Scenario 12.1 - Charm City
Avon Barksdale's operation uses large quantities of prepaid cell phones,on average 500 per week with a standard deviation of 45.The lead time for their own brand of prepaid cell phones is two weeks and they have a lot size of 125 phones.
-Suppose Mr.Barksdale sets his reorder point at 1100 phones.What is his average cell phone inventory?
A)87.5 phones
B)105 phones
C)162.5 phones
D)257.5 phones

Question

Quizplus · Accepted Answer

To determine the average inventory, we need to calculate the safety stock first. 
Safety stock = z * standard deviation of demand during lead time
Assuming a service level of 95% and using a z-score of 1.65, 
Safety stock = 1.65 * 45 = 74.25
Reorder point = average demand during lead time + safety stock
Reorder point = 500*2 + 74.25 = 1074.25

Since the reorder point is set at 1100, the average inventory would be the average demand during lead time plus the difference between reorder point and lot size.
Average inventory = 500*2 + (1100 - 125) / 2 = 1625/2 = 812.5
Therefore, the average cell phone inventory is 812.5, which is closest to option C.