Question

A firm is reevaluating the safety inventory for an important item, for which the daily demand follows a Normal distribution with mean 100 and standard deviation 10 . The lead time is seven days. The firm uses continuous review and wants to meet a (product) fill rate of 95%. The order quantity is 700.

Which safety inventory level minimizes total relevant costs while meeting the service level constraint?

Answer 1

The safety inventory level that minimizes total relevant costs while meeting the service level constraint is 16.45 units.

Step-by-step explanation:

In order to determine the safety inventory level that minimizes total relevant costs while meeting the service level constraint, we need to calculate the reorder point and the safety stock level.

The reorder point is calculated by multiplying the lead time by the average daily demand:

Reorder point = Lead time × Average daily demand = 7 × 100 = 700

The safety stock level is calculated by multiplying the standard deviation of daily demand by the z-score associated with the desired fill rate:

Safety stock level = Standard deviation of daily demand × Z-score of desired fill rate = 10 × 1.645 (for a 95% fill rate) = 16.45

Therefore, the safety inventory level that minimizes total relevant costs while meeting the service level constraint is 16.45 units.