Executive Summary:
A Consumer’s Purchasing Policy and Store Choice: What is Optimal?
The replenishment of component parts, allocation of production inputs like machinery and labor, and even consumer shopping decisions are characterized by a common structure—a periodic choice between two sources of supply. Research by John Semple and Ed Fox of SMU Cox helps buyers make optimal supplier choices and decide how much to purchase when faced with two sources of supply. While the authors’ innovative model has implications and applications for firms when replenishing inventory, the model is particularly revealing about the purchasing behavior of consumers stocking their homes with groceries. Thus, their research represents a significant advance in understanding consumers’ shopping behavior and may offer retailers new insights for attracting, retaining and best serving their customers.
Background
This research is rooted in a stream of economic research dating back to the late 1950s. A group of world renowned economists—Arrow, Karlin, and Scarf—proved that the cost minimizing approach for buying and managing inventory from a single supplier had a specific mathematical structure. As Semple explained, “They were able to prove that the optimal way for firms to purchase inventory from a single supplier was governed by at most two parameters. One parameter determined whether to shop, the other determined how much to buy.” Researchers refer to this cost minimizing strategy as the optimal policy. From their new research, Semple and Fox can characterize how a household will purchase and choose a store when there are two suppliers. They found that there are three different types of households, each with a structured optimal policy that describes how rational shoppers of that type should purchase. Once you have data on a specific household, that household’s optimal buying policy should be ‘pretty much etched in stone’ according to Semple.
Consumer Strategies Emerge
So, how does the consumer (or firm) buy when there are two suppliers? In grocery shopping, a household may have a major supplier like Wal-Mart (low price) and a secondary store like Tom Thumb or Kroger (high convenience), for example. Semple illustrated, “We can show that the optimal policy has one of three possible structures governed by at most three parameters.” Re-stocking inventory depends on household demand, the cost of travel, and the cost of goods; but how does one make finer predictions?
The structure of the optimal purchasing policy for each type of shopper holds some of the answers. The three optimal policies use one, two, or three parameters (values). To illustrate the concept, suppose there are only two stores, represented by Tom Thumb and Wal-Mart. Most shoppers live closer to a Tom Thumb than a Wal-Mart. The first type of shopper is the “convenience shopper” who always goes to Tom Thumb. The optimal policy for this type of shopper consists of a single “buy-up-to” parameter that determines how much to buy. Whenever the convenience shopper goes to Tom Thumb, they buy a basket that brings household inventory (groceries) up to the level of this parameter. The second type of shopper is the “price shopper” who always goes to Wal-Mart. The optimal policy for this shopper has two parameters. The first is a trigger value—if household inventory falls below this value, then a trip to Wal-Mart is triggered (otherwise they postpone shopping). The second parameter value is a buy-up-to level describing how much to buy at Wal-Mart. The third type of shopper is the more prevalent “price-convenience shopper.” This consumer shops at both stores and has an optimal policy described by three parameters. The first parameter is a store choice parameter. If household inventory falls below this parameter, then the shopper chooses Wal-Mart. If household inventory is above this value, then the shopper chooses Tom Thumb. The remaining two parameters are buy-up-to levels that describe how much to purchase based on the store they select. Not surprisingly, a household’s buy-up-to parameter for a trip to Wal-Mart always exceeds its buy-up-to parameter for a trip to Tom Thumb. For each shopper type, the parameter(s) are sort of like ‘magic numbers’ that one should be able to estimate using historical data, Semple mentioned. Once these parameters are estimated, retailers could begin to predict which stores shoppers will choose in given situations and how much they will buy.
Implications for Retailers
So, why are the shopper types and their parameter values of interest to retailers? Consider, for example, that a large family would have higher buy-up-to levels and maybe a lower trigger value for a shopping trip. Parameters would need to be estimated for each individual household, but a firm should be able to gather some information on how individual households operate. Semple explained, “Once this happens, retailers then know how to promote certain items and how to get people into their store—but it all hinges on first understanding how individual customers behave.” He continued, “Retailers are fairly myopic in terms of pricing decisions and promotions to improve customer traffic flows. They have not been overly concerned with what happens at the individual household level. We think that you can in fact characterize each individual household and come up with their policy parameters; these could be estimated, in part, from loyalty card data.”
Parameters are sensitive to both price and convenience (store proximity). For example, if you’re Tom Thumb, one way to influence behavior is by offering coupons. If you lower the average price on certain items, you increase the buy-up-to parameter for convenience shoppers and increase the choice parameter for the price-convenience shoppers. The former increases the size of the basket purchased at Tom Thumb; the latter increases the likelihood of a trip there. Using the model could help a firm to categorize individual households and influence their parameters through, for example, customized store coupons issued at the point of sale. Firms differ in their level of sophistication regarding the use of analytical tools for determining pricing and purchasing behavior, but many stores have the technological infrastructure to begin thinking this way.
Conclusion
In the past, some firms adopted the structure of the optimal policy for a single supplier but did not bother to accurately estimate the parameters. “What we’re working on is in its infancy—analyzing and characterizing behavior on a household-by household-basis. This might have been impossible ten years ago,” Semple stated. “But with the rise of loyalty cards and other sources of information, we can now consider doing an analysis that could help retailers customize their promotional strategies for each individual household. However, first we must find a concise way to characterize, quantify, and predict each household’s behavior.” The first step in this direction has been to prove how a consumer should buy groceries assuming rational purchasing behavior—the optimal inventory policy.
This summary is based on “Optimal Inventory Policy with Two Suppliers” by Edward J. Fox, Richard Metters, and John Semple. The paper is forthcoming in Operations Research. A second paper using grocery store data will serve as an empirical testing ground for this model. New insights are expected to deepen understanding of consumer purchasing behavior.
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