On the selection of fill rate estimation method to determine the optimal base stock in periodic review systems

The fill rate is defined as the fraction of demand that is directly satisfied with the on-hand stock. Despite its definition is apparently simple, in the literature we find different interpretations and consequently different methods to compute it. In the majority of related works, the fill rate is computed by using the traditional approximation, which calculates the fill rate in terms of units short instead of computing directly the satisfied demand. However, the traditional approximation can lead to underestimate the real value of the fill rate under some conditions. The underestimation behaviour has important consequences when the optimal parameters of the policy are determined applying the traditional approach. However, in the literature the majority of authors derive approximate expressions to compute the fill rate based on it. This paper assesses when approximate methods provide accurate results when the stock level is defined given a target fill rate in periodic review systems. We design a large experiment and analyze the results using statistical techniques. The main result of this work can be used as a reference framework to help managers to decide the most efficient method to determine the stock level given a target fill rate.