Risk-Aware Decision-Focused Demand Forecasting for Multi-Channel Inventory Optimization under Promotion and Stock-Out Constraints

Abstract

Retail replenishment couples a forecasting problem with a constrained stochastic allocation problem, yet forecasters are still trained to minimise statistical error rather than the cost of the decisions they induce. The mismatch is aggravated by three features of real multi-channel retailing: channels of one region draw on a shared, capacity-limited stock; promotions inflate both demand and the penalty of a stock-out; and observed sales are censored precisely when a stock-out occurs. We propose RA-DFL, which trains a probabilistic forecaster through a differentiable multi-channel allocation layer that minimises a convex combination of expected cost and conditional value-at-risk under a shared capacity, a fill-rate requirement and omnichannel recourse. The layer solves the recourse stage in closed form and is optimised by a smoothed projected-gradient scheme with an exact line search, attaining a mean optimality gap of 0.32% against derivative-free solvers. A censoring-consistent decision loss removes the spurious overage signal created by truncated sales, and the forecaster emits a state-conditional risk level. On the real M5 (Walmart) and Stallion distribution panels we first establish a negative result: attaching a CVaR objective to strong predict-then-optimise forecasts raises realised cost by 9.7% and 11.2% respectively. Training through the risk-aware decision instead lowers mean cost by 3.7% and pool-level tail cost by 0.2% against the strongest predict-then-optimise pipeline on M5, and dominates its mean-risk frontier. Ablations show the censoring component helps significantly on the panel with 12% censoring and not on the panel with 1% censoring, evidence that it acts through the intended mechanism.