## Interview Question

Senior Product Manager Interview Mountain View, CA

Answer## How would I design the elevators for a new 40 story office

building that had an average of 100 people per floor to most efficiently fill and empty the building given a standard 9-5 workday and traffic conditions in my city? The answer needed to be completely detailed, including expected passengers per car, time per stop, average floors stops per trip at various hours, etc.

## Interview Answer

7 Answers

The idea is to "learn" from user behavior. Start with a blank slate where the elevators assume that all floors, except the first floor, have the same probability at all times.

Then, based on user behavior, alter the probabilities.

If the elevators can talk with the users' phones, via bluetooth, and identify to which floor this user goes, when he/she comes to and leaves work, how often does this person take the elevator to go to other floors or out on lunch, then improve the efficiency based on the aspects learnt.

The analytics in a spreadsheet can give you a working theory. The key for a good product is to TEST the theory before you build. With the data for the size of building, estimates for passengers, etc, there may be other similar buildings already in operation nearby. I would want to check out what is REALLY happening there to validate theories before moving from design to build stage.

A simple algorithm would be to note that there will be more people during the morning going up and slowly taper this down as the day progresses. For example, during the noon-afternoon period, the frequency and number of people going up or down would be almost the same.

So have a priority for the ground floor during the morning hours. Move the elevators as soon as possible to the higher floors. Mandate that people get in regardless of whether the elevator is going up or down, once the elevator reaches the highest floor, it would reverse and go non-stop to the bottom floor.

Increase the priority for people for the floors that have the buttons pressed as time passes.

To clarify, the expectation is for the respondent to be as specific as possible. How many elevators total? How long would they stop on each floor? What range of floors would each elevator access? What quantifiable algorithm would be used to maximize efficiency? @PF: the interviewer was clear that she wanted a precise theory as an answer. Though testing might ultimately be useful it was outside of the question scope. @AJ: Given the precision expected you'd need to nail down "more people", "slowly taper", "day progresses", "noon-afternoon period", "a priority", "morning hours", "the elevators", "as soon as possible", "higher floors", and "time passes". What if one of the occupants was a training company where classes ended every hour? What if there were a public movie theater on one of the floors? @PS: your adaptive system would also need specifics and could improve efficiency for the building's primary residents. Occupants would need to be willing to share their identity via Bluetooth, have a Bluetooth capable device, and visit the building often enough to make the investment of their time worthwhile. If the population includes a significant transient component (training, entertainment, consulting, etc.) it could reduce the data needed for optimization. What specific optimization algorithm would you use? What would the thresholds be?

The question is less about a practical solution and more about generating precise and testable mathematical models on-the-fly.

1) The first advice that I've read is to ask some questions before you start answering. It will show that you are strategic & don't jump to random assumptions. So I will probably ask questions like:

Is the efficiency goal focused only at the start & end of day & not in between (i.e. lunch time, breaks)?

How many elevators are there?

What is the capacity of each elevator?

2) Assuming that everything is average, i.e. 6 elevators, 15 people per elevator, and focus only on start and end date, then the sample data should follow a normal distribution.

730-8 - 2%

8-830 - 14%

830-9 - 34%

9-930 - 34%

930-10 - 14%

10-1030 - 2%

3) I will break this down & solve the worst case scenario first. This means, 34 people x 40 floors = 1360 people to be transported by 6 elevator x 15 = total 90 capacity during 830-9 or 9-930 am.

4) Focusing on this more manageable problem, 1360 / 90 means each elevator will make 15 full cycles (lobby to highest floor and back)

5) Since we want to minimize the cycle time for each elevator, we assign one elevator per subset of 40/6 consecutive floors. This should address the issue on minimizing time per stop.

6) That means, the final design should be a load balancing of the elevators by minimizing the travel time --- Elevator A - 1st to 7th floor, B - 8th to 14th floor, and so forth.

Do you guys see anything wrong with this line of thinking?

@Mark - Would you expect someone going to the 14th floor to get off the elevator and hop on to the next one?

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I use spreadsheets for 'what-if' analysis and struggled to make the math work on paper without the help of a calculator. I did note that my first step before doing a design would be to conduct research with builders who would know how reality impacts the theory of building design.

I recall a PBS episode where an academic tried to raise a roof over the Roman Coliseum to prove his theory that the games enjoyed shade. The producer of the documentary wisely invited two circus managers who raised tents for a living to attend and give advice. Even before the first attempt they chuckled and said it would never work - something about the length of the rope and the size of the canvas sheeting needed being wrong. The academic assured them that everything had been carefully calculated and would, of course, work. To his frustration (and the circus manager's enjoyment) it flopped utterly just as predicted by those with practical experience.

The question was apparently designed to evaluate my performance on detailed calculations while under pressure. I can count on one hand the number of times I've been faced with that situation in my 30 year career.