The Efficient Supermarkets Hypothesis

It’s always tempting to switch lines in the supermarket. After waiting for 5 minutes in one checkout line yesterday, Gweneth and I jumped to the next queue. Turned out we’d jumped in behind someone who was complaining about a price being wrong, and the ensuing price check cost us an additional 15 minutes.

At some point during that 15 minutes, it struck me. The efficient markets hypothesis tells us that (a) a stock’s price reflects all publicly available information (management skill, product demand, etc), (b) the best way of making money in stocks is to buy a slice of the stockmarket and sit tight, (c) churning your portfolio is likely to be inefficient.

So if we believe shoppers are as rational as traders (why not?), then there should be a parallel efficient supermarkets hypothesis. The efficient supermarkets hypothesis tells us that: (a) the length of the line reflects all available information about its speed (cashier skill, size of preceding trolleys etc), (b) the best way of getting through the supermarket checkout is to pick the closest line and stay in it, and (c) the worst thing you can do at the supermarket is switch lines.

Update 1: Joshua Gans prefers to think of this through the lens of auction theory, and offers his own deux et machina – get your child to cry. 

Update 2: A phone conversation with JG just now convinced me that I needed to be clearer in my exposition. The argument is this: if your fellow shoppers are rational, then there is no clever strategy that can get you out of the door faster. Just pick the nearest queue (or, if you want to take Russell’s advice, the queue with the nicest-looking shoppers), and stick in it.

Update 3: Harry Clarke’s view.

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33 Responses to The Efficient Supermarkets Hypothesis

  1. Russell Hamilton says:

    Such narrow thinking …. why wouldn’t you want to get in the line that had the nicest looking people in it, you might meet somebody while you’re waiting ? It’s not all about speed.

  2. Sinclair Davidson says:

    well, maybe. whenever I switch I end up regretting it, and whenever I don’t switch I end up regretting it. bit of a trend there. so following Russell’s advice, pick the queue with the nicest looking people or the one closest.

    In any event, not sure the EMH explains queues. they are a mom-market mechanism. you never see people paying the jump the queue (not in supermarkets anyway).

  3. derrida derider says:

    But EMH assumes a thick market with many players. In a supermarket with relatively few shoppers you ought to be able to rig the market somehow. Maybe you need game theory, not queue theory ….

  4. Joshua Gans says:

    I think that you haven’t really thought about this hard enough. There is more to it than that. See this post for more http://coreecon.blogspot.com/2006/05/optimal-supermarket-queuing.html

  5. I tend to pick the line, all things being just about (but not quite) equal, with the friendliest operator who I like chatting with… and Russell’s got a point too. Aren’t they also rational choices? It seems to me unrealistic to assume that the only motivation for picking a line is length.

  6. Russell Hamilton says:

    “The argument is this: if your fellow shoppers are rational, then ….”

    but they’re not – they’re incompetent and they’re cheats. You know that if you get in a short queue the person in front will try to use a credit card that has expired, then want to try another etc

    Even I, usually scrupulously fair, am inclined to count 4 items which are the same, as 1 item, when I’m in the ’12 items or less’ lane. (Also things picked up at the checkout – magazines, chocolates etc don’t count).

  7. derrida derider says:

    But how does it work out if information is asymmetric – some shoppers can observe how fast the checkout chick is in their queue, but not observe it in queues they’re not in? I was musing on this last night as I waited in a queue with an extraordinarily brachykinetic operator.

  8. Russell Hamilton says:

    BTW, what is the nutty ‘reverse queueing’ thing? Isn’t it actually no queue at all ? Queueing is what we’ve worked out based on fairness and a reasonable desire to avoid fights – I’ve lived in countries that don’t queue and I’ve seen the fights.

  9. Russell Hamilton says:

    Given that there’s no solution to the random horror of ‘price check’ and the roll of paper in the till running out etc I propose the Fortnum and Mason solution. I experienced this more than 30 years ago when I uncouthly stumbled into their premises to find that I was accompanied from the door by an immaculately dressed factotum with a stylish bag. He knew where everything was and could advise on products. I took the items from the shelf and handed them to him, and miraculously, at the end of the process he had already added up the cost, and I just handed over the money and left.

  10. Andrew says:

    I think the most efficient solution for the queuing conundrum, and one that should be applied to all supermarkets and all other locations where queuing is a ritual, is the single queue.

    That is, rather than taking a punt on which line might be most efficient, everybody gets in a single line that has multiple cashiers at its head.

    Thus we have no queuing decision to make, and it is the fairest mechanism available for all shoppers.

    Does this make it the queuing option for communists?

  11. Russell Hamilton says:

    See where efficiency leads you …..

  12. Andrew, they tried the single queue at my local Coles for about two months, but everyone hated it, so they went back to individual queues.

  13. Ben says:

    Queuing – a fine example of co-operation providing a more desirable, effective and fair outcome than “the law of the jungle”. Neoliberals must be aghast.

  14. Sacha says:

    “I think the most efficient solution for the queuing conundrum, and one that should be applied to all supermarkets and all other locations where queuing is a ritual, is the single queue.”

    I’ve thought similarly, although the length of one queue is much longer than a number of different queues.

    At WPP (Woolworths Potts Pt) a single queue is employed through necessity. While the length of the queue may be a negative in the eyes of the queuees, the increased speed at which people move through the queue may be a positive. In the single queue regime at WPP you may get through a 30 metre queue in ten minutes. The Coles in Kings Cross also employs a single queue. Another factor at these supermarkets is that most people buy only small numbers of items – they don’t do massive big shops as people often do in the suburbs. People will buy things as they need them every day or so.

  15. Sacha says:

    …and so you don’t have a great big trolley in front of each little checkout. People usually only have one or two baskets. The small number of items means that the time it takes less time for the goods to be scanned and packed for a single customer than if most people did enormous weekly shops.

  16. Peter says:

    I thought this post was a set-up for the joke about the guy at the supermarket in Cambridge, Mass, to whom the checkout person says:

    “Let me guess — You’re either an MBA student at Harvard Business School or a PhD student at MIT. ”

    And he says: “That’s right! I am one of those. How did you know?”

    “Well, this is the 6-items-or-less-lane and you have 8 items. So either you’re an MIT post-graduate who can’t read or a Harvard MBA who can’t add!”

  17. you should also check out the work by Rob Tibshirani et al. on changing lanes on the freeway.

    and what if Gweneth had switched, and you stayed put, and then you had two options (I see that kind of strategy fairly often here in Palo Alto, though more likely at Safeway etc than at the more upscale Whole Foods etc).

  18. Andrew Norton says:

    If you frequent supermarkets with many welfare-dependent clients there are skills in spotting likely problem lanes, where you may end up waiting while items are deducted to get back to the amount of money the person has, plus enduring them changing their minds about what they want most.

  19. Sacha says:

    Simon – that would work best if there are only two queues.

  20. Andrew Leigh says:

    Simon, the most embarassing thing is – we were employing a split strategy, and then became so confident that one of the lanes was the winner that we switched to it. Then waited in it for 15 minutes.

    Andrew N, under the efficient supermarkets hypothesis, this is already factored in. Unless you have inside information, you can’t beat the “pick a random line and stay in it” strategy.

  21. Brendan says:

    You then also have the situation where the 8 items or less queue is a single queue to multiple checkouts in combination with the standard checkout system of single queue to single checkout as is the case in most major supermarkets. Works magnificantly until there is a long queue on the 8 items or less checkout and suddenly rationality goes out the window as it looks much more tempting to join the short queue behind a full trolley of goods then join the long queue that will move faster. There is then the compunding factor of how much many registers are servicing the single queue and how effeiciently that demand is being met.

    Solution – find a long hours supermarket and do your shopping at 2300. Much more relaxing.

  22. Matt Cowgill says:

    Andrew Norton: As someone who has worked in retail, I’ve actually found the more ‘well-to-do’ customers to be more of a pain. If their card has exceeded its limit, or is damaged or expired, they will often insist that the fault lies with me (obviously of an inferior genetic heritage, as I worked behind a counter). This will frequently lead to 3 or so repeated attempts with the one card before they huffily procure another from their wallet. Less-well-off people usually know exactly how much is in their wallet/account and are less of a hassle.

  23. Mork says:

    A lot of this analysis is missing one important factor – it’s not just the number of people in the queue, it’s how full their shopping trolleys are. So, to find the queue that will result in the quickest service, you have to keep in mind both the rate at which an operator will scan the items and the time it takes to pay at the end and do a little bit of algebra-by-instinct.

    Also, as others have suggested, assuming that the only utility available to a rational customer is the quickest possible service will not always hold up. For example, I will willingly take a longer queue on a checkout with a magazine rack over a shorter queue without.

  24. Sacha says:

    Mork, these things would just be a variation to the utility function employed by the rational decision maker.

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