A Prescriptive Machine-Learning Framework to the Price-Setting Newsvendor Problem

We develop a practical procedure for solving the price-setting newsvendor problem employing (a) statistical estimation methods to recover only three distinct aspects of the demand distribution: the mean, quantile and superquantile, and (b) price optimization methods to estimate the optimal solution. This procedure is asymptotically optimal under mild conditions when the estimators are consistent and the price optimization has a unique global maximum. To estimate the quantities of interest in a data-driven, distribution-free fashion with multidimensional datasets, we investigate estimators based on generalized linear regression (GLR), mixed-quantile regression (MQR), and superquantile regression (SQR). We provide two extensions to these estimators that are of independent interest. First, we propose a novel and exact large-scale decomposition method that is computationally efficient for SQR, and second, we extend the MQR estimation method by relaxing its implicit assumptions of homoscedasticity. Our computational experiments indicate the importance of flexible estimation methods that inherently model heteroscedasticity (with improvements in absolute error of resultant profit as high as 90%), and suggest that quantile-based methods such as MQR and SQR provide better solutions for a wide range of demand distributions, although for certain location-scale demand distributions similar to the Normal distribution, GLR may be preferable.