The Dynamic Price Is Right

Retailers face a range of dilemmas when setting prices for trendy items like consumer electronics gadgets and fashion apparel. A new robust optimization model developed at the University of Maryland’s Robert H. Smith School of Business can help store managers make better decisions about when to offer discounts and how low they should go.

“Time-sensitive products have short selling seasons and long supply lead times, so retailers cannot simply wait until supplies runs low and then order more,” says Smith School professor Zhi-Long Chen, co-author of the study, featured in Manufacturing & Service Operations Management. “No inventory replenishment is possible during the compressed selling season.”

Unlike common household products such as food, beverage, personal hygiene products and home appliances, which have a long product life cycle and hence quite predictable demand, little historical data are available for the latest cameras, smartphones or designer bags. Store managers must make educated guesses instead about demand.

One tool available to maximize profit while facing demand uncertainty is dynamic pricing. “The decision maker needs to sell a given amount of inventory of each product by periodically adjusting prices over the selling season,” the co-authors write.

Additional complexities arise when consumers have substitute choices available side by side on store shelves. “Products do not exist in isolation,” Chen says. “Some products are similar in nature, so price adjustments to one product can effect demand for another.”

Existing dynamic pricing models account for this effect. But they overlook a second type of substitution that occurs over time, when demand shifts for a single product or multiple products during different periods within the selling season. 

Chen and his co-author, Ming Chen at California State University, Long Beach, account for both types of substitution. “Our model is much more practical than most existing multiproduct dynamic pricing models,” they write. “We consider both interproduct and intertemporal demand substitutions.”

The authors also account for real-world factors such as logistical constraints and consumer psychology. For example, most retailers understand that adjusting prices too often or too dramatically can backfire. “Frequent price changes and significant price differences from one period to the next may confuse the consumers who are searching for appropriate prices, not necessarily the lowest ones,” the authors write. “It has long been understood that frequent price changes can even make a retailer appear unfair or dishonest.”

No simple pricing rules work for every case, but the robust optimization model developed by the authors provides a relatively straightforward tool for finding optimal or near-optimal prices for the products over time with a reasonable amount of computation. The model also allows for a relatively wide margin of error, which results from over- or underestimating demand.

“No precise knowledge of the demand bounds is required to use our model to generate satisfactory solutions,” the authors write.

Read more: Robust Dynamic Pricing with Two Substitutable Products is featured in Manufacturing & Service Operations Management.