Scenario 9.5
Cranium,Inc. ,purchases term papers from an overseas supplier under a continuous review system.The average demand for a popular mode is 300 units a day with a standard deviation of 30 units a day.It costs $60 to process each order and there is a five-day lead-time.The holding cost for a paper is $0.25 per year and the company policy is to maintain a 98% service level.Cranium operates 200 days per year.A normal distribution table is appended to this exam.
-Use the information in Scenario 9.5.What combination of changes in lead-time and service level would result in exactly the same level of safety stock as indicated in the table?

Question

Quizplus · Accepted Answer

To calculate the safety stock, we first need to find the reorder point:

Reorder point = (average demand per day x lead time) + safety stock

Safety stock = z-score x standard deviation of demand during lead time.

Using the normal distribution table, we find that the z-score for a 98% service level is 2.05.

Reorder point = (300 x 5) + (2.05 x 30 x sqrt(5))
Reorder point = 1500 + 46.22
Reorder point = 1546.22

Now we can calculate the safety stock:

Safety stock = 2.05 x 30 x sqrt(5)
Safety stock = 46.22

To find the combination of lead time and service level that results in the same safety stock, we can use the formula:

Safety stock = z-score x standard deviation x sqrt(new lead time)

Let's use choice C as an example:

New lead time = 20.54 days
z-score = 1.75 (from the normal distribution table for a 90% service level)
Standard deviation = 30

Safety stock = 1.75 x 30 x sqrt(20.54)
Safety stock = 45.98

This is very close to the original safety stock of 46.22, so we can conclude that choice C is the best option.

Scenario 9.5 Cranium,Inc. ,Purchases Term Papers from an Overseas Supplier Under a Under