Problem set #2
Due
Session 10
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 maketoorder (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 maketostock. (i.e., the manufacturer must decide
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 Spring '05
 DavidSimchiLevi
 $10, $50, $20, 3rd millennium, $40

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