Fill rates of single-stage and multistage supply systems

A supply system's fill rate is the fraction of demand that is met from on-hand inventory. This paper presents formulas for the fill rate of periodic review supply systems that use base-stock-level policies. The first part of the paper contains fill-rate formulas for a single-stage system and general distributions of demand. When demand is normally distributed, an exact expression uses only the standard normal distribution and density functions, and a good approximation uses only the standard normal distribution function. The second part of the paper derives the probability distribution of the finished goods inventory level for serial systems with buffer inventories between stages. The distribution leads to fill-rate formulas and the conclusion that shorter supply chains have higher fill rates.