## What I Would Do With This: Groceries

[following up from here]

All other things being equal, which lane is the fastest?

This problem has obsessed me for years. It’s my DaVinci code. It’s my love for math, for mathematical reasoning, for the relentless deconstruction of something that seems simply intuitive into data, models, and computation.

This is also my love for WCYDWT media.

Perfunctory Pitch For WCYDWT Math Instruction

You have here a simple question that anyone can access. Doesn’t matter that you’ve never run a linear regression in your life. If you’ve ever shopped for groceries, if you’ve ever stood in line with a candy bar, a soda bottle, and a matinee starting across town in ten minutes, you have an opinion here. And I can use that.

The question is simple and so is the answer but the justification is extremely complicated, which is exactly how I’d like to balance the learning experience. We will argue. There are easily a dozen variables affecting the line speed that have nothing to do with the number of customers in each line or the number of items in their baskets. You could assign some field research here. I spent ninety minutes last week just watching, counting, and timing groceries as they slid across a scanner.

The question is also scalable. We can remix this single image into endlessly difficult scenarios (or easier scenarios) that will push a student’s hypothesis to the crumbling point and back again.

A (Broad) Lesson Plan

Gather the data. Or supply the data. Graph the data. Develop a model. Test the model. Talk about the effect of outliers. Assign weight to outlying variables.

I threw some questions on a worksheet five years ago, fairly predictable stuff like “what does it mean when a point is above the line of best fit?” At this point, though, I’m hesitant to constrain the activity even that lightly. I’d almost rather pick a fight with a student who finished early and let the rising pitch of that conversation fold in a few more learners.

Other Remarks

1. Check is slower than credit which is slower than cash. Students are sometimes surprised that cash is faster than credit. From my observations, the fastest cash transaction will outpace the fastest credit transaction by a wide margin but there is also huge variance in credit transactions. I mean, some people have absolutely no idea what they are doing with that thing. The same can’t really be said of cash.
2. The store manager hooked up some checkout data, which was awesome. At first, he declined my request for numbers while agreeing to let me float around the store. Then he brought back the mother lode: checkout scanner data from a single six-hour shift. The data was aggregated in a few unhelpful ways but no way do I mind this particular excerpt, which gives away the store:
3. The y-intercept is non-zero! This never fails to trip my fuses. It should take you zero seconds to purchase zero items but you can’t ignore the fixed time cost of the pleasantries (“Hi. How are you doing? Do you need any help out?”) and the transaction itself.
4. The express lane isn’t faster. The manager backed me up on this one. You attract more people holding fewer total items, but as the data shows above, when you add one person to the line, you’re adding 48 extra seconds to the line length (that’s “tender time” added to “other time”) without even considering the items in her cart. Meanwhile, an extra item only costs you an extra 2.8 seconds. Therefore, you’d rather add 17 more items to the line than one extra person! I can’t believe I’m dropping exclamation points in an essay on grocery shopping but that’s how this stuff makes me feel.

Here’s the Photoshop template, which you’re welcome to remix with new numbers or, even better, revamp into something altogether less offensive to the eye.

[BTW: check out this fun snap from Dan Callahan of the Whole Foods staff bulletin board.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.

1. #### Tom Hoffman

September 8, 2009 - 8:59 am -

In 2009, the easiest way for kids to approach this problem should be by writing a computer program. Of course it isn’t for myriad reasons, including kids not having computers handy. Also, it isn’t clear that solving the problem that way is “math.”

2. #### josh g.

September 8, 2009 - 9:30 am -

Nice – the real-world data observation / gathering is a fantastic move. A lot of stores in my area are just recently adding the self-checkout stands; that might be a nice additional hook similar to the express / regular comparison.

Tom: Is programming any better of an option in this case than using Excel? I like coding stuff but I don’t see the advantage here, other than building programming literacy (which is good, but not “easier”).

3. #### David P

September 8, 2009 - 11:11 am -

I was going through my own head on a list of variables I either do or could use when choosing a line at the store and came up with something else to consider: visible vs. invisible variables.

Some visible/obvious variables: estimated # of items, type of items, presence of bagger(s), checker or customer on phone, chatty checker

Some invisible/non-obvious variables: payment type, actual # of items, chatty customer, coupon use, purchase of other items at checkout (cigarettes, lotto tickets, etc.)

While the invisible ones certainly matter, it would be hard to make your initial decision based on those directly (I suppose you could do some sort of probability with them, though).

4. #### Mr. K.

September 8, 2009 - 8:06 pm -

I suspect it’s mainly because, as computers become more prevalent, the need to actually program them has declined.

My guess is that the number of “computer teachers” in high school who could, say, program a factorial routine in the language of their choice, is less than 5%.

It still wouldn’t answer the questions of noisy variables and which simplifying assumptions are permissible and which end up skewing your model.

It might, however, make people appreciate just how tough making a computer model is. And then you’d find that if you want to get good at it, you have to learn all of that math that you were trying to avoid in the first place in order to be able to validate the model.

(Sorry for the poke at 2.0 tangent – I’ve had it building for a while).

5. #### Andy

September 9, 2009 - 5:58 am -

Credit is way faster than cash. I have not idea where you get your idea that it isn’t. In most stores you can swipe your card while the items are still being rung up, thus it only takes about 5 seconds extra to print a receipt.

6. #### David P

September 9, 2009 - 6:26 am -

Andy, you must be a “master” card user (pun intended). While that’s true for some people, many people don’t do it until afterwards and then when it makes you input your zip code and/or sign, they take forever reading the screen and trying to figure out what to do. If it’s a paper receipt to sign, then you take extra time finding a pen and stuff, too.

I agree that a card SHOULD be faster and often is, but doesn’t always seem to be.

7. #### shaun

September 9, 2009 - 6:53 am -

I confess. I profile. Older people tend to write checks = takes forever. If I see an older person in the front, I move on for faster processing.

8. #### Joe

September 9, 2009 - 7:13 am -

I profile age of cashier and age/sex of customers. Avoid a retired F cashier and retired F customer. Avoid all coupon holders. Cash is faster except for retired customers particularly penny searching retired Fs.

9. #### Kalieris

September 9, 2009 - 8:07 am -

See, this is why I love the one grocery store in my area that has little hand-held scanners you check out with your savings card and use to scan groceries as you buy them. I bag things as I shop, after I scan them, so that by the time I roll up to the check stand I just have to scan the “order complete” barcode, pay and leave. The shortened time is impacted by things like buying age-restricted items like beer, or buying cigarettes (which requires going to a separate cashier), but if you typically don’t buy those things it’s actually quicker than paying for one item at a cashier (no chit-chat).

Of course, this probably requires a look at revenue lost due to theft, impact on need for cashiers/baggers, etc. But purely as an additional option for getting done more quickly with shopping, it rocks.

10. #### M

September 9, 2009 - 8:46 am -

I am no expert, but this is the kind of problems given to us for queuing theory tutorials.

A simplified version, to be sure, with fewer variables (and I wouldn’t know how to go about including them), but I’m sure there’s a way to do it.

(I took an Operational Research class last year.)

11. #### Chris C.

September 9, 2009 - 10:10 am -

I agree with many of David P’s observations. I avoid a line with one or more elderly women; they often use checks and/or are chatty. Ditto for moms with kids.

The store at which I usually shop has self-checkout lanes, but the software is so kludgy, and the units are so old, that they can take much longer than the cashier lane when the reader doesn’t recognize your items, or refuses to recognize that I might want two of the same item (it often kicks the second one back).

I also know which cashiers are slow and/or prone to chattiness, and avoid them. Mostly, since it is on my way home, I tend to stop there 3 to 4 times per week and get a smaller number of items, as that has proven quicker than waiting in the regular lanes with a cart-load. It might only be the store I shop at, however.

12. #### rvman

September 9, 2009 - 10:25 am -

> Therefore, you’d rather add 17 more items to the line
> than one extra person!

I wondered why the Wal-Mart express line is “20 items or fewer,” which is a lot more items than most places I know of. I believe we are walking in the footsteps of some data miner in Bentonville.

13. #### John Thacker

September 9, 2009 - 10:43 am -

I avoid a line with one or more elderly women; they often use checks and/or are chatty. Ditto for moms with kids.

Ah. But, in the South at least, if you do that you’ll miss out on all the nice ladies who say, “Oh, you only have one or two items, please go ahead of me.”

14. #### Sigivald

September 9, 2009 - 12:34 pm -

In skilled hands, debit should be the fastest of all, since the entire transaction can be completed before ringing is over.

In the real world, of course, some people don’t even start until the items are done ringing up.

15. #### Dave

September 9, 2009 - 12:45 pm -

This reminds me of my Operations Management classes in college. There’s lots of fun real world math to be had there…

For example, you may notice that you are almost 100% likely to wait in line at Walmart, but that at other stores there will sometimes be an open cashier and you can checkout immediately.

That’s because Walmart’s view is that any time that a cashier is not actively checking out a customer is time that the store is paying them to do nothing. If you are trying to optimize for lowest cost, you want to schedule cashiers such that every cashier is always working all the time they’re on the clock.

You could fold that back in to your example. If you’re running the store, how many cashiers should you schedule? What if I provide a function that takes wait time as a parameter and gives customer happiness as an output?

And self-check! What if I can assign one cashier to watch 4 people check themselves out?

16. #### David

September 9, 2009 - 5:47 pm -

I worked at a grocery store for 3 years and totally have to agree. I know the average is about 20 items per minute, and 50 seconds to pay is fair.

17. #### emily

September 9, 2009 - 8:05 pm -

this, too, has plagued me for years. i pride myself on 95% accuracy on checkout lanes, cars at a red light and bank drive through lines. here are the simple methods i use.
at the grocery store: is the cashier old as shit? are the people in front of me old as shit? simple as that. young people move faster, they have things to do.
at red lights: is it a small car with bumper stickers all over it? is it a mini truck? was the car made from approximately 1990-2004? is the car yellow? all of the above scenarios will most likely go faster. is it a huge truck, van or suv (or a bus, but you will never catch me behind a bus)? are there children visible in the back seat? it the person old as shit? was the car made before 1990 or after 2004? are there jesus fish on the car? yeah, those people are going to go slow.
in the bank line: screw everyone and go in the commercial lane that no one is in. they wont make you go back around, they wont even say a word.

there you go guys. i hope you get to wherever you need to be 45 seconds faster.

<3
-emily

18. #### T J Sawyer

September 9, 2009 - 8:44 pm -

Rule # 1: Avoid any line with a male cashier. Slow as ‘lasses in January.

Rule # 2: Look out for strange produce in the baskets in front of you. “What is this?” Counts double if the cashier is young and x4 if Rule #1 is not used!

Rule #3: Look out for the old lady in line. As other commenters have mentioned, she won’t even start to look for the damn checkbook until every item is rung.

19. #### Tim S

September 10, 2009 - 2:18 am -

Would be curious which store in your said grocery store chain has the most boozers, and which has the most teetotalers. You could make a months worth of lessons just using the booze sales data.

20. #### J Morton

September 10, 2009 - 3:54 am -

FYI – the credit card machines at Target stores (including those with supermarkets) are so fast that, on average, it takes 2 seconds for the entire transaction, from swipe to receipt print. Only exact change cash transactions come close to competing.

21. #### Peter

September 10, 2009 - 5:41 am -

I’ve always shopped at night for the last 15 years. Rarely have to wait at all. Sometimes it’s a bit of a struggle with tiredness etc. but totally worth it.

22. #### Jim B.

September 10, 2009 - 6:09 am -

Interesting, and generally correct, however, with respect to:
“It should take you zero seconds to purchase zero items but you can’t ignore the fixed time cost of the pleasantries (“Hi. How are you doing? Do you need any help out?”) and the transaction itself.”
I think you are ignoring the fact that the relationship is discontinuous at zero items, and certainly non-differentiable. Thinking of the time it takes to check out minus-one items, i.e. return one item, there is probably an entirely different relationship.

23. #### Elliott

September 10, 2009 - 10:57 am -

So, each person in line is worth 17 items, in seconds?

So for a quick assay of the line situation, I should add around 17 (we’ll round to 20) items to the carts of everyone?

6 people in line with a couple items = 1 person in line with 100 items. That’s like a giant cart full.

24. #### bitpunk

September 10, 2009 - 12:07 pm -

There’s one underlying hypothesis you haven’t tested: linearity itself. What if there are increasing returns to scale?

Running your regression, I get R-squared = 0.45 and AIC =389.8 (log-likelihood of the null = -203.7, whereas the model gets -192.88).

Running a similar regression of the logarithm of total time over number of items, I get a R-squared = 0.54, AIC = 52.9 (log-likelihood of the null and the model respectively -39.54 and -24.45).

Running a nice regression controlling for bagger, checker, payment method *and* an interaction between payment method and number of items (why? larger transactions are slower with cash, relatively), we get a nice model with R-squared = 0.81, AIC =35.9, log-likelihood of the null and the model being respectively -38.5 and -8.9). As I predicted, the interaction term of cash payment with number of items is significantly negative (t=-4.25), while the cash payment dummy itself is dubious.

Here is the Stata output from the “nice regression”:

http://imgur.com/vzTpU.png

25. #### An actuary

September 10, 2009 - 1:40 pm -

Its not that it takes zero time to buy zero items. That is a mistaken interpretation of the results. What the nonzero intercept is really saying is this: Given that items will be purchased, there is an amount of time (the intercept) spent during the transaction that is independant of the number of items being purchased.

26. #### Stacy

September 10, 2009 - 6:48 pm -

More factors to consider:

Whether or not the customers in line have fists full of coupons. Those are scanned individually, just like each food item is. This doesn’t even include the time spent by the cashier reading the coupons for information and explaining why some coupons cannot be accepted (expired, wrong size, wrong brand, only applies if you buy two of the item, etc.)

Cash sales are frequently slow and I disagree about the low variability in cash transactions. Customers paying with credit cards do not keep others waiting to mine through overstuffed handbags in search of \$0.23 to avoid getting \$9.77 change.

Express lines often have no one bagging at the end of the belt. It can be faster to go to a regular line if that line has baggers, regardless of scanning or payment efficiencies

While the number of items purchased may correlate with the time taken to bag them, at some point the efficiency drops a great deal. If someone purchases a completely stuffed cart of grocery items, the bagger will not be able to keep up with the cashier. The amount of planning (heavy cans at the bottom, potato chips on top) for very large number of items makes the bagging process less efficient. Same applies to arranging the bags in the cart. At some point, the efficiency of scanning and payment method becomes irrelevant because the rate-limiting step is the bagging.

And don’t get me started on cashiers having to leave the register to retrieve cigarettes from a locked case behind the Customer Service counter!

27. #### Sheldon (Marketing Consultant, Tauranga)

September 10, 2009 - 7:54 pm -

Blah, blah, blah. Which line do I choose Dan? What formula should I memorise so I can make these decisions?

28. #### Chris R

September 11, 2009 - 8:12 pm -

This is freaking awesome. I don’t even teach math… somehow I will get his into a science lesson though.

29. #### SteveH

September 12, 2009 - 5:28 am -

This is all very “mathy”, but how does it fit into the big curriculum picture. Math is not all about collecting data and graphing. Sometimes mastery of skills is required. Sometimes m=n. What about the case where you have more variables than equations? What happens when guess and check is just not enough? Math is not just a top-down learning process. In the real world, it’s all about skills. I once had an employee who wanted to “discover” a solution. I told him to go read the technical literature.

30. #### David B. Cohen

September 12, 2009 - 7:46 am -

Hi Dan – just happened to turn on KPIX-5 News around 8:30 this morning, just to set my DVR to record some US Open Tennis today, and boom – there you were!

They sure made a story for people who are interested in grocery lines – I would have liked it even more if it were somewhat about how this relates to teaching! But the media make the story they want. Still, congratulations.

31. #### Vangel

September 12, 2009 - 8:06 pm -

A more interesting study would be to look at queuing times variations based on the number of cashiers. I looked at a paper once that showed that when there are just enough cashiers to handle the line-ups the variations are very large. There are times when there is hardly anyone waiting but others when the line-ups are very large.

32. #### Dave

September 12, 2009 - 9:07 pm -

The monkey-wrench in this is that some chains put the worst cashiers on the ‘quick’ lane, to maximize the better cashier’s work on the larger ‘regular’ registers.

33. #### spf

September 13, 2009 - 7:56 am -

In the graph you have numbers with five significant digits. Surely that’s about four too many?

y = 3x + 40

34. #### Bob

September 13, 2009 - 9:22 pm -

@45 Dunno Shel, maybe you ought to crib off the smart kids who sit near you. It might explain why you’re a marketing consultant. And an ass.

35. #### Marcus

September 14, 2009 - 12:27 am -

I was obsessed with this, too, and I came to the very same conclusions: cash is much faster than credit card, there’s a base cost per customer, express lines and self-checkout lanes don’t work, etc. It takes a little practice, but it is entirely possible to come up with a reasonable relative estimate (based on the combination of shopping cart content and customer) and pick the fastest line.

What you completely ignored however are the “catastrophic” checkout events that are unpredictable and can completely throw off your calculations:
* a cash customer drops his change; picks it up, is a dime short, and has to write a check after all
* the system doesn’t accept a credit card on first and second try
* a couple starts a fight over something
* (my favorite) there’s no sticker on a bag of apples and the cashier has to run across the store to weigh the contents again.

Nothing is more frustrating than watching the other lines advance much faster that the one that _should_ have been the fastest (which is the one you’re in). Made me really unhappy!

So I came up with a new strategy:I now always pick the line with the prettiest cashier. I still watch the other lines, but since I’m no longer part of the “race” I can at least enjoy the wait.

36. #### charbour

September 14, 2009 - 6:52 am -

60 posts, and no one has posted the obvious solution: Which line is fastest? The one I’m not in.

37. #### Sue

September 14, 2009 - 7:48 pm -

I was at the grocery store today, bought two items, express lane had two people with not so many items, the other lane had one person with kind of a lot. Last week I would have chosen that express lane. Today I chose the other. It was a win for algebra. ;^)

38. #### JJ

September 14, 2009 - 8:19 pm -

2 things. First, if line length is appx equal you should try to get in an edge lane (ie one with only one other lane next to it rather than two). This is so that the chances of you perceiving that you’ve made the wrong decision by having the line next to you go much faster is halved (all other things being equal).

Second, Australian supermarkets have a few factors which really help speed things. No cheques anywhere (good thing), pre-purchase swiping of card (you swipe card, select account type and transaction, including cash out amount if any and then wait to input PIN number) and we now have PINs on credit cards so you don’t have to sign for them which further speeds things up. Plus, no pennies!

39. #### arieh zimmerman

September 15, 2009 - 3:33 am -

Sorry folks, even those in the know can’t see the forest for the trees…The slowest line will always be the one you chose.

40. #### Andrew

September 16, 2009 - 4:23 pm -

I avoid the woman clutching her purse, who won’t even think of opening it until the total is given, then digs around for a cheque book and starts to fill it in. No thought of getting it out adn filling in all the details including date and payee, and certainly no conception of holding up the people behind.

41. #### Vincent Clement

September 22, 2009 - 10:00 pm -

Woah, wait one minute there. I see one set of data. How can you state that the “express lane isn’t faster”. You need two sets of data to make that statement: one for the express lane and one for the regular lanes.

Based on the Customer/Hour number, each customer spent an average 1.56 minutes in the express lane (I’m assuming the data are for the express lane – it isn’t explicitly stated). How does that compare to a non-express lane over the same 6 hour shift?

42. #### Lauren F.

September 23, 2009 - 5:03 am -

I think the bagging situation should be factored in, as well–it’s a lot faster when the cashier can just ring up the items, without having to stop and bag them too. Anyone have a strategy for arranging your items on the belt so that they can just be popped into a bag? I try to do this but I don’t always get it right.

43. #### F.Baube

September 25, 2009 - 11:52 pm -

If more checkout staff could chat and scan at the same time, that would be great. But there seems to be a cultural bias against it, or else a lack of ability.

44. #### Whatsup

September 29, 2009 - 1:55 pm -

I can’t wait to see you waste another Saturday of your life collecting data on self-checkouts. You should like write a book or something. I’ve been waiting for a resolution all my life, and here it is! Clap your hands, people! This guy’s a nerd!

45. #### BSR

September 29, 2009 - 5:25 pm -

In my local store, I noticed that the row of checkout clerks is bisected by the manager’s or head cashier’s desk. This person is supposed to add cashiers when the lines get too long.

Usually the checkout stations immediately adjacent to the manager are kept empty, until they add a cashier for a few minutes to deal with a rush.

If all the lines are long, I usually pick one next to the empty station. When the manager opens up that extra line, I’m right there, ready to hop over and I’m usually 1st or 2nd in that line.

Lots of good advice here — get to know your store, too. You’ll figure out quickly which clerks to avoid. My least favorite at a previous store was a guy who hit on every female who went through the line, and threw bad jokes at every male. He seemed to work quickly, but his lines always moved slowly.

46. #### pete in Welly

September 30, 2009 - 3:55 am -

#45 Sheldon – it was in your fair city near Tauranga ( New World at the Mount ) I pointed out the truth to the teenage daughters of my g/f – “Always queue behind the single guys because they don’t muck around”
Works for me

47. #### bob parker

September 30, 2009 - 11:34 am -

Credit can’t be slower then cash – Visa told me so. They told me I am a social pariah if I pay in cash.

I trust Visa in all I do.

The bridge they sold me I am told is wonderful.

48. #### Pierce Presley

September 30, 2009 - 1:03 pm -

First off, thank you for crunching the numbers on this. I always wondered what the best strategy for choosing a line was. Of course, with my local Wal-Mart and HEB never seeming to have more than 1 lane per million or so customers open, so this may be moot in my situation.
Second, on the cash vs. credit thing, my favorite instance of cluelessness was an elderly couple valiantly attempting to use the credit card machine. At one point, the woman said, and I quote, “Touch English, because we’re English.” This happened in Arkansas, and if this couple were from England it had to be the small town outside Little Rock. I managed not to question them about their opinion of the royal family, but just barely.

49. #### slowmo

September 30, 2009 - 5:06 pm -

It’s easier to think that if a person carries more than 16 (I rounded the numbers) items, you count her as two people and so forth. then choose the lowest number.

50. #### Erica Pionke

October 8, 2009 - 1:52 pm -

Is this like when you are waiting in line at the porta-potty at a show and you have to factor in the number of men in line versus women in line and figure the men will go faster, so long as noone drops a #2…but that is not gender specific anyway–and just an unpredictable aberration from my calculations. Is it like that? Why is there no quantitative study on porta-potty lines?

51. #### T. Grill

October 9, 2009 - 12:03 am -

I ususally go out with the groceries without paying. A lot faster I can promise!!

Mr T

52. #### Scott

October 10, 2009 - 5:59 am -

My observation is that for some unknown reason management always puts the newest and or least efficient knowlegable peson on the express lane.
Example Lowes and Home Depot puting high school females (yes this is stero typing) on contractor check out. Last week I had one of these so call associates call management to ask what this piece of wood was. it was a full sheet of OSB.

53. #### Sandy

October 10, 2009 - 6:15 am -

Check writers are no slower than credit or cash users if they have their act together and don’t stand there balancing their checkbook before giving the check to the cashier. Which line I get into depends on the cashier, the people in the line: older is slower and a bunch of kids is so annoying I avoid. One cashier where I usually shop is so deliberately slow I avoid her no matter what is going on with the lines. I even avoid going in during her usual shifts.

54. #### E.B. Berman

October 10, 2009 - 11:27 am -

I believe that cash is faster than credit on average. Unless someone is running a scam or adds/changes bills after the tender amount is entered into the machine (this shouldn’t trip people up as badly as it does, but . . .) then cash is clearly the most straightforward. Letting people swipe their own credit cards slows down that process too much. What always slows the credit purchase down for me is all those damn discount membership cards. I go through my whole credit process, I think I’ve paid, then ten seconds after the cashier totals out my groceries they go, “Oh, you’re discount card didn’t read right.” And I always have to say, “I don’t have one; I’m just trying to pay.” And they they push some buttons on their end and tell me, “OK. Do your card again.” I don’t know why I bother.

55. #### emily

October 10, 2009 - 12:19 pm -

I’m a girl and I was a pretty fast cashier, but the boys at my store liked to be competitive with eachother and get the best numbers. So, though some boys are dumb and slow, other’s are extremely fast and efficient just because of their competitive nature.
So I would say to get to know the boys in your store before you avoid them completely..

56. #### Peter

October 10, 2009 - 12:21 pm -

You totally ignored the Peter Principle that no matter what line I’m in, it is always moving slower then the other lines.

57. #### Peter

October 10, 2009 - 2:05 pm -

I read some of the replies, but not all of them, so someone might have already pointed this out in a reply I haven’t read:

The express lane in a grocery store is slower than a regular lane because the express lane never has a second person bagging your groceries while the cashier is scanning them and taking your payment, whereas the regular lines usually have two people working the line. The express lane cashier has to handle your items twice: first to scan them, then to bag them plus handle your payment.

58. #### Joe

October 10, 2009 - 2:20 pm -

When you include all of the variables, we’re talking about a difference of minutes. With that being said, any lost time could be made up by knowing where things are in the store and being able to “shop faster.” Those that get upset by a slow line must have much more valuable time that me. Slow down and enjoy the ride…the world will be there when you are done.

59. #### kelly

October 10, 2009 - 2:54 pm -

use all the science and math you want only to realize the faster line is the one you are not in……..everytime. doesnt take a rocket scientist to know that.

60. #### Howard

October 12, 2009 - 5:21 am -

Our ipm rate is 27, and I’m running at around 20. What slows me down is the WIC and EBT transactions, especially when they must be entered manually. When the check reader won’t read the microcode we enter the routing, aba, check number, and wic id manually, and when the ebt card won’t scan we enter the whole 16 digit id number manually, all on a touch-screen keypad. I tried to get them to post a “No WIC” sign on the express line, but they won’t do it.
I do “chat” with customers while checking them out, but I’m constantly scanning while doing so. About half the time (or more) I don’t have a packer, so that can slow things down a bit.
But I’ve got a lot of customers who would rather wait a couple of minutes longer in my line than go to a “shorter” line, and most of the time I can get them through without anyone dying of old age.
Oh, I’m male, and I’ll be 68 next month.

61. #### heather

October 14, 2009 - 8:54 am -

Elderly women not only tend to write checks, they also have coupons and vigilantly watch the checker’s screen to make sure all their discounts (coupon and in-store) are being accounted for correctly. Unfortunately, many of the stores that offer “membership” discounts tally all of the discounts only after the checker hits “total” – setting off these elderly ladies in a frenzy of horror that they’re being charged 10 cents a pound too much for their hamburger. Also unfortunately, most of the checkers cannot articulate an explanation to the satisfaction of an elderly woman. Management has to be called. Then they write a check and want to stand there for another 3 or 4 minutes complaining about that newfangled technology.

Avoid old ladies at all costs. At least people with small children want to get out of there just as fast (if not faster) as you do.

62. #### Amy

October 15, 2009 - 7:42 am -

Kelly has got it about right. If I’m in a hurry, the whole world manages to get to checkout before me with unpriced items and if I happen to get in a quick line, something I have won’t scan. If you can ask the cashier when they are slowest, and plan to go to the store then. But don’t forget to ask when they restock or you could be running an obstacle course. lol

63. #### alice

October 15, 2009 - 5:58 pm -

Ahh the checkout lines how they anger me.

Having worked at a supermarket for way too long when I was a student I’m pretty convinced that unless you frequent a store and get to know the cashiers that you cannot safely predict how a line will move.

We would have staff moving anything from 7 – 40 items/min when the reports were done. It doesn’t matter why kind of person is in the line moving at 7 items/min it will be slow no matter what. Some staff people hold up the line for 5 minutes to check the price of 2 apples while others would take it on themselves to give them to the customer for free – after all if they were the wrong price and the customer decided they didn’t want them anymore they’d be thrown straight into the bin or the supervisor would give them for free anyway…

Interestingly when our store rolled out fancy new touch screen computers rates went down for the fastest staff . Instead of knowing the 4 digit codes for all the produce from memory we were forced to navigate 3-4 stages of menus to enter an item by clicking on images. At least the store looked ‘advanced’ though!

These days when I shop I prioritize packing skill over speed. Yes I brought my own bags but that doesn’t mean that I want the leaking red meat in the same bag as the vegetables I plan to eat raw…

64. #### Howard

October 15, 2009 - 6:42 pm -

“Mother lode” and “spelt” are both correct.

We just got new touch screens at our market — a 17 store chain that was bought out by a mega-market from out-of-state. My ipm rate went down. The screen is simply not as fast as the older keyboard, and I constantly have to retype, slowing down my keystrokes (touch strokes?) to enter data.
In the old store we had what we thought was an archaic system. We had to actually enter non-standard codes for produce, even some of the produce that had barcodes on it. Now we use the standard codes. BUT in the old system we sold garlic, for example, by weight. I placed the garlic on the scale, entered code 246, and the correct price was entered on the register tape. Now we sell it by the piece. I count the number of heads, then press the following sequence:
Item Entry
Produce screen
E-GA (to get to the picture of the garlic)
press the picture
hit OK on the “quantity needed” box
enter the number of heads in the quantity field
press Enter

That’s 7 keystrokes to register one item — garlic! And if I miss a head, and find it later in the order, 7 more keystrokes! Likewise most of the other produce items. As I memorize the codes (most of them have changed) I can enter them directly, without having to resort to the picture screen, but for many of them, we sell by quantity instead of weight, which slows things down even more.

I try to pick like items — grab all the frozen items, for example — that I can reach. That way I can pack them correctly, or present them to the packer (if I have one) in some sort of order. Same with meats, produce, etc. The meats all go into plastic (unless the customer screams at me) then into their bags or into paper, if that’s what they asked for.

Again — EBT and WIC orders tend to slow things down, especially now that we’re based on a system in the home state of the company. They’re addressing that, but it’s slow.

Any item voided must be recorded on a form, using the printer, and voids over \$2.00 must be acknowledged by the front-end coordinator, who enters a code, turns the key, and initials the void slip.

For “Items not found” we try manually entering the upc number, and if still not found, we have to send for a price check. Deli items not found are usually the faule of the label printer, so we enter the price. I keep trying to get a Deli key (and Produce key) put on the main screen with the Grocery and Meat keys so that we can credit the correct department, but I get nowhere with that. So we have to go to the All Depts screen, run the slider to the correct dept, touch it, and enter the price. Too many keystrokes.

Think this is a long post? It’s all for only one customer! Repeat as necessary!
:-)

65. #### Jon

November 7, 2009 - 7:05 pm -

The real problem is really about assessing risk. How many people ahead of you are writing checks? Will they start writing their check while the groceries are being scanned? Will the start looking for their checkbook at the bottom of a suitcase sized purse only after the total has been announced? Are they 80 years old and will take 10 minuteds to fill out a check? and will try it multiple times? How many will have their credit card or debit card declined? How many are using Food Stamps, WIC, etc. and don’t know how many items they can really buy with the money they have left? How many are 8 years old, pay with cash, and will sort through their coins, all day if necessary, to find the exact change? How many are shopping with a partner who will bring 10 additional items at the last second, completely disrupting your analysis? How many people ahead of you, if you are in the self checkout line, have never done it before, and appear to have never seen a scanner used before, and take FOREVER to learn how to do it? Does the checker in your line have experience, or is this their first day on the job? Is a person in line ahead of you a friend of theirs? Is a person ahead of you on their cell phone and in no hurry to pay before they finish the call? Does someone ahead of you have a defective item, and someone has to go get a replacement?

The math may favor a certain approach, but the real world tells you that any line, on any day, can become the line from hell. Odds on a coin flip are 50-50, but that doesn’t mean that every other flip is tails.

66. #### Debbie

November 14, 2009 - 8:27 pm -

What grade do you teach? Which class is this? I often run into examples like this one. I think they are great. Linear functions and ratio and proportion are all over the place, and all students should have a solid real-world experience working with those topics. But to me, this fits in somewhere between 7th a nd 9th grades.

The lowest level I teach is algebra II. I find it hard to take an idea like this and use it to help teach the curriculum that I am trying to teach. Any ideas on how to use this for Algebra II? And while I could teach calculus this way, I’m not convinced that’s the best way to go for the honors level seniors.

Opinions?

67. #### Melissa

January 7, 2010 - 4:33 pm -

This was great, and I think it’s awesome that you worked out an equation for something I see all the time as a cashier. THe thing is, it’s not an exact science, because you have to factor in extra chatty customers, slightly faster customers, and things like that. Very cool stuff, I must say.

68. #### Aaron F.

April 10, 2010 - 9:35 am -

This is great! :) My favorite part is that if you think about how a grocery store checkout works, it seems obvious that the expected checkout time should be a linear function of the number of items. And, from the looks of your data, the obvious seems to be more or less true! I love it when that happens. :)

69. #### Claes

April 19, 2010 - 3:15 am -

Hey,

Just saw your TED talk which was great. I never had a problem with math in school but I found the textbooks that I was forced to learn in extremely boring.

Anyways, about this problem. I have obsessed about it for the last 10 years or so. Every time I’m choosing a lane in the grocery store I scan off the people in the line (unless the lines are around 10-15 people in each lane, then I just don’t bother and just choose the shortest lane and hope for the best).

Some of the stuff I check:

1. Age of the people in the lanes. This is so important. Old people are basically so slow compared to young people. I treat checkout lanes with old people in them as I treat dogshit on the sidewalk – I avoid it. Old people also often pay with cash (which is slower, explanation further down).

2. I check the cashiers in the lanes. Also very important. If there is a cashier I don’t recognize I’m unlikely to choose that lane since they probably are unexperienced and are probably going to fuck something up, having to ask a colleague how to solve it and time ticks. I also avoid lanes with cashiers that I know from previous visits are slow.

3. Sex of the people in the lanes and the cashier. Now I know this is offensive but in my experience men are simply more efficient when buying groceries. Women are more likely to chat with the cashier making her checkout take more time than what’s reasonable.

3. Number of groceries are of course a big deal aswell. But you really shouldn’t put too much weight into it. Some people are very efficient!

Nowadays most grocery stores (at least where I live) have express lanes where you check out your groceries yourself. It CAN be a huge timesaver. But sometimes those lanes are crowded and then you probably are better off choosing a normal checkout lane (because some people are SO slow with those checkout machines).

And if I’m buying lots of groceries I normally avoid the express checkout lanes just for the risk of being selected for random inspection. Because being selected for inspection with a lot of groceries take ages because you first gotta take out everything from the bags letting the inspection cashier check them and then put everything back in the bags again.

You say cash is faster. I disagree. In the stores I shop in you can drag your card and put in your PIN number before all the groceries are scanned so there is no way that a cash purchase could be faster.

There are – in my world at least – lots of variables to consider when choosing a checkout lane. But based on your pictures in your post I would most likely just choose the lanes with the least amount of people in them. Because if the amount of groceries is the only data you are provided with you are best off just choosing the shortest lane.

(Make new pictures including age and gender and it will be more interesting. You could also add a random integer between 0 and 100 showing how experienced the cashier is (0 being first day on the job and 100 being 1 year work experience). Cash or credit could also be added to the people in the lanes although it isn’t very realistic.)

70. #### Howard

April 19, 2010 - 3:46 am -

Hey indeed, 135whatever — Your post came off as self-centered and condescending. Your world must be simple indeed if the only thing that concerns you is how much time you spend in the supermarket line, and if you have all that time to consider the different scenarios.
Lots of generalizations there — what’s your standard, YOU? There are other people in this world too — and thank God 95% of them understand that, and have the patience to get in line behind one of those “old people” who are so slow, or where there’s a new, inexperienced cashier who’s “probably going to f*ck it up …”
Yeah, “time ticks” for everybody — not just you, so get over it, and learn to enjoy the stuff that happens between the ticks. That, if you haven’t noticed, is a thing called life. And since you don’t have the foggiest idea when that last one will happen, it’s best to enjoy all those little spaces in between, and learn from them.
I had a little old lady, 98 years old, come through my line on Friday, who is almost totally deaf, and easily confused. I take the time to make sure she knows what’s going on, and that she leaves with a smile. She comes through my line because she knows I care about her. You know what? I have never gone that extra step to help her without someone — usually more than one — in line behind her THANKing me for doing it, and telling me that’s why they come through my line.
Another came through and had a bottle of cooking wine, for a special recipe. I told her about the salt content in cooking wine, and she was flabbergasted, and thanked me for sending her to the liquor stor down the block instead, because her husband has extremely high blood pressure, and is on a no-sodium diet. She was grateful, ditto the folks in line behind her, who all appreciate the few ticks it took to learn something that might save them some grief.
Had one guy — who was concerned about the ticks, who was in so much of a hurry that he had grabbed a couple of items and jumped into line, in a big hurry. He was impatient, but I pointed out that the two items he had grabbed were “Buy One Get One” meaning that he had left two free items (over \$7 total) on the shelf, and did he want me to send a packer back to get them for him. He couldn’t believe that someone would do that, and thanked me profusely, as he waited for the packer. I went on to the next customer while he waited — all of two minutes extra, and again I heard “That’s why I come through your line. You care”
Not trying to tootle my own horn, understand, just pointing out that you’re definitely in the minority, and the rest of the 95% seem much happier and more relaxed than the ones who only see the ticks …
BTW — my ipm rate is pretty good for an old fart.

:-)

71. #### Claes

April 19, 2010 - 4:47 am -

Howard,

These are split second decisions, I quickly scan off the lanes and make a decision. Sometimes I’m wrong but most of the time I’m right.

The point of my comment was to show that this isn’t a problem you can just reduce down to items in the basket and the number of people in the lanes.

I don’t really find spending time in a checkout lane annoying or anything which you seem to assume. But that doesn’t mean that I want to wait 3 minutes extra by choosing a worse lane.

I note that you misunderstood the age factor in my comment. I never said that old cashiers are slower than young cashiers. Only that old customers are slower than young customers. And being a cashier you gotta be able to agree with me on that?

I know that my comment has lots of generalization but the way I see it you have to generalize when choosing a lane in the grocery store. And naturally with generalizations you come off as condecending :)

I just want to clearify that I’m not really that concerned with “the ticks” as you put it. It’s about trying to be efficient and having some fun (YES, I find choosing the fastest line in the grocery store as something fun). I’m a very very very relaxed guy although I know my initial post can be interpreted different.

72. #### Bottyguy

May 13, 2010 - 10:51 am -

I believe the man vs. women in line thing is based on the issues discussed in the post. I will tend to favor men on equal length queue because; 1) they have less startup/end time (less pleasantries, fumbling, checking the cashier). 2) they are more likely to pay with cash, and least likely to pay with check.

73. #### MD

July 2, 2010 - 8:33 pm -

You think you can run OLS on this without clustering by cashier? There are going to be obvious dependencies between observations accounting for time and staff.

Also, items are not all equal when it comes to checkout. Compare scanning a candy bar to scanning a large bag of dog food to scanning some produce where the cashier has to look up the PLU code and then weight it. You need some additional variables in the model.

74. #### Lane

November 3, 2010 - 8:44 pm -

No further discussion should be considered until a definition of “standing in line” has been agreed upon.

Plus, there has to be a sound equation and definition. This study only defines the point of entering a line to payment acceptance. But the experience does not end there. You may have to bag your own groceries, so at what point does “standing in line” terminate?

(Is there a belt that moves the food or do you have to hand everything to the cashier?)

(Is the store taking a few seconds to ask you for a POS donation?)

(B.S. on the zero seconds zero items; I just stood in line for 5 minutes with 15 items, rang everything up and my card was declined. Do the math. I just spent 10 minutes buying zero items).

Standing in line needs specific defining because there is the “check out, ringing up” process followed up by the payment process followed by exiting the line to gather your groceries. May I suggest:

“Standing in Line” will be defined as “from the moment the customer commits to a line to the moment the cashier handles the customers first item”.

This is based on measuring the customers anxiety level about standing in line. Usually, for most customers the anxiety grows until their “turn” comes by the cashier handeling their first item.

So in the end, you have opened up a large can of worms (on sale, .99c), have fun with it.

75. #### Hinheckle Jones

November 4, 2010 - 6:57 am -

I learned an important lesson from my brother:

Always get in the line with the prettiest cashier. Then the speed doesn’t matter so much.

76. #### Numbat

November 4, 2010 - 6:26 pm -

Great comments all and I like #147’s solution the best.

My question has always been why don’t supermarkets introduce single point queuing? A number of stores here do it for their express lanes, so why not all lanes?

77. #### R. Wright

January 19, 2011 - 7:24 pm -

I raised this question (in a pretty mild, watered-down way) on the second day of a College Algebra course last week. We finished up the discussion today. I had the students guesstimate the transaction time and per-item time, without seeing any actual data, and they came up with 40 seconds and 4 seconds, respectively. They showed a lot of mathematical intuition and seemed to enjoy it.

In short, thanks for the great idea, Dan.

78. #### Robyn Coburn

December 6, 2011 - 12:36 pm -

I like single lines where you go to the next available cashier, no matter what. I don’t know whether it is faster overall – that would be a whole other study – but it does feel fairer. I wish more grocery stores would institute this method.

79. #### lakawak

January 2, 2013 - 5:11 pm -

This is based on a lot of assumptions that are totally made up out of thin air. First off…credit card/debit cards are often FASTER than cash. I even know some stores with dedicated express express lanes that only take plastic for added speed. Especially since they can often be swiped while the items are still being scanned. At lot better than someone fumbling through their purse or wallet for exact change, or holding up the line after receiving their change to neatly put it all away before allowing the next person to move up. VERY few stores have dedicated baggers anymore, which more than doubles the time per item since it takes more time to bag than it does to scan.

Not to mention…who is counting the items in a cart? Often someone in an express lane of 10 items or less has 2 or 3. Whereas someone in a regular lane almost ALWAYS has more than 10. Often considerably more.