III. Decision-making under Uncertain Demand - Newsvendor Chapter 12 (20 Points):
ID: 433101 • Letter: I
Question
III. Decision-making under Uncertain Demand - Newsvendor Chapter 12 (20 Points): Montanso is a large bio firm that sells genetically modified seed to farmers. Montanso needs to decide how much seed to put into a warehouse to serve demand for the next growing season. They will make one quantity decision. It costs Montanso $16 to make each kilogram (kg) of seed. They sell each kg for $90. If they have more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, they only earn $6 per kg from the overseas market (but this is better than destroying the seed because it cannot be stored until next year). If local demand exceeds their quantity, then the sales are lost – the farmers go to another supplier. As a forecast for local demand they will use a normal distribution with a mean of 300,000 kgs and a standard deviation of 100,000 kgs. (8 points) Newsvendor Quantity: How many kilograms (kgs) of seed should they place in their warehouse before the next growing season to maximize their expected profit?
Explanation / Answer
Cu = Cost of underage = Selling price - Cost of production = $90 - $16 = $74
Co = Cost of overage = Cost of production - Salvage value = $16 - $6 = $10
Criticality factor = Cu / (Cu+ Co) = 74 / (74+10) = 0.881
For optimal order quantity, the service level must be equal to the criticality factor. In other words,
F(Q) = 0.881
or, Z = NORMSINV(0.881) = 1.18
Optimal order quantity = Mean demand + Z * Sigma = 300,000 + 1.18 * 100,000 = 418,000.
So, the expected profit will be maximized when they place 418,000 kgs in their warehouse.