A small grocery store buys one-gallon bottles of milk from a local dairy farmer. The store sells milk at $3.50 per gallon. The demand for milk is normally distributed with a mean of 30 one-gallon bottles per day and a daily standard deviation of 4 bottles. At the end of each business day, any unsold milk is purchased by local restaurants for $1.00 per bottle. Management uses a service level of 90%.

a. At what price per gallon does the store buy milk from the dairy farmer?

b. Calculate the cost of underage, Cs. Calculate the cost of overage, Co.

c. Calculate the stockout risk and the safety stock. What is the optimal stocking level? 

Answer:

The newsvendor model also called single-period model is nothing but the mathematical model which is used to determine the optimal quantity of perishable product that needs to maintained which is calculated based on fixed price and uncertain demand. Since the product is perishable and demand is uncertain the unsold items are worthless at the end of the day so newsvendor problem is solved to identify the optimal inventory level.

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