Constructing decision rules for multiproduct newsvendors: An integrated estimation-and-optimization framework

In this paper, we develop an integrated estimation-and-optimization framework for constructing decisions rules for the order quantities of multiple perishable products. The framework accounts for substitution in case of scarcity by providing models incorporating substitution rates, received as input. Specifically, it builds decision rules minimizing the empirical risk and accommodates multiple classes of functions, including those leveraging exogenous features. We provide a continuous reformulation of the empirical risk minimization problem that is quadratic in the decision rules. In addition, we show how to incorporate information from in-sample optimal decisions to derive a linear approximation to it. The dual of this approximation allows us to estimate decision rules that exploit nonlinearities and interactions of features. The numerical results on real and simulated datasets suggest that decision rules computed within the proposed integrated framework have the potential to outperform separated estimation and optimization methods. In particular, larger improvements are obtained under low service levels requirements or high volatility of the demands. Furthermore, we empirically observe that information provided by exogenous features may be particularly significant in the presence of large fluctuations of the demand.