How many elevators should an average office building have?

1. From the one-liner, its an open ended question. But beware: The interviewer might be having some specific building config/plan in mind (G+29 tower, 29 floors are rented out office space with different companies working in it, each floor with 200 seating capacity, a roof-top restaurant and recreation area /reception in ground floor. The tower is located in a city-centre of a busy city) - Very important to clarify these with the common WWWWH probings explcitly. It will be captastrophic if you discover this after you start off with (valid-sounding) assumptions thinking that its the right approach to do a top-down break-down.

2. You should also ask some additional probing questions about possible shifts of operations etc (what if this is a BPO?) by clarifying things like hours of operation. Imagine the difference in your answer if you are informed later that there could be 2 shifts and end-time of one has some overlap with begin time of the other!!

3. If the question is about determining the number of elevators, then clearly the building is not built (it cant be an after-thought!). So certain design considerations are important:

Most important part - Parking. In a setting like above with 6000 employees, and addiotnally visitors to offices and restaurants, you need 1000+ car parking facility (even with a conservative estimate). One need to clarify where/how is this planned
1. Basement (then how many basement levels are needed based on floor area of the building and number of cars that can be parked realistically in each level) - This need elevators to start from these basement levels and over-all number of levels to be considered increases (30 stories + basement levels). One need additionally build a strategy to ensure that 'some' elevators start from basement whereas many are from ground floor (imagine waiting in a mall for 10 minutes for the elevator only to see that its full when it arrives) to ensure uniform utlization and avoid build-up
2. In a seperate parking tower - This will then need additional elevators, though not part of the office building. Do we need to factor those in?
3. Ground level - Very limited, specifically once you are tipped off that the location of the building is a city-center / CBD. So, then need to clatify if parking will be a combination of different parking facilities?
4. Outside public paid parking as in some tech-parks or many EU cities. Our design/count is then not affected
Access control . The building hosts many different offices. Very likely that such a high rise has sections (1-5, 6-10 etc) and an individual is allowed to enter only to a section with her respective office in it. Many office towers also enforces this partially by having elevators that will go to only those sections and allow individuals access to only those elevator bays. If everything is uniform and normally distributed, then this will not impact the elevaror design/count. But redundancy planning is never done with such simpler assumtptions
Special Needs - Accessible elevators are mandatory in most countries these days. As this has a roof-top restaurant (and with possible in office cafe areas) there must be additional service elevators. Elevator bays need seperation and some reduncancy policy has to be there in place. Which need to be either factored in or explcitly termed as out-of-scope

4. Finally, if you are being interviewed for TechPM role (for teams that build platforms, dev-tools, verticals in telecom, compute for PaaS etc), its better to make it explcit about scientific assumptions you make regarding things like distribution. As we know Qing theory has many complex models - Poisson distribution for incoming traffic or people arrival rates, exponential distribution for wait-times, Little's formula for Q-length etc. Assuming that these are all normally distributed and linear might be an issue in certain settings. You need to explcitly call these out and why you think its a reasonable assumption

The primary consideration that I would like to bring up here is that an "estimation" sounding question will have number of elments of a "design" question as well. It might be a prudent idea to think who are the actors here (building owner / emplyers who takes building on lease / individuals working there / security and admin staff) and think about the needs, pain-points and experience of these personas before limiting this as a formula based estimation question, specifically as in a real interview setting, no-one will classify that this is an estimation question...so better ask up-front.

Cheers, Val

Nimesh · Answer 2 · 2018-08-12T18:44:06+0000

Structure is critical when answering estimation PM interview questions. In this case:

Let’s say an average office building is 30 floors and there are 200 employees per floor. That means a total of 200 x 30 = 6,000 employees work there. Assuming that 10% are out of office at anytime and the number of visitors are negligible, we can say total number of employees in the building is 6,000 x 0.90 = 5,400.

Given people in the office usually arrive to work within a short window of time, I’d like to design the elevator in a way that employees don’t wait for longer than 30 seconds. Let’s assume that the 5,400 people arrive uniformly within 60 minutes in the morning.

Let’s say that the elevators are designed in a way that in the building are going to stop at a max of 5 floors, the speed of the elevator is 3 meters per second, each floor is 3 meters long, and it takes an elevator 15 seconds to open, unload some people in each floor and close and it takes elevator 60 second to get filled in ground floor. Let’s also assume the stops are disrtibuted unifromly. In other words, distance between the stops is 30 / 5 = 6 floors or 6 x 3 = 18 meters.

This means that each round takes the elevator time to travel to the floors + time to open and close in each floor + time to fill up the elevator in ground + time for the elevator to come back to ground floor. Let’s calculate the number:
5 stops x (18 meter / 3 meter per second) + 5 x 15 seconds + 30 seconds + (30 floors x 3 meters / 3 meters per second) = 30 + 75 + 30 + 30 = 165 seconds or around 3 minutes. In other words, one elevator can do 60 minutes / 3 minutes = 20 rides in an hour in the peak time. Let’s say each ride can consist of 20 people. This means that one elevator can help move 20 x 20 = 400 within one hour in the morning. Given total number of employees in the building is 5,400, we would need 5,400 / 400 = 13 elevators to move everyone to their floor in the morning in a way that no one has to wait for longer than 30 seconds.

srinatar · Answer 3 · 2022-11-12T16:36:14+0000

clarifying question

1. can i assume that most average office buildings has only employees and not other recreational activities such as rooftop restaurants or other sight seeing to attract non employees. - yes

2. can i also assume that 70% of the people in the buildings (employees) mostly come to work between 7-9 am at a steady state. - sure

ok. in US, we have 2 kinds of Cosmopolitans (thinking New York) and Metropolitans (thinking SFO, Seattle etc.)

for this exercise, can i focus on a metropolitan

let us think about what is an average office buildings. we have 2 kinds of cities

metropolitan
1. let me assume that an office building has 10 floors and each floor hosts 3 companies and 100 employees work per company per floor. So, total employees entering office building between 7-9 = 3000.
2. let us also assume that 80% of the total employees enter the office have a normal distribution. so, 1200 (80%of 3000= 2400/2) people per hour or about 20 people per minute.
3. each elevator can carry about 10 people and takes about 1s to go to each floor and stops 5s on each floor on its way up = travel time for elevator = 1m.
4. so, we need 2 elevators to serve 20 people arriving per minute.

summary: average office building have 10 floors with 1200 people arriving per hour between 7 - 9. assuming that elevators can carry 10 people . we need 2 elevators in most office buildings.

Devashish Verma · Answer 4 · 2022-07-20T17:06:11+0000

Clarifying questions
1. Are we talking in the context of us or India– US
2. Average number of floors → you decide
3. Average no of seats/ floor → to find out
4. Should we assume that 80% people visit on office on average -Yes
What we know
1. On average ofc building will have height of 20 floors
2. No of seats
3. Peak time → 80% of people will leave enter the building during this time . remaining 20% will come at different time. Some may use stairs
  1. Incoming time → 7-9 am
  2. Outgoing – 3-5pm
4. Wait time should not exceed 120 seconds on ground floor
5. Time for lift to go from 1-2 floors —>fast elevator → 3 secs (assuming

high speed elevator)

Assuming it stops at half of the floors → stay time will be another 5-6secs— stops→gates open→ people exit→ people enter → gate closes

All lifts may not go to all 20 floors all the time but given that we are only considering peak time we can assume that each lift goes to 20 floors

Capacity of lift → 10 people

Computation
1. In two hours time 64%(80%*80%) people should be able to enter the building.
2. Assuming each floor has 300 seats → 20 floors will have 20*300 = 6000 seats
3. 64% ~65% *6000= 3900
4. Elevator stops at 10 floors = 10*6 sec= 60 sec
5. Total time to go from ground floor to 20 floors = 20*3+60= 120 sec one side
6. 120* 2 sec to come back = 4 mins
7. In two hours time → number of trips/ lift= 120/4= 30 trips
8. Average number of people = 30*10 =300
9. Number of lift needed for 3900 people = 3900/300=13 lifts

PM_NG · Answer 5 · 2021-10-31T20:19:21+0000

Assuming this in city or suburban:

Suburban:

Average number of floors: 10

Number of people : 200

Number of people coming in peak hour (2 hours period): 80% of 2000= 1600

Total number of people per hour: 800

Number of people per min: 15 (approx)

Assuming that lift takes 10 mins to complete a trip (average stop on 5 floors )

Number of people on the floor in 10 mins wait time: 150

Number of people which can be accomodated in a lift : 25

Number of lift needed: 6 (150/25)

Tim Jones · Answer 6 · 2021-09-10T22:08:53+0000

1: Overview

First, let's create a formula to solve the general problem: How many elevators should any office building have, given its characteristics?

Then, let's solve the specific problem: How many elevators should an average building have, given characteristics that we guess to be average?

2: Define our variables, and some simple pre-formulas

EC: Elevator count, number of elevators

WC: Worker count, numer of workers we need to move

AT: Arrival time, length in minutes of window in which all workers arrive

ED: Duration of avg elevator journey

ES: Elevator Size, number of people who fit in one elevator

WAavg (Workers Arriving per minute) = WC/AT (Assuming: Workers arrival is spaced evenly over AT)

WDmax (Max capacity for Workers Departing per minute) = ES * EC / ED

3: Set goals

Goal:

If we want maximum efficiency then let's try to make WDmax = WAavg

Notes:

To save money at the expense of wait times, then we could make WDmax < WAavg
To ensure we can handle surges or broken elevators etc, then we could make WDmax > WAavg

4: Derive our ultimate formula

WDmax = WAavg

ES * EC / ED = WC / AT

ES * EC = WC * ED / AT

EC = (WC * ED / AT) / ES

EC = (WC * ED) / (AT * ES)

In english:

In order to make our maximum rate of elevator transporation equal to our rate of worker arrival,

our elevator count should equal (the number of workers, times the duration of the journey,)

divided by the (length of the arrival window, times the elevator capacity)

5: Calculate elevator count in an "average" building

Let's guesstimate "average" values for each of our four input variables.

Worker count: 5000

Ride duration in minutes: 2

Arrival window in minutes: 120

Elevator capacity: 8

Now let's calculate:

EC = (5000 * 2) / (120 * 8)

= 10000 / 960

= 10 elevators!

productmanager1644 · Answer 7 · 2021-02-03T23:51:31+0000

CLARIFY:
1. Is there a type of office that I should have in mind to help me with what the average size of the office is? Your choice.
2. Is it OK to not account for COVID / i.e. elevators that likely have to run at less capacity than normal? Yes. (I will account for an elevator that's running at max capacity.)
3. Are the elevators smart elevators - i.e. able to dictate which elevator bank to go to so elevators minimize the floor stops they make? Your choice. In this case, I assume there is no smart directing.
AVERAGE OFFICE BACKGROUND: To size the average office, I think about the corporate offices I have been to. Let's assume:
1. Total Employees: 1000
2. Total Floors: 25 floors
3. Employees / Floor: 1000 employees / 25 floors = 40 per floor (assuming even distribution)
ELEVATOR BACKGROUND: Below are assumptions I am making about the elevator given my experience riding corporate elevators in the office. I'm assuming these elvators are functioning normally / not jamming, etc.
1. Elevator Capacity: 10 people at one time
2. Each Stop: 15 seconds (open doors, people walk in or out, close doors) (Assumes no one is holding the elevator).
3. Time to Move between Floors: 5 seconds
CALCULATION:To calculate the number of elevators the office should have, I want to think about how many elevators are needed to deal with at peak times to ensure that people wait no longer than 10 minutes for an elevator.
BREAKDOWN UNKNOWNS:
1. Peak Hours: 8 AM - 9 AM (morning rush) or 5 PM - 6 PM (evening departure).
2. Behavior During Peak Hours: I will use morning rush as an example. Departure behavior will be the same given it is the same time length (1 hour).
  1. Let's assume that all 1000 people arrive between 8 AM - 8:50 AM to make any 9 AM meetings. Again, we do not want people to wait more than 10 minutes for the elevator, so if they arrive at 8:50 AM, they can make the 9 AM meeting.
  2. If groups of people are arriving every 10 minutes, 1000 people / 5 groups of 10 minute time intervals = 200 people arriving every 10 minutes.
3. Elevator Behavior:
  1. Max Time for Elevator Ride: The max time for a round trip elevator ride from Lobby to Floor 25 is if the elevator was at full capacity and had to stop at every floor. (Someone gets on and someone gets off.)
    1. Total Time Moving Between Floors: 25 floors * 5 seconds of movement per floor = 125 seconds
    2. Total Time for Stop on Floors: 25 Floors * 15 seconds of wait per floor = 375 seconds
    3. Total Ride Time for Max Ride: 125 seconds + 375 seconds = 500 seconds or 8 1/3 minutes
  2. Number of Elevators Needed:
    1. Best Scenario (No Wait): Let's say 200 people arrive in the building and all want an elevator at the same time. 200 people / 10 people per elevator = 20 elevators
    2. Minimum Elevators (< 10 minutes Wait): We want people to wait no more than 10 minutes for an elevator ride. Let's calculate the minimum elevators we can have that allows people to wait under 10 minutes.
      1. In the worst case scenario, someone is in the Lobby and the elevator makes the max ride time (500 seconds or 8 1/3 minute).
      2. If we had half the elevators in Best Scenario (i.e. 10 elevators) with 200 people showing up during peak hours, 100 people get in the elevator and 100 people wait. Those 100 people waiting in the lobby wait 8 1/3 minute at most for next elevator to come. We cannot reduce the number of elevators any farther because some of those people would be waiting in the Lobby would wait double the max elevator ride time.
      3. For example, if we had 9 elevators and 200 people showed up, 90 people (9 elevators * 10 people per elevator) ride. 8 1/3 minute goes by. The next 90 people get in the elevator, but there are 20 people (assuming everyone arrived at the exact same time) who would wait 16 2/3 minute (8 1/3 minute * 2) at max if all elevators were making max elevator ride times.
SUMMARY: Best case scenario to deal with peak hours is to have 20 elevators. At minimum, we need 10 elevators to ensure that people are waiting no more than 10 minutes for an elevator.
ASSUMPTIONS:
1. Elevators are not held or do not jam during a trip.
2. Most likely, elevators are not making the max stops every trip; however, the answer is calculated assuming worst case scenario so no one waits more than 10 minutes.

KN · Answer 8 · 2020-07-12T10:48:29+0000

Lets assume there are 1200 employees in the company.

Also there are 12 floors and 100 employees in each floor.

Now, the elevator will have maximum traffic in Morning and Evening Hours.

Lets assume that all employees come from 9 AM to 11 AM and all leave from 6 PM to 8 PM

Thus the elevator has to handle maximum traffic in 2 hours.

Now, solving for that maximum traffic.

2 hours= 1200 employees

1 hours= 600 employees

1 min= 10 employees

Thus about 10 employees come to the elevaror arena every minute.

Now, lets turn to one elevator.

Carrying capacity of 1 elevator= 10

In the average case, the elevator stops in 5 floors.

Lets calculate the total time of 1 elevator's round trip.

Per Floor stoppage= 15 sec

5 Floors stoppage= 75 sec

Ground Floor stoppage time = 30 sec

Going Up( other than stopping)= 30 sec

Coming Down( other than stopping)= 30 sec

Total= 165 sec= 3 minutes

So every 3 minutes, an elevator completes a round trip.

lets have the average waiting time as 1 minute.

In 1 minute, we have 10 employees waiting.

Every minute, we have to transport 10 employees.

Every 3 minutes, we have to transport= 30 employees

Number of elevators required= 30/One elevator capacity= 30/10=3 elevators