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%

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