Expressions for item fill rates in periodic inventory systems

The authors examine the problem of estimating the item fill rate in a periodic inventory system. They show that the traditional expressions for line item fill rate, found in many operations management textbooks, perform well for high fill rates (above 90%), but they consistently underestimate the true fill rate. the problem of underestimation becomes significant as the fill rate falls below 90% and is greatly amplified in cases with very low fill rates (below 50%). The authors review other more accurate expressions for fill rate, discussing their relative merits. They then develop an exact fill rate expression that is robust for both high and low fill rates. The authors compare the new expression to others found in the literature via an extensive set of simulation experiments using data that reflect actual inventory systems found at Hewlett-Packard. They also examine the robustness of the expressions to violations in the underlying assumptions. Finally, the authors develop an alternative fill rate expression that is robust for cases of high demand variability where product returns are allowed.