The Inverse Newsvendor Problem: Choosing an Optimal Demand Portfolio for Capacitated Resources

Abstract
The classical newsvendor problem is one of optimally choosing a level of capacity to respond to a known demand distribution. The inverse newsvendor problem is one of optimally choosing a demand distribution with fixed capacity. The applications of the inverse problem include industrial settings where demand management is relatively less costly than capacity adjustments. Demand distributions are chosen from an opportunity set, which reflects the set of market opportunities for the firm. We analyze the firm's profit as a function of these demand alternatives, provide solution methods and insights, and identify inefficient and dominated distributions. We provide results when the opportunity set is known or only partially known. We extend the results to cases in which there are multiple prioritized customer classes that share the firm's productive capacity. This paper was motivated by an industrial application in a firm selling a semicommodity product into three prioritized industrial sectors. We review the application of our methods to this setting.