1. The following payoff table shows profit for a decision analysis problem with two decision
alternatives and three states of nature:
States of Nature
Decision alternative S1 S2 S3
D1 250 100 25
D2 100 100 75
a. Construct a decision tree for this problem.
S1 = 250
D1 S2 = 100
m
er as
S3 = 25
co
Decision
eH w
S1 = 100
o.
rs e
D2 S2 = 100
ou urc
S3 = 75
o
aC s
b. If the decision maker knows nothing about the probabilities of the three states of nature,
vi y re
what is the recommended decision using the optimistic, conservative, and minimax regret
approaches?
Decision Maximum Profit Minimum Profit
ed d
D1 250 25
ar stu
D2 100 75
is
Optimistic approach: select D1
Th
Conservative approach: select D2
Regret or opportunity loss table:
sh
S1 S2 S3
D1 0 0 50
D2 150 0 0
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, Maximum regret for d1 = 50
Maximum regret for d2 = 150
3. Southland Corporation’s decision to produce a new line of recreational products resulted in
the need to construct either a small plant or a large plant. The best selection of plant size
depends on how the marketplace reacts to the new product line. To conduct an analysis,
marketing management has decided to view the possible long-run demand as low, medium, or
high. The following payoff table shows the projected profit in millions of dollars:
Long-Run Demand
Plant Size Small Medium High
Small 150 200 200
Large 50 200 500
m
er as
a. What is the decision to be made, and what is the chance event for Southland’s problem?
co
The decision that needs to be made is to choose the best plant size. There are two
eH w
alternatives to choose: either a small plant or a large plant. The chance event is the
o.
market demand for the new product line. There are three possible outcomes, low, medium
and high. rs e
ou urc
b. Construct an influence diagram.
o
aC s
Plant Size Market
vi y re
Demand
ed d
ar stu
Profit
is
Th
sh
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alternatives and three states of nature:
States of Nature
Decision alternative S1 S2 S3
D1 250 100 25
D2 100 100 75
a. Construct a decision tree for this problem.
S1 = 250
D1 S2 = 100
m
er as
S3 = 25
co
Decision
eH w
S1 = 100
o.
rs e
D2 S2 = 100
ou urc
S3 = 75
o
aC s
b. If the decision maker knows nothing about the probabilities of the three states of nature,
vi y re
what is the recommended decision using the optimistic, conservative, and minimax regret
approaches?
Decision Maximum Profit Minimum Profit
ed d
D1 250 25
ar stu
D2 100 75
is
Optimistic approach: select D1
Th
Conservative approach: select D2
Regret or opportunity loss table:
sh
S1 S2 S3
D1 0 0 50
D2 150 0 0
This study source was downloaded by 100000805705997 from CourseHero.com on 04-28-2021 01:26:34 GMT -05:00
https://www.coursehero.com/file/13400343/QMB5355-12-Week-4-1/
, Maximum regret for d1 = 50
Maximum regret for d2 = 150
3. Southland Corporation’s decision to produce a new line of recreational products resulted in
the need to construct either a small plant or a large plant. The best selection of plant size
depends on how the marketplace reacts to the new product line. To conduct an analysis,
marketing management has decided to view the possible long-run demand as low, medium, or
high. The following payoff table shows the projected profit in millions of dollars:
Long-Run Demand
Plant Size Small Medium High
Small 150 200 200
Large 50 200 500
m
er as
a. What is the decision to be made, and what is the chance event for Southland’s problem?
co
The decision that needs to be made is to choose the best plant size. There are two
eH w
alternatives to choose: either a small plant or a large plant. The chance event is the
o.
market demand for the new product line. There are three possible outcomes, low, medium
and high. rs e
ou urc
b. Construct an influence diagram.
o
aC s
Plant Size Market
vi y re
Demand
ed d
ar stu
Profit
is
Th
sh
This study source was downloaded by 100000805705997 from CourseHero.com on 04-28-2021 01:26:34 GMT -05:00
https://www.coursehero.com/file/13400343/QMB5355-12-Week-4-1/
