“One line to rule them all”?

Jane Galt writes:

Everyone knows the unified queue is the best way to move checkout traffic. So how come every time customers in a crowded drugstore try to form a single queue, the cashiers force us to line up at the registers? Do they get some kind of psychic job from knowing in advance which customer they’ll check out?

You might try to argue that the indirect utility function is convex (risk-loving) in prices, and that people, when they realize that their personal line-choice algorithms result in shorter (longer) waits, make more (fewer) trips to the store.  Samuelson once proved a theorem about that in the QJE.  The intuition is that consumers can take advantage of price variability, in this case "time price" variability, and come out ahead.  Admittedly the notion of "going to the store more often when your innate line-choosing algorithm turns out to be good" requires a mental stretch.

People also might like knowing that the end to waiting is in sight.  On the phone they put you on hold and tell you the expected wait time, or they should.  At least five times in my life I’ve bolted a supermarket and abandoned the groceries, simply because the lines appeared too long.  It is harder to estimate how long a single line will take, and it is harder to compare single lines across supermarkets.

And might there be "line price discrimination"?  Hurried people like me can scout out the best lines (don’t you have visual algorithms for speedy cashiers?…young girls are best), whereas the conversation-starved, check-writing old ladies might even prefer a slower line.

There are thousands of papers on queuing theory, but I’ve never seen a good study of when single lines are to be preferred.  How sad indeed is my profession…

Comments

I do not know what drug store she goes to, but the ones I go to everyone forms a single line -- both at the main counter at the front and the prescription counter at the back of the store.

Multiple queues take up less floor space. (You don't need to leave space between the single queue and the checkers for shoppers to move to the open clerk.) Retailers are evaluated based on sales per square foot. Ergo, multiple queues.

mki, I have never once been to a grocery store that had every checkout line staffed and open. Extra, unused lanes are all wasted floor area, from a revenue standpoint. A single queue may waste some space (though I don't think it has too) but would make more profitable use of manpower by allowing more efficient allocation of workers to check out duties because single queues have much less risk of server under-utilization. Maximizing profit per sq ft also fails to explain why some businesses (even retail businesses) do use single queues. Best Buy is notorious for scientific attempts to maximizing profit margins, but I've been in a few with single queues.

Is it really the case that young girls are fastest, or is there an element of Einsteinian relativity going on here? (Sit down with a pretty girl, and time just flies...)

My theory is that there are multiple lines when every customer takes (within reason) a similar amount of time to get through, but there is one line when some customers might take much, much more time than others.

For instance, there are multiple lines at McDonald's. But for customs and immigration at the airport, there is one line. That way, if some suspicious-looking guy gets a thirty-minute interrogation, nobody has to wait half an hour behind him.

Banks, same thing. Some people have complicated banking transactions that take forever, and this way nobody has to wait for those people.

I'm glad someone has noticed the advantage of women grocery check-out clerks. Not necessarily the young ones. I think it's because there is still more "opportunity" for middling-competent men (often they're the one who have become managers and OK checks from the people they don't know but the checkers do) than for middle-aged women.

I'll go for a forty-ish gal any time. I think the "young" part is an "extra" courtesy of Tyler.

I think multiple lines is also advantageous in terms of pushing impulse items. A fast moving single line prevents one from picking up a gossip rag or a pack of gum.

just a thought

I posted a similar item (more specifically about the Whole Foods example)on

I posted a similar item (more specifically about the Whole Foods example)on my blog earlier in the week. There are a number of young economists that are specifically studying supermarkets,
and they have a lot to say on the topic...it's only a matter of time until they
get around to studying the lines leading up to the registers.

Well... I had a teacher in one of my principles of economics classes relate this one, he always said it didn't matter which lane you chose, your average expected waiting time would be the same, and this was according to the efficient markets hypothesis. I always think about that when looking for parking spaces or waiting in grocery lines, or even driving on the freeway.

Incidentally, I've been to several stores that have single-line queues. Marshall's most recently. It seems pretty efficient and fair in that setting. Single-line queues wouldn't work in grocery stores because of item count disparity. It enables grocery stores to capture additional small-item sales by reducing the opportunity cost to less numerous item purchasers.

See a discussion on the single-line problem (and related design issues) here.

It seems like a single long line would be less efficient, since it takes time for customers to go from the single line to a particular cashier, and the cashier will not be doing anything during that time. This is especially true in grocery stories, where many customers have a cart to unload, but it is also true to a lesser extent in places like drug stores. If there is one line per cashier, and customers easily outnumber cashiers, then each cashier will be working pretty much constantly, since there will almost always be another customer in place for the cashier to deal with (with some of their purchases waiting on the counter) as soon as one customer is finished. A single long line would be more equitable (less variability in waiting time) but less efficient (higher average waiting time).

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"Everyone knows the unified queue is the best way to move checkout traffic."

I don't know that. In efficiency terms (# people served/time unit) they'd be nearly identical, since to first order every cashier is dealing with a customer at any given time. If anything, as some commenters above point out, with multiple lines you might even have less waiting time since people can take a while to find and get to available cashiers. (The store can try has to pay someone to direct traffic).

On the other hand, multiple lines have a higher variance in waiting time, which might be particularly undesirable (as Phil B points out, above), and might lead to costly "short-line-seeking" behavior by customers.

On the whole, I'd say it's usually a wash, and I'd understand a decision by a store to pick either way. And, having picked such a way and organized to checkout system & store layout around that way, I can understand a decision by a store to enforce this regime.

If it's store policy for people to line up in front of cashiers but people start forming a long line on their own, is it "cutting" for someone to ignore the line and walk up to a cashier? The store policy says it's not, but the people on line probably wouldn't be too happy. Best to force Jane Galt to line up at a register so they don't have to deal with her complaints later.

Having just come back from Atlanta, what I really wanna know is how to make airport security lines move faster...

Unilines are preferable on the basis that losses hurt more than pleasure given by an equivalent gain. That is, if a multiple lane scenario I zip through faster than everyone else due to a lucky/clever pick of lane, I don't actually get much joy out of it and (by definition) the experience doesn't last long. However if I am in a stuck lane, I get pain and frustration from watching other lanes zip past me, and the experience lasts much longer (by default). The overall sum of happiness is decreased by the multi-lane experience.

Also - those who comment that there is always a need to remind the front person about an open cashier strike me as the same as the type A person who leans on the horn if the driver in front is a microsecond too slow off the line. Chill out.

"Hurried people like me can scout out the best lines (don't you have visual algorithms for speedy cashiers?...young girls are best)"

The best lines have no cashier at all -- they end in a bank of 'U Scan' stations. Not only is there a single line for 4 stations, but the people in those lines want to get out of the store quickly and definitely aren't interested in chit-chat. Old people and check-writing ladies are not found in these lines. And if your bread gets squashed or your chips get broken in your bags, you have only yourself to blame.

U-Scan lanes -- the next best thing to not having to go to the store at all.

At my local drugstore, uni-lines often spontaneously develop. I think there are two reasons for that. There are only 3 registers, all close together and easy to see. Each register has a small counter next to it so you can't put your items down until the previous customer has left (but you can see when the person is about to leave).

At the supermarket next door, there is never a uni-line. Ten registers are spread well apart. And there is a long belt extending back from each register. You can put your itmes down on the belt and have them ready to be scanned while the previous person is still being attended to.

"I think that Unilines usually reduce the *median* wait-time, whereas multiple lines reduce the mean wait-time."

How would multiple lines reduce the mean?

Anyway, another big advantage of 'unilines' nobody's mentioned is that it makes it possible to add cashiers to the system smoothly, thereby reducing everybody's wait time in the order they arrived rather than setting off a mad dash to the new register.

Good thread!

Having just come back from Atlanta, what I really wanna know is how to make airport security lines move faster...

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