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.

a. 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?
b. A European supplier has offered to deliver washing machines with a guaranteed lead time of 1 week but at a cost of 210 euros. How much safety stock is required with this supplier? What is the annual cost of holding this safety stock?
c. Should Karstadt stay with the Chinese supplier? (Hint: Compare the increase in holding cost v. the decrease in material cost over the course of one year; assume 50 weeks in a year)

Answer 1

To calculate the safety stock required, use the formula: Safety Stock = Z * Standard Deviation * Square Root of Lead Time. For part a, the safety stock required with the Chinese supplier is 30.24. the annual cost of holding the safety stock with the Chinese supplier is 1,512 euros. For part b, no safety stock is required with the European supplier due to the guaranteed lead time. for part c, compare the increase in holding cost with the decrease in material cost over one year to determine if Karstadt should stay with the Chinese supplier.

Step-by-step explanation:

To calculate the safety stock required, we need to use the formula: Safety Stock = Z * Standard Deviation * Square Root of Lead Time. for part a, the lead time for the Chinese supplier is normally distributed with a mean of nine weeks and a standard deviation of six weeks. Since we want a 99% service level, the Z value is 2.33. After substituting the values into the formula, the safety stock required is: Safety Stock = 2.33 * 6 * sqrt(9) = 30.24. the annual cost of holding safety stock can be calculated using the formula: Annual Cost = Safety Stock * Average Cost * Inventory Holding Cost Rate. Substituting the values, the annual cost of holding the safety stock with the Chinese supplier is: Annual Cost = 30.24 * 200 * 0.25 = 1,512 euros. for part b, the lead time for the European supplier is guaranteed at one week, so the safety stock required is zero.

For part c, we need to compare the increase in holding cost with the decrease in material cost over the course of one year. To do this, we can calculate the annual cost of holding the safety stock for the Chinese supplier, as we did in part a, and subtract the annual cost of holding safety stock for the European supplier (which is zero). If the difference is positive, it means it is more cost-effective to stay with the Chinese supplier. If the difference is negative, it means it is more cost-effective to switch to the European supplier.