Question

A parts supply store orders a particular item on a weekly basis. The weekly demand is 30 units with a standard deviation of four units. The holding cost is $5 per unit per week and a 90% in-stock probability is desired. What is the store’s average on-hand inventory for this item if lead time is three weeks?

Answer 1

To calculate the average on-hand inventory, multiply the expected demand per week by the lead time and add the safety stock. The safety stock is calculated using the z-score corresponding to the desired in-stock probability.

Step-by-step explanation:

To find the average on-hand inventory, we need to consider the lead time, demand, and desired in-stock probability. The formula to calculate the average on-hand inventory is:

Average On-Hand Inventory = Demand during lead time + Safety stock

For this question, the demand during lead time is the expected demand per week multiplied by the lead time, which is 30 units/week * 3 weeks = 90 units. The safety stock is calculated using the z-score corresponding to the desired in-stock probability. For a 90% in-stock probability, the z-score is approximately 1.28. The formula to calculate the safety stock is:

Safety stock = z-score * standard deviation of demand per week

Given that the standard deviation of demand per week is 4 units, the safety stock is 1.28 * 4 = 5.12 units.

Therefore, the average on-hand inventory is 90 units + 5.12 units = 95.12 units.