Question 1: Consider the following demand scenario:

Quantity Probability
2000 3%
2100 8%
2200 15%
2300 30%
2400 17%
2500 12%
2600 10%
2700 5%
Suppose the manufacturer produces at a cost of $20/unit. The distributer sells to end customers for $50/unit during season; unsold units are sold for $10/unit after season.

a.) What is the system optimal production quantity and expected profit under global optimization.

b.) Suppose the manufacturer is make-to-order, that is, the timing of events is as follows:
• The distributor orders before it receives demand from customers
• The manufacturer produces the amount ordered by the distributer
• Customer demand is observed
i. Suppose the manufacture sells to the distributer at $40/unit, how much will the distributor order? What is the expected profit for the manufacturer and distributer?
ii. Find the option contract such that both the manufacturer and distributer enjoy a higher expected profit than (b)(i). What is the expected profit for the manufacturer and distributor?

c.) Suppose the manufacturer is make-to-stock; that is the timing of events is as follows:
• The manufacturer produces a certain amount.
• The distributor observes demand.
• The distributer orders from the manufacturer

i. Using the same wholesale price contract as part (b)(i) calculate production/inventory level of the manufacturer. What is the expected profit for the manufacturer and distributor? Compare the results with (b)(i).
ii. Find a cost-sharing contract such that both the manufacturer and distributor enjoy a higher expected profit than in (c)(i), and calculate their expected profits.

Question 2) Using the data of Question 9, suppose the manufacturer has an inflated demand forecast as follow:
Quantity Probability
2,200 5%
2,300 6%
2,400 10%
2,500 17%
2,600 30%
2,700 17%
2,800 12%
2,900 3%

Suppose the manufacturer is make-to-order (timing of events as in (9)). Using your contract in Question 9(b) (ii), find the order quantity, and expected profits of the distributors and of the manufacturer. Compare your answers with 9(b) (ii).

If you are the distributors and you have the choice of revealing the true demand forecast or inflated demand forecast to the manufacturer, what will you do in each case? Explain.