A Robust Price-Setting Newsvendor Problem

1 Sep 2020

Operations Research and Operations Management

Rongchuan He, Ye Lu

Published in Production and Operations Management, September 2020

In a competitive market, demand and revenue are largely affected by a firm’s pricing strategy. Meanwhile, as demand is price-dependent and stochastic, a firm needs to coordinate pricing and inventory decisions to better match demand with supply. This is especially important for perishable products because leftover inventories are disposed of without any value while unsatisfied demand may lose customers’ goodwill. However, making joint decisions is not an easy task because the demand as a function of price is usually not completely known. In reality, a retailer may have very limited information on a demand model because a retailer who has exercised only a few prices does not have sufficient information to accurately estimate a demand model, which creates a big challenge on making the pricing and inventory decisions.

In this research, Professor Ye Lu of the Department of Management Sciences, and co-author Rongchuan He, Associate Professor Department of Management Science University of Science and Technology of China, overcome this difficulty by assuming that the expected demand on a few exercised price points is known. The retailer makes price and inventory decisions to minimize the maximum regret, which is defined as the difference between the expected profit based on limited demand information and that based on complete demand information.

“We show that this robust optimization problem can be reduced to a one-dimensional optimization problem, and we derive the optimal price and inventory decisions. This enables our solution to be easily implemented in practice,” says Ye Lu.

“We also provide a demand learning policy that can reduce the regret. Extensive numerical studies show that our method has a great performance on profitability, which dominates that of the regression method.”

In summary, this research provides a practical and efficient way for retailers to optimize joint pricing and inventory decisions without knowing the complete demand information.