If you’re managing products for a national department store chain, should you charge the same price for a pair of shoes in Cleveland and on Madison Avenue? What’s the impact on your gross margin if you mark cashmere sweaters down a week before Christmas versus a week after? And how do you decide when to salvage unsold merchandise to make room for new inventory?
Professor Garrett van Ryzin has spent 15 years developing methods to efficiently compute optimal prices in industries with complicated pricing structures. His research has contributed to a revolution in the airline, hospitality and retail industries, where pricing decisions involve subtle tradeoffs with regard to the timing of each sale.
Van Ryzin’s work merges consumer behavior models with mathematical optimization models. This approach helps you analyze the economic impact of pricing decisions: How will raising or lowering the price affect demand? If you sell a product now versus later, what are the opportunity costs? “We embed all that into a model that lets you say, OK, this decision or this set of prices generates the most revenue,” van Ryzin says.
Large retailers offering thousands of products at hundreds of stores often adopt rules that make pricing easier, such as charging the same price for a given item in every store in the country. And that sort of simplification can make you lose out on opportunity, van Ryzin says. “The product might be too expensive in Florida and too cheap in New York because you’re constraining yourself and can’t make the right adjustments.”
Van Ryzin and his colleagues have developed models that can help companies find prices that maximize profits — even for a very large number of products — in industries where the timing of pricing decisions is crucial. “The economic tradeoffs are difficult to reason out manually because you’re dealing with significant uncertainties about what the demand will be if I change the price,” says van Ryzin. “These models can capture and reason through the tradeoffs in a way that most human decision makers can’t.”
For a large airline, pricing decisions must take into account demand on a point-to-point basis for thousands of flights per day, multiplied by hundreds of possible itineraries and several fare classes. “You have hundreds of thousands of different things that you’re selling at one point in time,” van Ryzin says, “and you’re making decisions about those things every day for 90 days prior to the departure of all these flights. So trying to manage that level of complexity in pricing by purely relying on people to make manual decisions is extremely difficult.”
Traditional optimization models tend to project demand for each flight segment separately. But van Ryzin’s recent work considers the possibility that if you make fares too expensive on one route, consumers might choose a different route. He is also studying strategic consumer behavior — how consumers respond to anticipated price changes. “If you offer different prices over time, that affects their behavior,” he says, “because now instead of buying spontaneously they’re going to wait until you drop the price.”
While the optimization approach doesn’t eliminate human error, it does ensure that you’re making pricing decisions in a consistent way, which makes it easier to figure out if you’re doing something wrong. This method also has a productivity advantage. “Rather than paying lots of people to rack their brains, if you have a system that automates the decision making, you can get away with a lot fewer people,” van Ryzin says.
In the airline industry — the first to adopt dynamic pricing models — this method has generated revenue gains of 2 to 6 percent annually. “Since you’re dealing with revenue, very small refinements in how well you make those decisions can translate into quite a big number,” says van Ryzin. “The fine-tuning is economically significant because there’s a lot of leverage: if you can do 2 to 3 percent better on the top line, that can mean the difference between making a profit or not making a profit.”
Garrett van Ryzin is the Paul M. Montrone Professor of Private Enterprise at Columbia Business School.
Read the Research
"Revenue Management Under a General Discrete Choice Model of Consumer Behavior"