Problem:
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 distributor sells to end customers for $50/unit during season and 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 (i.e., the distributor must order before it receives demand from end customers).
(i) Suppose the manufacturer sells to the distributor at $40/unit, how much should the distributor order? What is the expected profit for the manufacturer? What is the expected profit for distributor?
(ii) 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?
c) Suppose the manufacturer is make-to-stock. (i.e., the manufacturer must decide how much to produce before the distributor sees the demand and places an order.)
(i) Using the same wholesale price contract as part (b)(i), calculate the production level of the manufacturer. What are the expected profits for the manufacturer and for the distributor? Compare your results with part (b)(i).
(ii) Find a cost sharing contract such that both the manufacturer and distributor enjoy a higher expected profit than that in (c)(i), and calculate their expected profits.
2. Using the data from problem 1, assume that the distributor knows the true forecast, given in problem 1; but for this problem we assume that the manufacturer has an inflated demand as follows:
Quantity Probability
2200 5%
2300 6%
2400 10%
2500 17%
2600 30%
2700 17%
2800 12%
2900 3%
a) Suppose the manufacturer is make-to-order. Using your proposed contract in Problem 1(b)(ii), find the order quantity and expected profit of the distributor, and the expected profit of the manufacturer. Compare your answers with 1(b)(ii).
b) Suppose the manufacturer is make-to-stock. Using your proposed contract in Problem 1(c)(ii), find the production quantity and expected profit of the manufacturer, and the expected profit of the distributor. Compare your answers with 1(c)(ii).
c) If you are the distributor 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.