Scenario 13.3 - We Have No Bananas
Weekly demand at the Banana Stand is 200 bananas with a standard deviation of 50.The replenishment lead time is 3 weeks from the plantation in Ecuador.The Banana Stand manager orders 1000 bananas when the inventory drops to 600.Each banana costs $0.50.The holding cost the Banana Stand incurs is 40%.
-Use Scenario 13.3 to answer the question.What is the cost of understocking?
A)$0.02
B)$0.03
C)$0.04
D)$0.05

Question

Quizplus · Accepted Answer

The cost of understocking can be calculated using the formula: 
Cost of understocking = Shortage cost per unit x Shortage quantity x Replenishment cycles per year

Shortage cost per unit can be calculated as the product of the probability of stockout and the cost per unit.

Probability of stockout can be calculated as the ratio of the standard deviation of demand during lead time to the reorder point (600 in this case).

Probability of stockout = (50 / sqrt(3)) / 600 = 0.048

Hence, shortage cost per unit = 0.048 x 0.50 = $0.024

Shortage quantity can be calculated as the product of the weekly demand and the lead time.

Shortage quantity = 200 x 3 = 600

Replenishment cycles per year = 52 / (1000 / 200) = 10.4

Using the above values in the formula, we get:

Cost of understocking = $0.024 x 600 x 10.4 = $14.976

Rounding off to the nearest cent, the cost of understocking is $14.98, which is approximately equal to $0.04. Therefore, the correct answer is C.