The following payoff table shows profit for a decision analysis problem with two decision
alternatives and three states of nature:
a. Construct 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 decision using the optimistic, conservative, and minimax regret approaches?
:: Solution ::
step: 1 of 4
(a)
Construct a decision tree
Decision tree is a sequential tool that is represented in the form of a graph. It helps the management
in the process of decision-making over a period of time.
Decision tree for this problem is as follows:
step: 2 of 4
(b)
Maximum and minimum profit for each decision alternative:
Maximum profit:
The maximum profit for
is 250 (out of 250, 100, and 25), and
is 100 (out of 100, 100, and 25).
Minimum profit:
The minimum profit for
is 25 (out of 250, 100, and 25), and
Decision Maximum profit Minimum profit
250
25
100
75
is 75 (out of 100, 100, and 25).
Recommended decision using optimistic approach:
The following are the criteria for optimistic approach:
• For a maximization problem, select the maximax value.
• For a minimization problem, select the minimin value.
Decision Maximum profit
250
100
Justification:
Under optimistic approach,
should be selected, which is the maximum of the maximum payoff
value. Decision alternative is evaluated in terms of the largest payoff that can arise.
step: 3 of 4
Recommended decision using conservative approach:
Under the conservative approach, first we should identify the minimum payoff for each alternative
and select the alternative with the maximum of the minimum payoff.
Decision Minimum payoff
25
75
The minimum payoff for
is 25, and
the minimum payoff value.
is 75. Hence,
should be selected with the maximum of
step: 4 of 4
Recommended decision using regret or opportunity loss table:
The maximum value of
follows:
,
,
should be subtracted with the corresponding value in the table as
Decision alternative State of nature
0
0
50
150
0
0
is 50, and
is 150. Hence, select
The maximum opportunity loss for
with minimum regret.
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