Supermarket Checkout Challenge
We’ve all been there. You’re in your local supermarket, there’s a choice of queues to join at the cashiers - which do you go for? Does it always seem like the other queue is going faster? Too bad, I’m not dealing with that today.
Given the amount of time the average British person spends in queues, I had plenty of time to come up with the best strategy when it comes to getting out of the supermarket as quickly as possible. It all came about because of those “express” checkouts. I wondered: are they really faster?
Consider the fact that there are two parts that make up the total time required to pass through a checkout - scanning the items, and paying for them. The more items you have, the longer the first part will take. However, paying for 100 items takes no longer than paying for 10. So we might describe a formula for queue time like this:
Queueing time = (number of items * X) + Y
Where X is the amount of time it takes to scan one item (let’s say, 2 seconds), and Y is the amount of time it takes to pay (say, 30 seconds).
Y is always the same (more or less - I’m choosing to ignore those prats that still insist on paying by cheque) but the other half of the equation is variable. So whether there’s one person with 100 items, or 10 people with 10 items each, it will take the bored-looking cashier the same amount of time to scan all the items. However, the “express” queue will take a lot longer! See for yourself:
( 100 items * 2s ) + ( 1 paying customer * 30s ) = 230 seconds
( 100 items * 2s ) + ( 10 paying customers * 30s ) = 500 seconds
Now, I know I’ve confused you a little. One trolley load is quicker than 10 baskets? You bet your sweet ass it is. This poses another question - why call them express queues? Look at it from the supermarkets point of view - how many customers can each cashier clear in an hour? Given there’s 3,600 seconds in an hour:
customers per hour = 3,600 ÷ time for each customer
regular checkout: 3,600 ÷ 230 = 15.7
express checkout: 3,600 ÷ 500 = 7.2
Initially it looks like the express lane is slower but remember that 500 seconds is the time take for 10 customers, so this till churns through 72 customers an hour, compared to a paltry 15.7 per hour for the regular checkout. Whoa - I thought we’d already decided that express queues were slower - what’s going on? What we have here is a difference in perspective. While the supermarket is concerned with how many customers per hour it can process, you are only concerned with how long it takes you to get through the queue. So remember kids, look at the number of items in the queue, not the number of people. That’s the key to sailing through the checkouts.
* if this post gets enough praise, I might take the time to draw some little diagrams. Which will make it accessible to those plebs at Digg. In the meantime, feel free to critique my maths.
13 comments January 4th, 2008
