A conditional effect of autocorrelated demand on safety stock determination

Fotopoulos, Wang and Rao (FWR) proposed a useful method for determining the size of safety stocks when daily demand is autocorrelated and lead time follows an arbitrary distribution. They also presented a numerical illustration based on the proposed method in order to quantify the independent effect of autocorrelation on safety stock requirements. The numerical illustration manipulated both the lead time distribution and the variability of the random error term in the AR(1) demand process, as well as the strength of the autocorrelation parameter. The findings demonstrated that substantial error results when autocorrelation is ignored in the determination of safety stocks. Note, however, that their operationalization of the AR(1) demand process forced the mean and variance of daily demands to differ across ‘treatment conditions’ in their illustration. That is, the mean and the variance of daily demands changed whenever the value of the autocorrelation parameter (b) changed. As an extension to the FWR paper, this investigation holds the mean and the variance of daily demands constant for all treatment conditions. This is based on the assumption that the inventory manager uses historical data to arrive at an accurate estimate of the mean and the variance of daily demand. While in this case the presence of autocorrelated demand would still be expected to necessitate increased levels of safety stock, the magnitude of that conditional effect might be expected to differ from the independent effect examined in FWR. As a result, from a managerial perspective, the following question is most germane: What is the extent of error incurred in setting safety stock if autocorrelated demand goes undetected or is ignored?