Question

The annual demand for a product is 14,500 units. The weekly demand is 279 units with a standard deviation of 85 units. The cost to place an order is $32.00, and the time from ordering to receipt is six weeks. The annual inventory carrying cost is $0.20 per unit. a. Find the reorder point necessary to provide a 95 percent service probability. (Round your answer to the nearest whole number.) Reorder point b. Suppose the production manager is asked to reduce the safety stock of this item by 55 percent. If she does so, what will the new service probability be?

Answer 1

a) 2082 units

b) 0.6923

Step-by-step explanation:

a) Recorder point

Lead time = 6 weeks

Expected demand during this time is 6*279 = 1674 units

Standard deviation = 85 units

Standard deviation for the 6 week period is 85 units* 6^0.5 = 208 units

At the 95% probability level, the z-score is 1.96 (look up on table)

Safety Stock = 1.96×208 units = 408 units

Recorder point = Safety stock + expected demand during the time period so,

1674 + 408 = 2082 units

b) 45% of 408 is about 184, so using the safety stock formula:

Safety Stock = X*180 = 184

X is your z-score which comes out to about 1.02. Look up on your table and correspond to the probability value.

p-value = 0.6923