Problems 2
1. The following payoff table shows profit for a decision analysis problem with two
decisions alternatives and three states of nature
State of Nature
Decision Alternatives
S1
S2
S3
d1
250
100
25
d2
100
100
75
. a. Conduct a decision tree for this problem
b. If the decision maker knows nothing about the probabilities of the three states of
nature, what is the recommended decisions using the optimistic, conservative,
and mini-max regret approaches?
2. Southland Corporation’s decision to produce a new line of recreational product
resulted in the need to construct either the small plant or a large plant. The best
selection of plant size depends on how the market place reacts to the new product
line. To conduct an analysis, marketing management has decided to view the
possible long-run demand as either low, medium, or high. The following payoff table
shows the projected profit in millions of dollars
Plant Size
Small
Large
Long-Run Demand
low
Medium
150
200
50
200
High
200
500
What is the decision to be made, and what is the chance event for Southland’s
problem?
b. Construct an influence diagram
c. Construct a decision tree
d. Recommend decision based on the use of optimistic, conservative, and minimax
regret approach
a.
3. The following profit payoff table was presented in problem (1) suppose that the
decision maker obtained the probability assessments P(s1) = 0.65, P(s2)=0,15
P(s3)=0,20. Use the expected value approach to determine the optimal decision
Decision Alternatives
d1
d2
State of Nature
S1
S2
250
100
100
100
S3
25
75