General Hospital uses disposable diapers at a rate of 200 per day,with a standard deviation of 20.To place and receive a replenishment of diapers from the third-party logistics provider typically takes three days.The hospital never wants to run out of diapers,so it holds enough safety stock to ensure 99.9 percent availability.Hospital purchasing managers order diapers along with other items every 30 days.It is time to place an order,and there are 800 diapers on hand.How many units should be ordered? (Pick the closest answer.)

Question

Quizplus · Accepted Answer

First, we need to calculate the reorder point, which is the demand during lead time plus safety stock. 
Demand during lead time = 200 diapers per day x 3 days lead time = 600 diapers.
Safety stock = (z-score for 99.9% availability x standard deviation of daily demand x square root of lead time) = (3.090 x 20 x sqrt(3)) = 106.1 diapers (rounded up to 107).
Reorder point = 600 + 107 = 707 diapers.
Next, we need to calculate the order quantity. Total demand for 30 days = 200 diapers per day x 30 days = 6,000 diapers. Adding the reorder point, we get 6,707 diapers. Subtracting the current inventory of 800 diapers, we get 5,907 diapers. However, since the order is for a specific number of packages of diapers and not individual diapers, we need to round up to the next full package, which contains 96 diapers. Therefore, the order quantity is 5,852 diapers (rounded up from 5,851.46).

General Hospital Uses Disposable Diapers at a Rate of 200