Consider the following product line:

Item i	Demand Di(untis/year)	Vi($/units)	i,1 (untis)	A ($)
1	100	250.00	45	100.00
2	200	30.00	140	100.00
3	300	250.00	210	150.00
4	60	210.00	35	150.00

Inventory carrying charges are 0.12 $/$/year, and the lead time is 3 months. Management feels that a fractional charge of 0.3 for each item short should be considered. Assume that lead time demand is normally distributed.

a. Determine the optimal (s,Q) policy, identifying SS, reorder point, and reorder quantity for each item using the EOQ.

b. After more careful study, management realized that lead time demand is better described

by the Gamma distribution. Adjust the (s,Q) policy in the previous question to account for the actual distribution.

c. Data from the previous 10 cycles give the actual lead time demand for item 3 as follows:

0

32

308

77

60

105

6

81

208

8

What would have been the actual shortage per year under each of the suggested policies?

d. What would be the re-order point for this SKU, if the targeted cycle service level is: a) P₁ = 0.8? and b) P₁ = 0.95?