A simple and robust model for computing the service level impact of lot sizes in continuous and lumpy demand contexts

Lot sizes that cover material requirements for more than two periods’ demand have a built-in service level impact. The lot sizes act as a buffer for variations in demand for every period (week) but the last. However, procedures for including the service level effect of the lot size in the lot-sizing decision have not been developed. This article develops a very simple but robust mathematical model for computing the service level guaranteed by any lot size, Q, in both continuous and lumpy demand contexts. The model turns out to be a very simple mathematical expression involving the lot size, Q, the number of periods of demand covered by the lot size, n, and the standard deviation of the demand, σ. The results show that the model’s prediction of the service level generated by any given lot size, Q, was very precise and reliable. The performance of the model was excellent even for cases where demand variability, as measured by the standard deviation, was high. Moreover, the built-in service level of lot sizes turned out to be high, ranging from 95% to 100%.