How many elevators are needed in a mall?

Do we have any information on the size of the mall? àYou can assume

Can you share any information on the location of the mall? à You can assume (asked this because malls in the heart of the city will likely see more footfalls than the malls on the city outskirts)

Is there any specification on the number of passengers the elevators can accommodate at a time? à You can make appropriate assumptions

Number of elevators needed in a mall = No. of people coming into a mall in a specific time-period (A) /No. of people that can be transported by 1 elevator within that time-period (B)

Considering the city of Bangalore to estimate the number of elevators needed in a mall.

Let’s start with the estimation:

A mall should have sufficient elevators to serve people at times of highest rush which are in the evenings of Friday-Saturday.  

There are around 25 malls in the city of Bangalore. For simplicity, assuming all the malls are of similar size and are uniformly distributed across the city.

The area of Bangalore is ~ 800 sq.km and population of Bangalore is ~ 9M.

Area served by 1 mall = 800 sq.km/25 = 160/5 = 32 sq.km.

Assuming uniform distribution of population across Bangalore,

800 sq.km accommodates 9M folks

Therefore, 32 sq.km will accommodate 9M*32/800 = 9M*4/100 = 0.36M

So, 1 mall serves around 0.36M people.

People generally in the age group of 0-70 years go out for entertainment (children are accompanied by the parents and older folks are accompanied by their grown-up children). Assuming life expectancy of 80 years of age and assuming there is uniform distribution of the 3.6M population across the age group of 0-80 years,

People falling in the age group of 0-70 years = 0.36M*7/8 = 0.045*7 = 0.315M ~ 0.32M

On weekend evenings, these people go out for dining, to each other’s houses, for shopping, for watching movies, for entertainment in game zones and so on.

For the latter 3, people mostly visit malls.

Let’s say 30% of the folks remain at home, 30% go to each other’s places or for dining or shopping in standalone shops and 40% visit the malls.

People visiting the mall = 40% of 0.32M = 0.4*0.32M = 0.128M

These people visit mainly in the time-period of 4pm-9pm or within 5 hours (300 minutes)

Within 300 minutes, 0.128M or 128000 people visit a particular mall.

Let’s assume a mall consists of 5 floors of shops and 3 floors of parking space.

Each floor height in a mall ~ 20ft.

Total distance to be travelled by an elevator from bottom to top and back to ground floor = 2*5 floors*20ft = 200ft.

1 foot ~ 0.3m

So, 200ft = 0.3*200 = 60m

Average speed of elevator ~ 0.5m/sec and let’s assume the elevator waits for around 10 seconds at each floor for people to get in and get out of the elevator

Time taken by an elevator to travel from bottom to top floor and back to ground floor = Total distance to be travelled/Speed of elevator + Wait time at each floor * No. of floors - 1

= 60m/0.5m/sec + 10sec*4*2= 120sec + 80 sec = 200sec ~ 3.2 minutes or 3 minutes.

Malls generally have separate elevators for to and from between parking space floors and ground floor of the mall. Malls also have escalators for people to move from 1 floor to another.

I am considering that the 128000 people have come to at the ground floor of the mall and they need to go to the other mall floors having shops.

Lets assume 50% of the 128000 people use the elevators and the other 50% use the escalators.

So, people to be transported by elevator = 50% of 128000 = 128000/2 = 64000.

Let’s consider an elevator in a mall can accommodate around 30 people at a time as malls don’t want shoppers to spend more time in escalators.

As we have estimated above, 64000 people want to use the elevators within 5 hours or 300 minutes.

People coming into the mall and use the elevator within 3 minutes = 3*64000/300 = 640 0r 600.

Within 3 minutes, 30 people can be transported in 1 elevator.

Number of elevators required = 600/30 = 20.

20 seems to be higher since we generally see 5-6 elevators in a mall.

I feel that the 40% of 0.32M assumed above to visit the mall is quite high. Assuming it to be 20%,

People going to the mall within the 5 hours’ time window = 0.2*0.32M = 0.064M or 64000.

People preferring to use elevators = 50% of 64000 = 32000.

People coming into the mall and prefer to use the elevator within 3 minutes = 3*32000/300 = 320 or 300

Then, the number of elevators required = 300/30 = 10 which seems quite reasonable.