41. Fill Rate in a Periodic Review Base Stock System Under Discrete Distributed Demand for the Backordering Case

The fill rate is the fraction of demand that is satisfied directly from shelf. In the literature, this service metric is usually computed by using the traditional approach, which calculates the fill rate as the complement of the quotient between the expected unfulfilled demand and the expected demand per replenishment cycle, instead of directly the expected fraction of fulfilled demand. Furthermore the available methods to estimate the fill rate apply only under specific demand conditions. This paper shows the research gap regarding the estimation procedures to compute the fill rate and suggests: (1) a new exact procedure to compute the traditional approximation for any discrete demand distribution; and (2) a new method to compute the fill rate directly as the fraction of fulfilled demand for any discrete demand distribution. Simulation results show that the latter methods outperform the traditional approach, which underestimates the simulated fill rate, over different demand patterns. This paper focuses on the traditional periodic review, base stock system when backlogged demands are allowed.