I like the approach @Nimesh, but I didn’t quite understand how the 30 seconds wait time came into play in your solution.

Here’s mine. Please let me know what you think.

To answer this, we need to figure out the rate at which we can move people (supply) and how many people to move (demand). We also need to consider: elevator capacity, acceptable wait time, and peak times.

Demand assumptions:

– 15 floors

– 200 people per floor

– 8-10AM peak times, so 2 hours

– 2/3 of the people arrive within the peak time

Given assumptions, we need to move

15×200 =3000 people

3000/2 = 1500 people per hour

1500*2/3 = 1000 people per hour after adjusting for not everyone coming to work in peak time.

We want to use peak time as our basis for the demand because if we can handle the load in peak time, we can be sure we can handle the load during off peak.

To figure out the supply, we need to calculate how quickly one elevator can return.

Supply assumptions:

– 2 seconds per floor

– 15 seconds per door open

– 5 door opens per trip

2 seconds x 15 floors x 2 round trip + 15 seconds x 5 door opens = 60 + 75 = 135 seconds

this is approximately 2 minutes.

So it takes 2 minutes for an elevator to be re-used.

In that time, how many people will be waiting?

1000 people/60 min = aprx 17 people per minute, so 34 people every two minutes.

If we want 30 seconds as the max wait time, then we need to move 9 people per 30 second increment (17 people per minute /2).

If each elevator can carry 10 people, then in 2 minutes we’d need 4 elevators because there are 4 30-second intervals in 2 minutes.

If we want to have wait time be 1 minute max, then we’d need to carry 17 people every minute. If the elevator can only take 10 people, we’d need two sets. In 2 minutes, there’s 2 1-minute intervals, so that requires 4 elevators.

If the elevator can take 20 people and acceptable wait time is 1 minute, then we’d only need 2 elevators!

So the levers are elevator capacity and acceptable wait time. A sanity check is in my building there’s 4 elevators. It’s 15 floors. I don’t think I’ve ever waited for longer than 1 minute. So it is reasonable estimate.