Monday, May 29, 2006

Optimal supermarket queuing

Economists think alot about queues whenever they are standing in them. For example, Steve Levitt became preoccupied with Disneyland queues earlier this month.

Today, my co-author, Andrew Leigh recounts his supermarket experience. He ponders the difficult issue of what line to stand in and concludes that it may be best to make your assessment, go to the nearest queue and stick to it. Queue picking is a hard issue. It is a little like an auction. You are observing check-out's bids for your patronage. The shorter queue reflects supply and demand. It may be short because checking out is efficient or it may be short because others have worked out that it is hopelessly inefficient. What is the truth also depends upon the ratio of queues to queuers.

This means that a static assessment of your options is not enough to make a long term judgment. You need to observe the dynamics of the situation before you can judge and you may want to update and change queues. The problem is that involves a switching cost as you have made a sunk investment in a particular queue and would be forced to go back to the start by re-optimising.

What you need to make this all much better is one of the following:

  • Real markets: you should be able to pay to get a better place in the queue. See this article in Slate.
  • Reverse queuing: Steven Landsburg in Slate suggested that we might change the convention and have arrivals to queues go to the front rather than the back. His issue is that everytime someone joins a queue that imposes costs on those who come later. That won't happen if people can join the front of the queue. In the context of supermarkets it would be those at the back of the queue jumping around to see if they should join a longer queue; assessing the speed of the checkout and so forth.
  • The one queue hypothesis: queuing theory tells us that having many check out queues is hopelessly sub-optimal. Better to have a single queue leading to multiple check outs as they become available. Average waiting times are much much less.
  • Crying children: the best way to improve your own waiting time is to have a crying child. If your child is not crying, do something to make them cry. I can tell you that it works a treat. No one wants to stand in a long queue with a crying child and you can move to the front so minimise that pain.

3 comments:

Jeremy said...

I'm sure it works even better if you have a crying adult.

Anonymous said...

Joshua, I think you've just confirmed that economists are not nice people.

Charlene said...

Awesome!