A Dynamic Pricing Model for Non-Clairvoyants

Setting prices for trendy items with limited sales history requires a certain amount of guesswork — unless you're clairvoyant. Then you can look into the future and anticipate demand. But for everyone else, professor Zhi-Long Chen at the University of Maryland's Robert H. Smith School of Business and two co-authors have developed a dynamic pricing model that allows retailers to "minimize maximum regret."

The pricing standard, used by marketers since 1951 in situations of high uncertainty, assures that actual revenue remains close to the ideal sales target that clairvoyant analysts could hit.

"We consider a dynamic pricing problem where the decision maker is a retailer who sells a given inventory of a single product over a short selling season consisting of two time periods, a regular sales period and a clearance period," the authors write in their paper, featured in Production and Operations Management. "There is insufficient time to replenish inventory during this season, hence sales are made entirely from inventory."

The scenario occurs with products with a short life cycle such as fashion apparel, some consumer electronics, and some toys. Unlike items with a long life cycle — such as home appliances and staple foods — retailers who sell items with a short life cycle don’t have much sales data to draw upon.

Decision makers sometimes rely on sales data from the same product family to estimate demand scenarios. But Chen and his co-authors consider cases of even greater uncertainty, where the wisest approach is to identify the lower and upper bound on demand at given price points and to minimize the maximum regret.

"Regret is the difference between the total revenue of a clairvoyant pricing solution and that of the actual solution used by the decision maker," the authors write.

In their computational study, they tested the effectiveness of two models. "We consider a dynamic model where the decision maker chooses the price for each period contingent on the remaining inventory at the beginning of the period, and a static model where the decision maker chooses the prices for both periods at the beginning of the first period," they write.

The authors also benchmarked their results against classical pricing solutions. After crunching the numbers and considering maximum regret, average relative regret, variability and risk measures, the clear winner was the dynamic model. "Further, our dynamic model generates a total expected revenue which closely approximates that of a maximum expected revenue approach," they conclude.

Read more: Dynamic Pricing to Minimize Maximum Regret is featured in Production and Operations Management.