The first part of the article presented the essence of the difference in defining and calculating the service level determining stock availability in probabilistic terms (POP – probability of satisfying demand) and quantitative terms (SIR – stock-out rate/fill rate). For illustrative purposes, these issues were presented for a case where the demand distribution can be described by a Poisson distribution.
This article develops this issue, and the problem will be presented for a normal distribution, which is applicable in the case of fast-moving goods. This distribution is also commonly used in various types of applications and IT systems supporting inventory management. As indicated in earlier publications in this field, the key value necessary to determine the SIR indicator is the expected number of shortages in the inventory replenishment cycle. In the first part of the article, the formula based on summing the products of the probabilities of the occurrence of specific demand quantities in the inventory replenishment cycle p(PT), exceeding the stock level available at the beginning of the cycle (ZI) by the differences between them and the ZI stock, was used to calculate the expected number of shortages […].
The presented analysis results indicate the significance of errors made when defining and interpreting the service level related to inventory management. The most common error is calculating safety stock based on formulas appropriate for a service level defined as the probability of satisfying demand, while – in the assumptions – the service level was intended to mean the fill rate. The consequence of this error is an unnecessary overestimation of this indicator (although usually slight and difficult to notice), at the cost of a significant increase in safety stock. Committing an error of the second type (determining safety stock based on formulas appropriate for a service level defined as the fill rate, while the service level was intended to mean the probability of satisfying demand) consequently means a lower than assumed actual service level.
The article comes from the “Logistyka” magazine 1/2011.