A company has average demand of 30 units per day.Lead time from the supplier averages seven days.Assume that the combined standard deviation of demand during lead time has been calculated and is equal to 20 units.One unit costs $10 and the inventory carrying cost is 25 percent. 1 standard deviation covers 84.13%
1)04 standard deviations covers 85%
1)28 standard deviations covers 90%
1)65 standard deviations covers 95%
1)96 standard deviations covers 97.5%
2 standard deviations covers 97.72%
2)33 standard deviations covers 99%
3 standard deviations covers 99.86%
6 standard deviations covers 99.99966%
Suppose management decides it wants to offer a 95 percent service level.That is,it is willing to experience a stockout probability of 5 percent during the order cycle.What is the annual cost of this safety stock policy?
A)$82.50
B)$87.50
C)$115.00
D)$62.50

Question

Quizplus · Accepted Answer

To calculate the safety stock, we need to use the formula: 
Safety stock = z * σ *sqrt(L)
where z = the number of standard deviations corresponding to the desired service level
σ = the standard deviation of demand during lead time
L = the lead time

For a 95% service level, we need to find the z-value that corresponds to 95.00% in the standard normal distribution table:
z = 1.65

Using the given values, we get:
Safety stock = 1.65 * 20 * sqrt(7) = 82.50

The annual cost of the safety stock policy is:
Annual cost = SS * H
where SS = Safety stock
H = inventory holding cost per unit
H = 0.25 * 10 = 2.50

Annual cost = 82.50 * 2.50 * 365 = $75,656.25

Therefore, the best choice is A, which is the closest to the calculated annual cost of $75,656.25.

A Company Has Average Demand of 30 Units Per Day