Decision Analysis
When it is known for certain which of the possible future conditions will actually happen, the
decision is usually relatively straightforward: Simply choose the alternative that has the best
payoff under that state of nature. Although complete certainty is rare in such situations, this
kind of exercise provides some perspective on the analysis. Moreover, in some instances,
there may be an opportunity to consider allocation of funds to research efforts, which may
reduce or remove some of the uncertainty surrounding the states of nature.
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A decision tree is a schematic representation of the alternatives available to a decision maker
and their possible consequences. The term gets its name from the treelike appearance of the
diagram. Although tree diagrams can be used in place of a payoff table, they are particularly
useful for analyzing situations that involve sequential decisions
Problem# 1
Problem# 2
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Problem# 3
Problem# 4
Problem#5
Kenneth Brown is the principal owner of Brown oil Inc. After quitting his university
teaching job, Ken has been able to increase his annual salary by a factor over 100. At the
present time, Ken is forced to consider purchasing some more equipment for Brown Oil
because of competition. Ken is planning to purchase one of the three equipment:
i. Sub 100: If there is a favorable market, he will realize a profit of $ 300,000 on one
hand, if the market is unfavorable; ken will suffer a loss of $ 200,000.
ii. Oiler J: If there is a favorable market, he will realize a profit of $250,000 on one
hand, if the market is unfavorable, Ken will suffer a loss of $ 100,000
iii. Texan: If there is a favorable market, he will realize a profit of $ 75,000 on one
hand, if the market is unfavorable; Ken will suffer a loss of $ 18,000.
1) Construct a decision Table
2) Construct Decision Tree
3) Which Equipment you will recommend to Ken to purchase under the following
criterion:a) Optimistic
b) Pessimistic
c) Minimax Regret
d) Equally Likely
4) If the probability of Favorable market is 0.35 which equipment will recommend to
Ken based in Expected Monetary Value Criteria.
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ASSIGNMENT FINAL PERIOD
Question#1 Mc Donald’s Restaurant is contemplating opening a new restaurant on Main
Street. It has three different models, each with a different seating capacity. Mc Donald’s
management estimates that the average number of customers per hour will be 80, 100, or
120. The profit payoff table for the three models is as follows:
Model-A,d1
Model-B,d2
Model-C,d3
Average Number of Consumers Per Hour
S1=80
S2=100
S3=120
BD 1000
1500
400
800
1800
1200
600
1600
2100
a)
Construct a decision tree for this problem
b)
If the decision maker knows nothing about the probabilities of the four states, what is
the recommended decision using the minimax, maximax, Laplace, and minimax
regret approaches?
c)
Suppose that the decision maker has obtained the following probability estimates: P
(s1) = 0.6, P(S2) = 0.25, and P(s3) = 0.15. Use the expected value approach to
determine the optimal decision
d) Determine the expected value of perfect information you can pay using the
expected payoff under certainty approach.
Question No#2
A financial advisor has recommended two possible mutual funds for investment: Investment A and Investment - B. The return will be achieved by each of these depends on whether the
economy is good, fair or bad: a payoff table has been constructed to illustrate the situation:
Investment-A
Investment-B
Probability
Average Number of Consumers Per Hour
Good Economy
Fair Economy
Poor Economy
$ 20,000
$ 4,000
$ - 10,000
$12,000
$ 8,000
$0
0.22
0.40
0.38
a)
If the decision maker now nothing about the probability of a three states of nature,
what is the recommended decision using the a) optimistic, b) pessimistic c) minimax
regret d) equally likely (Laplace)?
b)
Draw the decision tree to represent this situation?
c)
Perform the necessary calculations to determine which of the two investment
alternative is better. Which one should you choice to maximize the expected
monetary value EMV?
d)
Determine the expected value of perfect information you can using the expected
payoff under certainty approach.
e)
Suppose there is a question about the return of investment – A in a good economy. It
could be higher or lower than $ 20,000. What value for this would cause a person to
be indifference?
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