Tuesday, March 15, 2016

Grocery shopping and Braess' paradox

Some time ago, our local grocery store introduced self-checkout, where we can scan our grocery items ourselves. My wife and I like to use this option since there are several stations open and not many people are using it, so we can get through the checkout quicker. However, recently we noticed that the lines at the self-checkout are getting longer, while the lines at the checkout clerks are sometimes shorter than the self-checkout lines. I believe this is an example of Braess' paradox.  Braess noticed that when a new road is added to a network of existing roads, the congestion can actually increase. His reasoning is that each driver follows a selfish routing algorithm and chooses the shortest route to the destination.  If the new road is a shortcut, then everyone who can use this road will choose it, and this can actually increase the congestion through the network. This seems to be happening with the self-checkout lines as well. Everyone assumes it is quicker to use them and this leads to longer lines. One way to achieve optimal throughput in a road network is if there is a centralized control to route each driver, but this would require information about the speed and travel plans of all drivers and it might favor some drivers over others for the overall good. To implement this would require cars to talk to each other using technologies such as connected vehicles, vehicle-to-vehicle communications and dedicated short range communication (DSRC).

Back to our grocery shopping trips.  Yesterday the self-checkout lines was quite long so we went to the checkout clerk who is much faster than us in scanning the groceries (plus there was an additional clerk to bag our groceries), and we got done much quicker than if we had used the self-checkout line.  Sometimes one or more of the self-checkout stations are out of order which is similar to lane closures on a multi-lane highway.  If more people realize that regular checkout is faster, we could have another Braess' paradox in the making and lead to longer lines at the regular checkout lines.  In the long run, this can lead to cycles of short and long lines forming alternately at the self-checkout lanes and at the regular checkout stations!  Fortunately this is unlikely to happen since the 2 types of checkout lines are in close proximity so the shopper has a good sense of the congestion of the entire system. But imagine a mega-store where for some odd reason the regular checkout lines are far away from the self-checkout lines!  The shopper needs to decide which line is more optimal based on incomplete information and what other shoppers would do.  On the other hand, the speed of checkout may not be the only objective.  Some people prefer self checkout because they feel like they don't make mistakes and make better bagging decisions (like not having eggs at the bottom of the bag) if they do it themselves.

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