Stochastic Inventory Optimization with Coherent Risk Measures: A Decision-Theoretic Framework for Probabilistic Forecasting and Constrained Optimization

Each year, inventory decisions made under demand uncertainty generate substantial economic losses, reflecting a persistent disconnect between forecasting models and the operational decisions they are intended to support. This paper addresses this gap by proposing a Decision Intelligence Framework that unifies three components typically treated in isolation: probabilistic demand forecasting via gradient boosting quantile regression, constrained newsvendor optimization under capacity and budget constraints, and coherent tail risk evaluation using Conditional Value-at-Risk (CVaR95). We establish a central theoretical result showing that calibrated quantile forecasts are mathematically equivalent to optimal newsvendor solutions, providing a rigorous decision-theoretic foundation linking probabilistic forecasting and inventory control. The framework is evaluated on the UCI Online Retail dataset (2010–2011), aggregated to daily demand at the country–SKU level and densified to a daily panel by treating missing transaction days as zero demand. Relative to median-based (P50) policies, P90 policies reduce tail risk (CVaR95) by 26.7% under empirical residual bootstrap, increase cycle service levels from 44.4% to 89.5%, and reduce mean cost by 48.7% (non-overlapping bootstrap CIs for CVaR95). A lognormal stress test shows larger reductions (72.3%), and a CV sweep confirms monotone gains in this setting.