Question

The annual demand for a product is 14,200 units. The weekly demand is 273 units with a standard deviation of 95 units. The cost to place an order is $32.00, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.10 per unit. a. Find the reorder point necessary to provide a 95 percent service probability. (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Round "z" value to 2 decimal places.) Reorder point b. Suppose the production manager is asked to reduce the safety stock of this item by 45 percent. If she does so, what will the new service probability be? (Use Excel's NORMSDIST() function to find the correct probability for your computed Z-value. Round "z" value to 2 decimal places and final answer to 1 decimal place.) Service probability %

Answer 1

(A) The reorder point necessary to provide a 95 percent service probability is 1406 units

(B) If the production manager reduce the safety stock of the item by 45%, the new service probability will be 81.8%

Step-by-step explanation:

(A)

Formula to calculate reorder point (R) = d * L + z * SD * √L

Z value for 95% probability = 1.65 from standard normal distribution z table

Reorder point

= 273 * 4 + 1.65 * 95 * √4

= 1092 + 313.5

= 1406 units

(B)

Safety stock = 313.5 * (1- 0.45) = 172.425

To calculate the service probability we need to calculate the z value

Z = SS / Standard deviation of lead time demand

Z = 172.425 / 190 = 0.9075 ~ 0.91

The probability from standard normal distribution table for the obtained z value is 0.8186

Probability = 0.818 or 81.8%