The Numbers Behind the Evacuation
A shore facility must be evacuated within 30 minutes of an alarm. It holds 240 people. There are two exits. Exit A can pass 12 people per minute; Exit B can pass 8 people per minute. In drills, only 70 percent of people use the nearest exit; the rest cross to the other, adding 40 seconds each to their own evacuation but not blocking the exits. A stairwell serving Exit B narrows so that no more than 6 people per minute can enter it, regardless of the exit's capacity. A headcount at the muster point takes 4 minutes and can begin only when the last person arrives. The standard requires the whole process, including headcount, to finish within 30 minutes. A recent drill achieved 33 minutes.
1. Calculate whether the standard can be met and identify the binding constraint.
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Exit A clears 12 per minute; Exit B is limited by the stairwell to 6 per minute, not its nominal 8. Combined flow is 12 + 6 = 18 people per minute. Clearing 240 people takes 240 / 18 = 13.3 minutes, so about 13 minutes 20 seconds. Add the 4-minute headcount: 17.3 minutes, comfortably inside 30. The binding constraint is the stairwell feeding Exit B, which cuts the theoretical combined rate from 20 to 18 per minute. The 40-second detours affect individuals' arrival times but do not reduce exit throughput, so they do not change the total clearance time materially.
2. The drill took 33 minutes. Given the calculation, where should you look for the explanation?
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The arithmetic says the physical flow is not the limit, so the extra 16 minutes must come from something not in the model: delay before people start moving (alarm recognition, people finishing tasks), congestion at the stairwell merging point, the headcount starting late or being conducted inefficiently, or people arriving at the muster point in a trickle after the last exit clears. The correct response is to measure the phases separately (time to first movement, time to last person out, headcount duration) rather than assume the exits are too small and widen them at cost. This is the difference between diagnosing and guessing.
3. A proposal would widen the stairwell to lift Exit B to its full 8 per minute. What improvement would that produce, and is it the best use of effort?
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Combined flow becomes 12 + 8 = 20 per minute, so clearance is 240 / 20 = 12 minutes, saving 1 minute 20 seconds. Against a 33-minute drill and a 30-minute standard, that is marginal. If the real loss is in start-up delay and headcount, the stairwell work buys little. The better use of effort is to find and fix the measured delay. The answer should show the calculation, then argue from it that the proposal addresses a constraint that is not currently binding on the observed performance.