Question

(7 points)

4. Suppose a store’s towel inventory is managed with a periodic review system and the vendor visits every week (reorder period = 7 days) to check the inventory and make an order. Once the order is placed, the lead time is three days. Suppose that over the reorder period plus lead time the demand for a popular item averages 80 with a standard deviation of 10. If a service level of 99% is desired and 30 units are on hand, then how many of the popular item should be ordered?

Number to order = ________

Answer 1

SOLUTION AND EXPLANANTION:

Let us define :Protection period” = P = Reorder period + Lead time = 7 + 3 days = 10 days

Z value for service level of 99% as per Z table= 2.33

Demand during protection period = = D = 80

Standard deviation of demand during Protection period = Sd = 10

Safety stock during protection period =
`Zxalue $*$ Sd $*$ Square root ( $P$ )`

`2.33 * 10 * \text { square root }(10)`
`23.3 * 3.162=73.67`

Therefore,

Gross quantity to be ordered = Demand during protection period + Safety stock during protection period = 80 +73.67 = 153.67

However, number of items already in hand = 30 units

Hence,

Net quantity to be ordered = Gross quantity to be ordered – Number of items already in hand = 153.67 – 30 = 123.67 ( 124 rounded to nearest whole number)