Starbucks sells gourmet coffee in bags. Each bag costs $10 and is sold at $25. I
ID: 431135 • Letter: S
Question
Starbucks sells gourmet coffee in bags. Each bag costs $10 and is sold at $25. It costs $20 to Starbucks to place an order to its coffee supplier. The replenishment lead time from the supplier is 3 months. Suppose that the demand during lead time is normally distributed with mean 50 and standard deviation 25. The internal rate of return for Starbuck's is 20% per year, which can be regarded as the carrying cost of inventory. Starbucks uses continuous replenishment policy to replenish its coffee bag stock.
a. What is the distribution of annual demand, i.e., mean and standard deviation
b. What is the EOQ lot size if we ignore the demand variability (uncertainty)?
c. What is the reorder point that achieves 96.5% of service level?
Explanation / Answer
a. Distribution of annual demand
We have mean and standard deviation during lead time that is of 3 months. We need annual demand that is of 12 months, so we will multiply the given demand of 3 months with 4 to get the 12 months demand.
Mean = 4 * 50 = 200
Standard deviation = Square root of (4 multiplied by square of standard deviation given)
=? (4 *25 *25) = ?2500 = 50
So, distribution of annual demand i.e. mean is 200 and standard deviation is 50
b. EOQ lot size if we ignore the demand variability (uncertainty)
EOQ = ? ((2*D*O) / C)
Here, D = Annual Demand = 200
O = Order cost = 20
C = Carrying cost = 20% of Unit cost of bag
= 0.2 * 10 = 2
EOQ = ? ((2*200*20)/2)
= 63.24 bags
c. Reorder point that achieves 96.5% of service level
Reorder point= Mean during lead time + (Standard deviation during lead time * Z)
Z= 1.811 (NORMSINV at 96.5% of service value)
Reorder point = 50+ (25*1.811)
= 95.28 bags
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