Intermittent Demand Forecasting

7Forecasting the Variance of Demand and Forecast Error

7.1 Introduction

In Chapter 4, we saw that if demand is Poisson, then its distribution is completely characterised by its mean. In Chapter 5, we found that the negative binomial and the normal distributions are not fully characterised by the mean alone, but are completely specified by the mean and variance.

We have already seen, in Chapter 6, how the mean value may be forecasted for intermittent demand series. In this chapter, we turn our attention to forecasting the variance of demand and the variance of forecast error. In inventory management, such forecasts are needed not only over a single period of time but over the whole protection interval.

Throughout the chapter, we assume that the demand variance is unknown. We begin our discussion by assuming that the mean demand is known. This is not a realistic assumption, but it allows us to conduct a careful analysis of how the variance of demand per unit time can be translated to the variance of demand over the protection interval. We then proceed to the more realistic case where the mean is forecasted, and there is a need to estimate the variance of forecast error rather than the variance of demand. In Section 7.4, we analyse the case of variable lead times. Finally, we draw together the main conclusions of the chapter.

7.2 Mean Known, Variance Unknown

In this section, we analyse the hypothetical situation where the mean is known but the variance is not and must be forecasted. ...