Feature Centralized Multiproduct Newsvendor with Substitution

In this paper we aim to improve the decisions taken in a Centralized Multiproduct Newsvendor problem by making use of information provided by exogenous features while allowing for substitutions between products in case of scarcity. In particular, we build decision rules that minimize the empirical risk and we show that these rules are also optimal to a continuous quadratically constrained quadratic program. Since the historical demands are known, we can compute the optimal order quantities for each period in the training sample. We show how to incorporate this information to approximate the empirical risk minimization problem through a linear program. Moreover, we prove that the optimality gap incurred by this approximation depends on the violations of the optimal direction of the substitution demand flow; if no violations are incurred, the quadratic and linear formulations are equivalent. We rely on dual theory and the well-known kernel trick in order to account for nonlinearities and interactions between features without drastically increasing the dimensionality of the problem. The numerical results show that the approaches proposed in this paper for the Feature Centralized Multiproduct Newsvendor problem with Substitution provide statistically significant performance improvements in comparison with the benchmark methods