On the Fill Rate Approximations in Periodic Review Systems for Discrete Demand

Abstract

One of the most common criteria used to measure the performance of a inventory system is the fill rate. In the literature we find two easy-to-compute approaches: the traditional and the Hadley-Whitin approximations, but unfortunately they only apply for normally distributed demand. In practice stock managers can use any of them, even when demand is not normal or discrete. This paper assesses the performance of these approximations in a periodic inventory system for different demand scenarios such as intermittent, erratic, lumpy and smooth. However, in the discrete context, simulation results show that both approximations present a significant bias including negative fill rate values. In keeping with these results, we re-formulate both approximations to be able to cope with any discrete demand distribution and asses their performance. In this case, simulation results show that the proposed discrete formulation of the Hadley-Whitin approximation seems to avoid the systematic bias observed before.