Analytics for Multi-period Risk-Averse Newsvendor Under Nonstationary Demands

Based on the practice of a Chinese food manufacturer, this paper presents a predictive-prescriptive analytics framework for the multi-period risk-averse newsvendor problem with nonstationary demands. We commence with predictive analysis aimed at converting nonstationary demand series into predictable stationary ones, then develop inventory models to derive prescriptive decisions based on the transformed stationary data. For demand transformation, we examine three widely adopted techniques—detrending (DET), differencing (DIT), and percentage change transformation (PCT)—all of which reliably render nonstationary demand stationary. These methods not only offer desirable simplicity and interpretability but also outperform the ARIMA methodology in predictive accuracy. Moreover, we propose an ensemble of the three transformations via a model averaging approach, achieving predictive performance comparable to state-of-the-art machine learning methods. For prescriptive inventory decisions, we formulate tailored dynamic risk-averse newsvendor models to align with the distinct structures of the three transformations. Our analysis reveals that optimal order quantities under DET and DIT exhibit monotonicity with increasing risk aversion of the newsvendor, while those under PCT do not necessarily follow this pattern. Similarly, we develop a heuristic ensemble of inventory decisions from the three methods, which delivers superior profit performance. Extensive numerical simulations using the manufacturer’s historical dataset demonstrate that the heuristic ensemble decision outperforms individual decisions derived from each transformation method, achieving an average performance improvement of up to 92.25%. Several extensions are also considered to validate the robustness of our results.