Replenishment delays for expensive slow-moving items

Traditional single-item inventory control policies operating under continuous review call for the immediate placement of a replenishment order each time a demand causes the inventory position to drop to or below the order point. In an environment where lead times are small relative to the average time between demands, and holding costs are large relative to other inventory costs, it may be more economical to delay ordering to achieve holding cost savings with little additional risk or cost of shortages. This paper introduces the concept of delayed replenishment orders for expensive items subject to intermittent, unit-sized demands. The inventory system modeled is one with complete back-logging, constant lead times, arbitrary inter-demand distributions, linear carrying costs, and emergency handling of shortages at a premium cost. Results are given for the optimal delay for inter-demand distributions with increasing failure rates. Specific expressions for the optimal delay are given for several commonly used inter-demand distributions.