Question

The annual demand for a product is 15,900 units. The weekly demand is 306 units with a standard deviation of 80 units. The cost to place an order is $33.50, and the time from ordering to receipt is eight weeks. The annual inventory carrying cost is $0.10 per unit.

a. Find the reorder point necessary to provide a 99 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 60 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

Answer to question   a :

Lead time = 8 weeks

Z value for 99 percent service probability = NORMSINV ( 0.99) = 2.326

Safety stock = Z value x standard deviation of weekly demand x square root ( lead time) = 2.326x 80 x square root( 8) =2.326x80x2.828=526.23

Reorder point = Average weekly demand x Lead time + safety stock = 306 x 8 + 526.23 = 2448 + 526.23 = 2974.23

Answer to question b :

Revised safety stock = ( 1 – 0.6) x 526.23 = 0.4 x 526.23 = 210.49

Let new z value = Z1

Therefore ,

Z1 x Standard deviation of weekly demand x Square root ( Lead time ) = 210.49

Or, Z1 x 80 x Square root ( 8) = 210.49

Or, Z1 x 80 x 2.828 = 210.49

Or, Z1 = 210.49 / ( 80 X 2.828) =0.930

Corresponding probability for Z1 = 0.93 as derived from Z table will be 0.8238 or 82.4%

Answer : Service probability 82.4%