Number of cash registers is still an incomplete description. We should ask what wait time if acceptable. We should also find out if we are talking about a mix of self checkout or employee managed cash register. What about cash registers for customer with less than 10 items?

If the plan is to only hire 5 people for cash register, then we are locked with a maximum of 5 cash registers. Here also, we are assuming that there will be 5 people available for the entire day. These points are worth clarifying upfront.

There are different cash register needs based on time/day of week.
> Weekends
> Holidays
> Weekdays
> Morning
> Evenings

Let’s start by mapping out a user’s journey in case of a employee managed cash register.

> User waits in line
> User arrives at employee managed cash register
> User unloads items
> Employee/User scans items
> User pays for items
> User completes checkout

A single cash register can do the job.
It would just make the customers wait longer and longer.

So if we have 2 customers in checkout line at any given time.
And each of them take 5 minutes to complete their transaction. Then with one cash register you could say that if they both arrived at the same time, then the wait would be roughly 5 mins before they are served, and we have solved our problem.

This means that we only need to know how many people will arrive in checkout at the same time. And, we simply put half of those in terms of cash registers.

So, if 20 people arrive at the same time, then we need 10 cash registers.
That’s it.

A visit to a Walmart store with comparable neighborhood would give some guidance.
We should also visit some nearby grocery stores to get some data to help with the analysis.

Let’s say we get the following numbers.
> Nearby Walmart, 50 miles away, wait time = 5 to 20 mins, 20 customers at the same time, 10 checkout registers.
> This Walmart neighborhood serves 20,000 people in their 5 mile circular neighborhood.
> People hate the wait time
> People have started to go to other grocery stores.
> Customer satisfaction is very low.

Now let’s build our model a bit with a goal of reducing the wait time.
> In our immediate 5 mile radius, we will be serving about 20,000 people as well.
> By looking at the traffic for the other Walmart & other stores, we could see that on average we have 20 customers in checkout at any given time. So putting 10 cash registers, would give each customer a 5 minute delay, which would seem to work.
> However, this solution does not account for the fact that there will be peak traffic which is when wait time could double.
> Therefore for peak traffic, when we have 40 customers in checkout, we should open up additional cash registers. So, we should need 20 cash registers.

10 is our min.
20 is our max.

Now 20 does seem a bit high. If you visit at Walmart, they never have more than 8-10 employee managed checkout stores.

Now we think again about measuring how much time it takes one person to go thru checkout if they have less than 10 items vs those that have more than 10 items.

Let’s put some number assumptions here.
If a buyer has less than 10 items, then they would take about 2.5 minutes.
For greater than 10 items, they take about 5 minutes.

Now, let’s break down the number of active people in our line by saying that we have 20 that have greater than 10 items. And, another 20 that have more than 20 items.

For the people that have greater than 10 items, we still have the same number of registers = 10.

For people that have less than 10 items, we would have less number of registers = 5.

So, now we are down to 15.

Here is how I would estimate it.

To estimate number of cash registers needed, we will need to design for the busiest time of the week in Walmart. From my experience, the busiest time is around Saturday and Sunday afternoon.

Let’s assume all check outs are 3 minutes long, Walmart is ok with max of 15 minutes wait time, and each cash register’s check out starts same as other cash register’s check out.

Now here is my main formula:

(time it takes to check out) x (rate at which shopping groups are coming to wait in line) = (total number of new shopping groups joining the waiting line during check out)

We know time it takes to check out is 180 seconds
I’ve noticed that people come to WAlMart at about 1 person per second during peak times (sat afternoon) so let’s say that rate at which people are coming during peak hours is 1 person per second or 0.5 shopper group per second (assuming each shopping group comprises of 2 people)

Based on above, total number of shopping groups joining the waiting line during one check out period = 180 seconds x 0.5 shopping groups = 90 shopping groups

And total number of shopping groups waiting in line = number of cash registers x total number of people waiting in each line

If we want the max wait time in each cash register be 15 minutes (900 seconds) and each check out takes 3 minutes (180 seconds), there can be a maximum of 900 seconds / 180 seconds = 5 shopping groups in front of each shopping group by the end of a check out. So, total number of shopping groups waiting in each line is 5

To avoid increasing the delay time, we want the number of people joining the waiting times be equal to number of people leaving the waiting times. In other words, max total number of shopping groups in rush hour remains to be 90 shopping groups

This helps us calculate total number of cash registers as

number of cash registers = max number of shopping groups in line / total number of shopping groups waiting in each line

equals to 90 / 5 = 18 cash registers

I would start answering this Google estimation interview question by asking the following:
1. Where are we planning to open Walmart store? Urban or Rural Area? If Urban, then Which City?
a. Assuming Urban and say City of Toronto
Answer:-
1. Population of Canada is 30M.
2. As the two most populous provinces are Ontario and British Columbia, we can assume that each have population of around 30% ~ 10M.
3. Out of this 10M Ontario Population, most would be concentrated in and around GTA, so assuming GTA Population of 70% ~ 7M
4. GTA has 5 regions, Dividing the population equally, indicates Toronto’s population will be around ~1.5 M
5. As per world population, around 70% of people are between age of 15 and 65, 14% are above 65 and 16% below 15. Keeping same percentage, we can assume that ~1M people are of shopping age or would go for shopping alone.
6. Following are the big retailers or competitors of Walmart –
a. Loblaws
b. Canadian Tire
c. Whole Foods
d. Freshco
e. Costco
f. Longos etc.
7. Assuming a consumer has 10 different choices, we can have this small table of % split (Need to provide reasoning for the split, i.e. Loblaws, Whole Foods are expensive compared to Walmart, Costco needs Membership etc)
Loblaws 10%
Freshco 20%
Costco 15%
Whole Foods 10%
Longos 15%
Walmart 20%
Others 10%

8. So, Walmart would be serving around 20% or 200,000 people in Toronto.
9. Generally 1 region has around 3-4 major cities, and we can assume that 1 city will have around 2-3 Walmart.
10. Assuming each Walmart supports equal distribution of customers, 1 walmart will be supporting around 70,000 – 100,000 customers.
11. Out of this 100,000 customers, we can assume that people go to Walmart atleast once every 2 week, so that is 50,000 customers shopping at Walmart at any given week. (* I would challenge myself on this)
12. Most of these customers will be shopping after office hours or during weekends. Assuming 70% shop on weekend and distribution is uniform every week, so we have around 35% shopping on a Saturday or Sunday.
13. So, around 20,000 Customers will be shopping on Saturday on Sunday.
14. Walmart stays open from 7:00 AM till 11:00 PM and most of the crowd will be coming during 11:00 AM (because people wake up late on weekends) to 6:00 PM (People want to spend evenings at club or movies or entertaining themselves) so, we can assume that 60% of 20,000 customers come during these hours, i.e. 12,000 customers between 11:00 AM – 6:00 PM
15. Doing a uniform distribution of hours, we can say that 1500 customers per hour
16. Let’s assume each person spends half hour at Walmart, so that is 600 people going to cash counter every half hour or ~ 20 people per minute.
17. 1 cash counter takes approx. 2 min to bill a customer, so applying little’s law, we will have a queue of 40 customers.
18. If 10 customers per queue is acceptable, we should have 4 operating cash terminals in Walmart.