Lecture 3 Decision Analysis
Decision Analysis
Example
Consider the following problem with three decision alternatives and three states of nature with the following payoff table representing profits:
States of Nature s1 s2 s3 d1
4
4
Decisions d2
0
3 d3 1
5
Which decision do you choose?
-2
-1
-3
Problem Formulation
• A decision problem is characterized by decision alternatives, states of nature, and resulting payoffs.
• The decision alternatives are the different possible strategies the decision maker can employ.
• The states of nature refer to future events, not under the control of the decision maker, which may occur.
States of nature should be defined so that they are mutually exclusive and collectively exhaustive.
Payoff Tables
• The consequence resulting from a specific combination of a decision alternative and a state of nature is a payoff.
• A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table.
• Payoffs can be expressed in terms of profit, cost, time, distance or any other appropriate measure.
Decision Making without Probabilities
• Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are:
– the optimistic approach
– the conservative approach
– the minimax regret approach.
Optimistic Approach
• The optimistic approach would be used by an optimistic decision maker.
• The decision with the largest possible payoff is chosen. • If the payoff table was in terms of costs, the decision with the lowest cost would be chosen.
Example
Consider the following problem with three decision alternatives and three states of nature with the following payoff table representing profits:
States of Nature s1 s2 s3 d1
Decisions d2 d3 4
0
1
4
3
5
-2
-1
-3
Example: Optimistic Approach
An optimistic decision maker would use the optimistic (maximax) approach. We choose the decision that has the largest single value in the payoff table.
Maximax
decision
Example
Consider the following problem with three decision alternatives and three states of nature with the following payoff table representing profits:
States of Nature s1 s2 s3 d1
4
4
Decisions d2
0
3 d3 1
5
Which decision do you choose?
-2
-1
-3
Problem Formulation
• A decision problem is characterized by decision alternatives, states of nature, and resulting payoffs.
• The decision alternatives are the different possible strategies the decision maker can employ.
• The states of nature refer to future events, not under the control of the decision maker, which may occur.
States of nature should be defined so that they are mutually exclusive and collectively exhaustive.
Payoff Tables
• The consequence resulting from a specific combination of a decision alternative and a state of nature is a payoff.
• A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table.
• Payoffs can be expressed in terms of profit, cost, time, distance or any other appropriate measure.
Decision Making without Probabilities
• Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are:
– the optimistic approach
– the conservative approach
– the minimax regret approach.
Optimistic Approach
• The optimistic approach would be used by an optimistic decision maker.
• The decision with the largest possible payoff is chosen. • If the payoff table was in terms of costs, the decision with the lowest cost would be chosen.
Example
Consider the following problem with three decision alternatives and three states of nature with the following payoff table representing profits:
States of Nature s1 s2 s3 d1
Decisions d2 d3 4
0
1
4
3
5
-2
-1
-3
Example: Optimistic Approach
An optimistic decision maker would use the optimistic (maximax) approach. We choose the decision that has the largest single value in the payoff table.
Maximax
decision