7.4 Consider an item with A = $25; D = 4000 units/yr.; v = $8/unit; L = 1 month;
σ
L
= 100 units; TBS = 6 months; r
= 0.16 $/$/yr.
a. Compute the reorder quantity of the (s, Q) policy using the EOQ.
EOQ =
(
) ( .
)
225 4000 8 0 16
= 395.28
D(TBS) = 2000 units
p
u
≥
(k) = Q/D(TBS) = 395.28/2000 = 0.19764
k = 0.85
s = 4000/12 + 0.85*100 = 418.33
b. Compute the safety factor, safety stock, and reorder point.
Safety factor k = 0.85, safety stock = 0.85*100 = 85 units, reorder point = 418.33
7.5 Consider an item that has an average demand rate that does not change with time. Suppose that demands in
consecutive weeks can be considered as independent, normally distributed variables. Observations of total demand
in each of fifteen weeks are as follows:
89, 102, 107, 146, 155, 64, 78, 122, 78, 119, 76, 80, 60, 115, 86
a.
Estimate the mean and standard deviation of demand in a one-week period and use these values to establish
the reorder point of a continuously reviewed item with L = 1 week. A B
2
value of 0.3 is to be used, and we
have Q = 1000 units, v = $10/unit, r = 0.24 $/$/yr., and D = 5200 units/yr.
Estimated mean = 98.47; estimated standard deviation = 28.52
Compute Qr/DB
2
= 1000*0.24/(5200*0.3) = 0.1538; solving p
u
≥
(k) = 0.1562 gives k = 1.02
s = 98.47 + 28.52*1.02 = 127.56
b.
In actual fact, the above-listed demands were randomly generated from a normal distribution with mean