Question

24. Store A uses the newsvendor model to manage its inventory. Demand for its product is normally distributed with a mean of 500 and a standard deviation of 100. Store A purchases the product for $10 each unit and sells each for $30. Inventory is salvaged for $5.What is its expected profit if Store A's order quantity is 400 units?

Answer 1

Mean = 500
Standard Deviation = 100
Quantity = 400

Purchase Price = $10
Sales Price = $30
Inventory Salvage = $5

Overage Cost = 10 - 5 = 5
Underage Cost = 30 - 10 = 20

Critical Ratio = 20/(20+5) = 0.8

Forecatsed Quantity = mu + critical Ratio * sigma
= 500 + 0.8*100
= 580

Sold = 400

Unsold = 580 - 400 = 180

Expected Profit = Profit made on actual Quantity sold - Loss on unsold inventory
= 400*(30-10) - 180*(10-5)
= 8000 - 900
= 7100