Forecasting of lead-time demand variance: Implications for safety stock calculations

Lead-time demand forecasting constitutes the backbone of inventory control. Although there has been a considerable amount of research on forecasting the mean lead-time demand, less has centered around forecasting lead-time demand variance, especially in the case of stochastic lead-times. This represents an important gap in the literature, given that safety stock calculations rely explicitly on the lead-time demand variance (or equivalently the variance of the lead-time demand forecast error for unbiased estimators). We bridge this gap by exploring the viability of three strategies to estimate the variance of the lead-time demand forecast error under stochastic lead-times: (1) aggregating the per period variance of forecast errors over the lead-time, which is the classical approach; (2) considering the variance of the aggregated (over the lead-time) forecast error; (3) considering the variance of the forecast errors resulting from temporally aggregated (over the lead-time length) demand. Analytical results are derived for a first order autoregressive moving average ARMA(1,1) demand process for both a single exponential smoothing and the minimum mean squared error forecasting method. A numerical investigation assesses the effects of demand autocorrelation and lead-time variability on the accuracy of each strategy, and the conditions under which one outperforms the others. The results show that the classical strategy presented in textbooks appears to be the least accurate one, except for cases with a high negative demand autocorrelation. An analysis of the inventory control performance also reveals that the classical strategy often leads to higher inventory costs and lower service levels for positive autocorrelation.