Question

KBC is a bike manufacturing company located in Asia which sells two models (a bike with a D-brake and a bike with a V-brake) in the United States. It takes 6 weeks to ship the bikes from their factory in Asia to their distribution center in the United States. The weekly demands for the bikes in the United States market follow Normal distributions as follows (and they are independent):

Bikes with D-brakes ~ N(µ=7, σ2 =6^2)

Bikes with V-brakes ~ N(µ=10, σ2 =8^2)

Calculate the mean and standard deviation of demands during the replenishment lead time for each type of bike.

The distribution center in the United States sets safety stocks so that the cycle service level is 95%.

Answer 1

For Bike with D-brakes, µ = 7, σ = 6

mean of demands = 7 * 6 weeks = 42

Standard deviation of demand during lead time= σdLT= σd * sqrt(Lead time) = 6*sqrt(6)= 6*2.5= 15

For Bike with V-brakes, µ = 10, σ = 8

mean of demands = 10 * 6 weeks = 60

Standard deviation of demand during lead time= σdLT= σd * sqrt(Lead time) = 8*sqrt(6)= 8*2.5= 20