Decision Theory
CHAPTER 5S
DECISION THEORY
PROBLEMS
P1.
Here is a payoff matrix; parentheses designate a loss.
The probabilities of the states of nature,
P(1) and P(2), are unknown.
States of Nature
Alternatives
1
2
A
B
C
$500
700
(300)
$300
100
600
a.
Which alternative should be selected under the maximax criterion?
b.
Which alternative should be selected under the maximin criterion?
c.
Which alternative should be selected under the Laplace criterion?
d.
What is the opportunity loss table?
e.
Which alternative should be selected under the minimax regret criterion?
P2.
Refer to Problem 1. Construct the sensitivity graph, as shown on p. 207 of your textbook.
a.
For what range of values of P(2) is alternative A preferred?
a.
For what range of values of P(2) is alternative B preferred?
b. For what range of values of P(2) is alternative C preferred?
1
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P3.
Fall has come, and the department manager of the Purple Pentagon Discount Store must decide
how many snow blowers to order for the winter season.
He believes there is an association
between the weather and the demand for snow blowers: a winter with heavy snow should produce
a high demand, and a winter with light snow should produce a low demand.
However, if he
guesses wrong and orders a large number of snow blowers when the weather turns out to have
light snow, he will suffer a loss.
Here is his payoff matrix.
States of Nature
Alternatives
Heavy
snow
Medium
snow
Light
snow
Large Order
Medium Order
Small Order
$5,000
2,000
500
$1,000
3,000
500
$(4,000)
(2,000)
1,000
a.
Which alternative should be selected under the maximax criterion?
b.
Which alternative should be selected under the maximin criterion?
c.
Which alternative should be selected under the Laplace criterion?
d.
What is the opportunity loss table?
e.
Which alternative should be selected under the minimax regret criterion?
P4.
Refer to Problem 3. Suppose that the following probabilities are available regarding the snowfall
next winter:
P(heavy snow) = .10
P(medium snow) = .50
P(light snow) = .40
a.
Which alternative should be selected under the expected value criterion?
b.
What is the value of the EVPI?
c.
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 Spring '08
 WILLIAMCOSGROVE

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