Question

Weekly demand for private label washing machines at Karstadt, a German department store chain, is normally distributed with a mean of 500 and standard deviation of 300. Karstadt’s annual inventory holding cost rate is 25% and they aim for 99% CSL on washing machines.Karstatdt currently has a supply source in China that delivers these machines at a cost of 200 euros. The lead time required by the supplier is normally distributed with a mean of nine weeks and a standard deviation of six weeks. How much is the safety stock required? What is the annual cost of holding this safety stock?

Answer 1

Karstadt must maintain a safety stock of approximately 2097 washing machines to achieve a 99% CSL, with an annual holding cost of 104,850 euros.

Step-by-step explanation:

To calculate the safety stock required for Karstadt's washing machine inventory, we must determine the z-score associated with a 99% Cycle Service Level (CSL). The z-score that corresponds to a 99% confidence level is approximately 2.33. To calculate safety stock, we use the equation: Safety Stock = z-score x Standard Deviation of Lead Time x Square Root of Average Lead Time.

The average demand during the lead time is the product of the average weekly demand and the average lead time: mean weekly demand x mean lead time (500 units/week x 9 weeks = 4500 units).

The standard deviation of the demand during the lead time is the product of the standard deviation of weekly demand and the square root of lead time: standard deviation of weekly demand x sqrt(mean lead time) (300 units/week x sqrt(9 weeks) = 900 units).

Thus, the safety stock is 2.33 x 900 units = 2097 units.

To calculate the annual cost of holding the safety stock, we use: Annual Holding Cost = Safety Stock x Cost per Unit x Holding Cost Rate. For Karstadt, this is 2097 units x 200 euros/unit x 25% = 104,850 euros.