Analytics for multiperiod risk-averse newsvendor under nonstationary demands

Abstract

Based on the practice of a Chinese food manufacturer, this article develops a predictive and prescriptive analytics research on a multiperiod risk-averse newsvendor problem with nonstationary demands. We start with a predictive analysis that aims to transform the nonstationary demand series into a predictable stationary one, and then develop inventory models for deriving prescriptive decisions based on transformed stationary series. When transforming the nonstationary demand series, we consider three commonly used methods—detrending (DET), differencing (DIT), and percentage change transformations (PCT)—which all effectively convert nonstationary demand series into stationary ones. These methods not only have desired simplicity and interpretability but also provide better predictive performance than the autoregressive integrated moving (ARIMA) process. Moreover, we develop an ensemble of the three transformation methods following the model averaging approach, which provides comparable predictions as the machine learning approaches. When developing prescriptive inventory decisions, we construct dynamic risk-averse newsvendor models for the three methods having different structures, and find that the optimal order quantities under DET and DIT monotonically change as the newsvendor becomes more risk-averse, but the optimal order quantity under PCT may not. Similarly, we also develop a heuristic ensemble of the inventory decisions under the three methods, which can lead to better profit performance. An extensive numerical simulation based on the manufacturer's historical data set shows that the heuristic ensemble inventory decision outperforms the sole decision generated by every transformation method and achieves an average performance improvement up to 92.25%. Several extensions are also considered to confirm the robustness of our findings.