The order and volume fill rates in inventory control systems

This paper differentiates between an order (line) fill rate and a volume fill rate and specifies their performance for different inventory control systems. When the focus is on filling complete customer orders rather than total demanded quantity the order fill rate would be the preferred service level measure. The main result shows how the order and volume fill rates are related in magnitude. Earlier results derived for a single-item, single-stage, continuous review inventory system with backordering and constant lead times controlled by a base-stock policy are extended in different directions. Demand is initially assumed to be generated by a compound renewal process. An important generalization then concerns the class of customer order-size distributions, i.e. compounding distributions, with increasing failure rate for which the volume fill rate always exceeds the order fill rate. Other extensions consider more general inventory control review policies with backordering, as well as some relations between service measures. A particularly important result in the paper concerns an alternative service measure, the customer order fill rate, and shows how this measure always exceeds the other two more well-known service measures, viz. the order fill rate and the volume fill rate.