EXPRESSIONS FOR ITEM FILL RATES IN PERIODIC INVENTORY SYSTEMS

We examine the problem of estimating the item fill rate in a periodic inventory system. We show that the traditional expressions for line it em fill rate, found in many operations management textbooks, perform w ell for high fill rates (above 90%), but they consistently underestima te the true fill rate. The problem of underestimation becomes signific ant as the fill rate falls below 90% and is greatly amplified in cases with very low fill rates (below 50%). We review other more accurate e xpressions for fill rate, discussing their relative merits. We then de velop an exact fill rate expression that is robust for both high and l ow fill rates. We compare the new expression to others found in the li terature via an extensive set of simulation experiments using data tha t reflect actual inventory systems found at Hewlett-Packard. We also e xamine the robustness of the expressions to violations in the underlyi ng assumptions. Finally, we develop an alternative fill rate expressio n that is robust for cases of high demand variability where product re turns are allowed. (C) 1995 John Wiley & Sons, Inc.