Intermittent Demand: Estimation and Statistical Properties

Abstract

Intermittent demand patterns are very difficult to forecast and they are, most commonly, associated with spare parts’ requirements. Croston (1972) proved the inappropriateness of single exponential smoothing (SES) in an intermittent demand context and he proposed a method that relies upon separate forecasts of the inter-demand intervals and demand sizes, when demand occurs. His method for forecasting intermittent demand series is increasing in popularity. The method is incorporated in statistical forecasting software packages (e.g. Forecast Pro), and demand planning modules of component based enterprise and manufacturing solutions (e.g. Industrial and Financial Systems-IFS AB). It is also included in integrated real-time sales and operations planning processes (e.g. SAP Advanced Planning & Optimisation-APO 4.0). An earlier paper (Syntetos and Boylan 2001) showed that there is scope for improving the accuracy of Croston’s method. Since then two bias-corrected Croston procedures have been proposed in the academic literature that aim at advancing the practice of intermittent demand forecasting. In this paper, these estimators as well as Croston’s method and SES are presented and analysed in terms of the following statistical properties: (i) their bias (or the lack of it); and (ii) the variance of the related estimates (i.e. the sampling error of the mean). Detailed derivations are offered along with a thorough discussion of the underlying assumptions and their plausibility. As such, we hope that our contribution may constitute a point of reference for further analytical work in this area as well as facilitate a better understanding of issues related to modelling intermittent demands.