Evaluating Safety Inventory For Slow-Moving Items

Devise a procedure for evaluating safety inventory for slow-moving items whose demand can be approximated using a Poisson distribution.

For slow-moving items, the normal distribution is not a good estimation for the demand distribution. A better approach is to use the Poisson distribution with demand arriving at a rate D. In such a setting (Q, r) policies are known to be optimal. Under a (Q, r) policy, an order is placed whenever the inventory position drops to or below the reorder point r, and the order size is nQ,

where n is the number of batches of size Q required to raise the inventory position to be in the interval (r, r + Q).

For the Poisson distribution, given a constant lead time L, the average demand over the lead time is given by LD, and the variance of demand over the lead time is given by

Efficient algorithms to obtain the Q and r are given by Federgruen and Zheng (1992). The results we present are based on Gallego (1992), who has given effective heuristics to solve the problem. If H is the holding cost per unit per unit time, p is the fixed shortage cost per unit per unit time, and S is the fixed order cost per batch, Gallego suggests a batch size of Q*, where

He shows that the use of batch size Q* results in a cost that is no more than 7 percent from the optimal batch size. The reorder point r* can be obtained using a procedure discussed by Federgruen and Zheng (1992). The long-run average cost C(r, Q) of an (r, Q) policy when demand is Poisson is given by

The reorder point r is obtained by inserting the batch size Q* from Equation 12.27 into Equation 12.28 and searching for the value, 'r' that minimizes the cost C(r, Q*). Given that C(r, Q*) is unimodal [as shown by Federgruen and Zheng (1992)], r can be obtained using a binary search over the integers.