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 distributor sells to the end customers for $50/unit during season, unsold units are sold for $10/unit after season.

What is the system optimal production quantity and expected profit under global optimization?

Suppose the manufacturer is make-to-order; that is, the timing of events is as follows;

The distributor orders before it receive demand from end customers.

The manufacturer produces the amount ordered by the distributor.

Customer demand is observed.

Suppose the manufacturer sells to the distributor at $40/unit, how much will the distributor order? What is the expected profit for the manufacturer and the distributor?

Find an option contract such that both the manufacturer and distributor enjoy a higher expected profit than (b)(i). What is the expected profit for the manufacturer and the distributor?

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 distributor orders from the manufacturer.

Using the same wholesale price contract as part (b)(i), calculate the production/inventory level of the manufacturer. What is the expected profit for the manufacturer and the distributor? Compare your results with part (b)(i).

Find a cost-sharing contract such that both the manufacturer and the distributor enjoy a higher expected profit than that in (c)(i), and calculate their expected profits.