Dynamic Inventory Control with Covariates : Risk Constraints, Regularization, and Folding-horizon Plan

Starting with historical demand trajectories of similar products and their covariate information, we develop a data-driven approach to dynamic inventory planning for new products. Specifically, we employ non-parametric machine learning methods to model the uncertain future demand and incorporate the newly available demand information in a folding-horizon manner. To alleviate the issues of sampling errors and model misspecification commonly seen in data-driven decision making, we introduce profit-risk constraints to regularize the prescription of order quantities. The model with profit risk constraints and information update brings computational and analytical challenges, e.g., issues of time-inconsistency. To address the computational challenge pertaining to high dimensionality, we have identified effective dominating rules that help greatly reduce the search space and speed up the computation. To analyze the performance of the proposed approach and address the challenge pertaining to time-inconsistency, we develop a time-consistent folding-horizon model, against which we benchmark the original, profit risk-constrained model with folding-horizon planning. We are able to establish the asymptotic optimality of the original model with respect to the sample size, i.e., the number of similar products. To assess the real performance of our approach, we have conducted extensive numerical experiments with real and synthetic data. Our approach demonstrates consistently superior performance than the existing approaches in the literature, and the superior performance is primarily attributed to the incorporation of profit-risk constraints