How to plan prices when you don’t know what’s coming

By Jon Gray

May 31, 2022

Businesses rely on data when pricing their products. Cost of labor and material, seasonality and consumer demographic information all have a part to play. And this pricing puzzle becomes even more complicated when the products are limited in supply and have different customizations to choose from—for example, economy, business or first-class plane tickets. 

Accurately pricing such products is no easy task, and mispricing runs the risk of businesses losing a lot of revenue over a single selling period. 

While most businesses can use sales data from previous years to predict trends, some industries have a harder time determining product demand from year to year.

Take online retailers in the fashion industry. Retailers, like Rue La La, buy and sell brand-new, limited-supply clothing items released by fashion designers each season. While the retailers might know that fashionistas start browsing winter coats as early as August, they don’t know which designer’s coat is going to be the most popular that fashion season. And since demand for each designer’s product may differ from year to year, they can’t rely on past data to accurately adjust prices over the selling season.

Yiwei Chen, assistant professor of statistics, operations and data science at the Fox School, says his research can help businesses optimize their pricing decisions for these customizable products in limited supply. 

“Customers are quite different across many dimensions, but supply for these products is always going to be a limited resource,” says Chen. “That’s the common feature for all these different industries—for the leisure industry, the sports industry and even retail. I thought about whether there could be some challenging issues behind these commonalities, and that’s what motivated my research on revenue management.”

Like businesses in the travel or hospitality industries, fashion retailers have been using traditional algorithms based on network revenue management to price their limited supply, customizable products. But the problem is that these traditional algorithms rely on data from past consumer demand—information that fashion retailers can’t fully rely on—to predict what future prices should be for each product customization. 

In addition, Chen explains that the traditional algorithms become even more inaccurate when there are too many different product customizations or alternatives to choose from.

“The performance of the traditional pricing algorithm suffers from the number of substitutable effects in products. Different pricing combinations can increase exponentially, and when the number is large enough, the projected revenue could be very far below the revenue that companies could have achieved.” 

To help these retailers and other businesses optimize their revenue when facing such a complex pricing puzzle, Chen developed a new algorithm, called the online inverse batch gradient descent (IGD) method. 

Chen’s IGD is not affected by an exponentially increasing number of customizations or alternates available for products. Instead, it estimates how different product customizations—and different pricing options—lead to different ratios of demand within the consumer group. By repeating this process through multiple batches of selling periods, the IGD is able to identify optimal pricing for each product customization, even when demand may initially be unknown.

While fashion retailers are sure to be delighted by the IGD, Chen notes that his algorithm can be used in a wide variety of industry settings, and may be of special interest to particular professional groups.

“Practitioners requiring revenue management knowledge, such as the luxury industry, the retail industry and the sports industry, can benefit from this research,” Chen says. “Those who use machine learning and data analytics may also find technical aspects of the IGD, such as the novel data analytics and algorithms, to be interesting.” 

Ultimately, Chen designed the IGD because he wants to help businesses from different industries make the best pricing decisions possible. Businesses leveraging Chen’s research should see improvements when making adaptive pricing decisions to optimize the revenue of their limited supply of customizable products, even without being able to anticipate what the demand might be.  

The full conceptualization, development and mathematical proofs of the IGD is extensively covered in Chen’s paper, “Network Revenue Management with Online Inverse Batch Gradient Descent Method.”