July 22, 2010

Revenue Management with Costly Price Adjustments

Determine when making price changes will — and won’t — pay off.

Topics: Operations

The Idea

Determine when making price changes will — and won’t — pay off.

The Research

Retail firms rely heavily on pricing policies to maximize their revenue, raising and lowering prices as they reassess customer demand or in response to external factors such as big swings in the economy or new competition.

But price changes are costly. To advertise new prices, a clothing retailer may need to republish and redistribute its catalog. Some states have consumer protection laws that require retailers to label individual units for sale, making the cost of paying staff to relabel products substantial, especially for retailers that carry a large number and variety of products. In a grocery store, for example, the cost of repricing may include relabeling individual units, staff supervision and correcting errors; the total cost can amount to 35 percent of a store’s net annual profit margins. Far-reaching price changes that require greater managerial attention and resources can further inflate costs.

Retailers must weigh the cost of relabeling against the expected increase in revenue when considering whether to reprice. In practice, firms tend to resist frequent price changes because of associated costs. But sometimes the retail environment demands it.

While many quantitative methods for pricing exist and are built into retail software packages, these models often call for frequent price adjustments but ignore the costs of making such adjustments.

Professor Alp Muharremoglu worked with Sabri Çelik of Columbia University and Sergei Savin of Wharton to create a better model for price changes, accounting for fixed costs, such as advertising, and variable costs, such as those that depend on the amount of inventory on hand.

The researchers created two models. The first is a dynamic model that reflects the complex considerations of price changes and sometimes results in making counterintuitive recommendations. For example, it may be profitable to lower a price when inventory for an item decreases by 20 percent but more profitable to raise the price again later if inventory drops by an additional 20 percent.

The researchers then created a second model that offers a pared down calculation for optimal price changes. The researchers recommend using this simplified version even when it might appear that the complex version provides a more accurate recommendation, because implementing a less precise but more streamlined change may offset the cost or effort of using the more complex model.

Practical Applications

Pricing managers

You can use this research in retail settings for markdown management or to fine-tune price changes in response to a broad range of environmental factors. This research is especially useful to retail firms that traffic in large numbers of products subject to the whims of consumer demand or that are particularly sensitive to external conditions.

Alp Muharremoglu is assistant professor of decision, risk and operations at Columbia Business School.

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