Distributions of forecasting errors of forecast combinations: Implications for inventory management

Abstract

Inventory control systems rely on accurate and robust forecasts of future demand to support decisions such as setting of safety stocks. The combination of multiple forecasts is shown to be effective not only in reducing forecast errors, but also in being less sensitive to limitations of a single model. Research on forecast combination has primarily focused on improving accuracy, largely ignoring the overall shape and distribution of forecast errors. Nonetheless, these are essential for managing the level of aversion to risk and uncertainty for companies. This study examines the forecast error distributions of base and combination forecasts and their implications for inventory performance. It explores whether forecast combinations transform the forecast error distribution towards desired properties for safety stock calculations, typically based on the assumption of normally distributed errors and unbiased forecasts. In addition, it considers the similarity between in- and out-of-sample characteristics of such errors and the impact of different lead times. The effects of established combination methods are explored empirically using a representative set of forecasting methods and a dataset of 229 weekly demand series from a leading household and personal care UK manufacturer. Findings suggest that forecast combinations make the in- and out-of-sample behaviour more consistent, requiring less safety stock on average than base forecasts. Furthermore we find that using in-sample empirical error distributions of combined forecasts approximates well the out-of-sample ones, in contrast to base forecasts.