.
- Inform higher headquarters of the revised ETA and the reduced margin.
Reasoning: the mission requirement is all four vehicles within 5 hours; the plan still meets it. Splitting the convoy reduces the risk that a single further delay affects all four vehicles. If the margin fell below zero, the correct call would be to request an extension or prioritise the most critical cargo rather than gamble.