If you are opening a new Walmart store, how would you decide how many cash register is needed for the store?

Put yourself in the worst scenario: peak time. Think about how many people are you expecting to serve, how many minutes per person are needed and what is an acceptable waiting time in the line. Think also about the percentage of customers that use automated cash registers.

Best,
Antonello

Very interesting question, and one that could well be a consulting project on its own (in fact I did that for a bank’s agencies). There are multiple ways of solving it, but there’s one unavoidable truth: trade-off between overcapacity & queueing time, which affects negatively customers’ shopping experience.

Assuming a normal distribution of customers throughout the day, if you draw a vertical line in the middle of it, what is above the curve on the left is overcapacity and the tail on the right represents the queued customers.

Now, let’s say on average we have 50 customers and the st. deviation is 20, the CX starts to decrease after 10min and 3min per customer attended.

So, if Walmart wants to have a positive CX in 83% of times (up until +1 st. dev), it will need (50+20)/(8/3+1), where 1 is the customer being attended. Thus, you end up ~19 checkouts.

If you replace 8min by 10min, you get 16, so it is a negative hyperbolic curve.

Additionally, you have to consider the following factors that affect this answer:

• Distribution of customers over the days – in real life I am expecting a non-symmetrical distribution function
• Profile of customers – are they digital-savvy and can do a DYI? What about Amazon’s Go tech?
• What is the time after which the shopping exp will deteriorate?
• How much time do tellers take to process the items per customer?
• What is the opportunity cost of dedicating area to checkouts?
• What is the propensity to buy stuff per minute spent queueing?

Cheers,

Francisco

Hello Piyush,

First of all you have to estimate the volume of customers that you have per day. In order to be safe and don't lose any potential revenues, I would choose a weekend of "high season" in the peak hours. The process is the folloqing:

• Calculate the number of customers in the peak hour
• Calculate how much time a customer could wait without affecting his willness to buy from us (queue + time to pay)
• # of cash registers: volume of customer during peak hour * time per customers / 60

Best,
Luca

Hi,

You need to assume:

• Output rate in peak hour (total people per minute exiting the store)
• Time to serve one person in peak hour at the register

Output rate x time to serve one person = total number of people at any given moment

Now you need to assume what's the desired size of the queue:

• Let's say your total number of people waiting is 50
• And you don't want to have more than 10 people in a queue
• Than you need 50 / 10 = 5 registers

Best