Ivars Peterson's MathTrek
When I go grocery shopping, I usually bring a list and have a good idea of where to find everything. So, it was quite disconcerting when my favorite supermarket was reorganized into a fresh, unfamiliar layout. Inevitably, my grocery shopping became less efficientat least until I got used to the new arrangement.
A team of marketing researchers at the University of Pennsylvania's Wharton School recently studied the paths taken by nearly 1,000 grocery shoppers, comparing their routes to paths in an idealized mathematical model known as the traveling salesman problem (TSP). They found that actual shopper behavior can deviate markedly from TSP efficiency. And shoppers who are most inefficient tend to buy more products than do those who do less wandering.
In the classic traveling salesman problem, a salesman must visit each one of a given number of cities before returning to his starting point. His goal is to minimize the distance that he has to travel to visit all the required cities. There are a variety of algorithms available for calculating or approximating such routes.
Sam K. Hui, Peter Fader, and Eric Bradlow defined the optimal path for a shopper to be the shortest path that connects all of his or her purchases. To match the efficiency of the hypothetical traveling salesman, a grocery shopper with a list would have to know the location of all the desired products and have a step-saving strategy for going from entrance to each product location to checkout.
Taking advantage of technology for tracking shopping carts and sales data from checkout scanners, the Wharton researchers mapped the paths of 993 shoppers in a supermarket and analyzed what they bought by food category (fruit, milk, salty snacks, and so on). They discovered that, on the whole, shoppers were reasonably good about the order in which they moved from bananas to milk to cookies. However, there were much greater inefficiencies in the paths taken to get from one product to the next.
The researchers conclude that "shoppers tend to pick up their purchased products in a relatively efficient order, but they are highly inefficient in the path they choose between each of these points in the store."
Indeed, an earlier study by Wharton's Peter Fader, Eric Bradlow, and Jeffrey Larson had already shown that, contrary to popular belief, shoppers don't systematically go up and down aisles (though that's my usual strategy). Instead, they tend to move counterclockwise around the perimeter of a store, making short treks into aisles to retrieve needed products, then returning to the perimeter. Shoppers also tend to speed up their shopping as they near the checkout.
Curiously, order inefficiency appears to have a greater influence on the number of products purchased than does trip length. People who tend not to follow a logical order typically end up buying products in more different categories. There's no such correlation for excessive trip length in going from point to point.
What such inefficiency tells a store manager isn't clear. "On the one hand, inefficiency gives the shopper additional opportunities to see (and perhaps buy) more productsthis might be a good outcome for the retailer," the researchers comment. "But on the other hand, part of the inefficiency may be due to confusing product placement and poor store layoutwhich will create dissatisfaction among shoppers."
There's much more to be learned from such analyses. For example, "it would be interesting to obtain additional information about each shopper . . . and link [it] to the inefficiency measures," Hui, Fader, and Bradlow note. "For instance, we may want to study how order and travel inefficiency differ across gender, age, and previous experience in the store."
Although the TSP model has been widely applied in operations research and engineering, the Hui-Fader-Bradlow study represents one of its first applications in the realm of marketing. It's unlikely to be the last.
Moreover, supermarketsand mallsoffer intriguing settings for studying how people go about handling TSP situations in everyday life.
2006. The 'traveling salesman' goes shopping: The efficiency of purchasing patterns in the grocery store. Wharton School, University of Pennsylvania press release. Nov. 29. Available at http://knowledge.wharton.upenn.edu/article.cfm?articleid=1608.
Hui, S.K., P.S. Fader, and E.T. Bradlow. Preprint. The traveling salesman goes shopping: The systematic inefficiencies of grocery paths. Available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=942570.
Larson, J.S., E.T. Bradlow, and P.S. Fader. Preprint. An exploratory look at supermarket shopping paths. Available at http://knowledge.wharton.upenn.edu/papers/1293.pdf.
Peterson, I. 2005. Artful routes. MAA Online (Jan. 3).
______. 2000. Calculating swarms. Science News 158(Nov. 11):314-316. Available at http://www.sciencenews.org/articles/20001111/bob10.asp.______. 1997. The traveling monkey. MAA Online (July 7).
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