## Optimization at the Checkout

On more than one occasion, while waiting in line to buy my lunch on campus, the cashiers at the front have asked those of us in the line to split into smaller lines - one line for each cashier. This seems to be met with hesitation on the part of those of us who are in line, and rightly so. Perhaps I am simply projecting, but it seems like they all know the same thing I do: that having only one line feed into all the cashiers is the most efficient way to manage a queue.

One would think the cashiers should know this as well, but apparently not. So, if you have ever asked people to form separate lines when waiting to be helped, pay attention, because you need to learn why people in line rarely pay attention to you.

For a person waiting in a single line, there is little incentive to break into smaller lines. This is because using several lines leads to longer wait times on average. You don't need any sophisticated machinery to explain why this is true - if you ruminate on the two choices for a moment, the benefits of the single line system should make themselves apparent.

With only one line, you never have to worry about getting stuck behind a coupon-clipper or a check-writer. You move forward whenever anyone's transaction is completed, which means that even though a single line will be longer than several shorter lines, it will also move much faster.

This is also a plus for those of us who have trouble with decision-making. With only one queue, there is no decision to make. You needn't worry about developing a strategy when picking your checkout line; for example, you don't have to size up those ahead of you to discern whether or not they are the type who will take a long time paying. Just get in the line and move - it's really as simple as that.

How much more efficient is the single line queue? Apparently there are tools available that allow to model these sorts of situations, but here is one such example, courtesy of the blog of Dr. Michael Trick:

Suppose you have a single queue with 20 customers arriving per hour. If the cashier can handle (on average) 22 customers per hour (close to saturation, but probably roughly what “efficient” managers would aim for), then the queue will grow so long that the average wait will be 27 minutes! Five such queues would end up with about 50 people waiting in line on average. If you go over to one line (with 100 arrivals/hour) being served by five cashiers, the average wait goes down to under 5 minutes, and the number of people waiting in line is only 12 on average.

This simple example shows that the benefit to a single line is quite significant. So significant, in fact, that many grocery stores are now organizing their checkouts to have a single queue. Whole Foods is perhaps the most prominent example, because of an article the New York times wrote nearly 2 years ago, which came to the unavoidable conclusion that the single line queue is the only way to play.

2 years seems like enough time for such an unequivocal conclusion to have begun seeping into our collective consciousness, but apparently not. I welcome the day when I am no longer asked to form separate lines while buying my lunch - it's like asking me to give you even more of my (quite valuable) time. It's not that we can't hear you, cashier, it's that we know what's in our own best interest. And frankly, so should you.

Is there any advantage to using multiple lines? There may be some psychological benefit to having many short lines rather than one longer line, especially for people who, for example, may go to the grocery store only to pick up one or two items. For them, the sight of a single line may be overwhelming, even if that line does move much faster than separate shorter lines would.

Also, there is perhaps something to be said for the use of express lines, which cater to those people who would be most turned off by a long line. However, with the single line system, that one line is already express! Neither of these points seem to matter much in the face of the data, which strongly points to having your customers stay put in a single line.

So, the next time you're waiting in line, and the cashier asks you to split into smaller lines, feel free to hold your head up high and ask what's in it for you. You certainly aren't doing yourself any favors by complying.

Psst ... did you know I have a brand new website full of interactive stories? You can check it out here!