Question

Store A orders on a weekly basis. Its weekly demand is 50 units with a standard deviation of five units. The holding cost is $10 per unit per week and a 0.99 in-stock probablity is desired. What is Store A's average on hand imventory if lead time is five weeks?

A. 285.40
B. 2500.00
C. 28.54
D. 25000 .

Answer 1

To calculate Store A's average on-hand inventory, we can use the formula: Average On-Hand Inventory = (Demand * Lead Time) + (Z-Score * Standard Deviation * Square Root of Lead Time). Using the provided values, the average on-hand inventory is approximately 273.36 units.

Step-by-step explanation:

To calculate Store A's average on-hand inventory, we need to consider the following:

• Demand: The weekly demand for Store A is 50 units with a standard deviation of 5 units.
• Lead Time: The lead time is 5 weeks.
• In-Stock Probability: The desired in-stock probability is 0.99.
• Holding Cost: The holding cost is $10 per unit per week.

To calculate the average on-hand inventory, we can use the following formula:

Average On-Hand Inventory = (Demand * Lead Time) + (Z-Score * Standard Deviation * Square Root of Lead Time)

Using a Z-Score of 2.33 (corresponding to a 0.99 in-stock probability), we can calculate the average on-hand inventory as follows:

Average On-Hand Inventory = (50 * 5) + (2.33 * 5 * Square Root of 5) = 250 + (2.33 * 5 * 2.236) = 250 + 23.36 = 273.36

Therefore, Store A's average on-hand inventory, when the lead time is five weeks, is approximately 273.36 units.