DECISION THEORY & DECISION TREE
•Components of Decision Making
•Decision Making Under Uncertainty (Without Probabilities)
•Decision Making Under Risk (With Probabilities)
•Decision Analysis with Additional Information
•Utility
The Six Steps in Decision Theory
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Clearly define the problem at hand
List the possible alternatives
Identify the possible outcomes
List the payoff or profit of each combination of alternatives
and outcomes
• Select one of the mathematical decision theory models
• Apply the model and make your decision
Decision Analysis
Components of Decision Making
• A state of nature is an actual event that may occur in the future.
• A payoff table is a means of organizing a decision situation,
presenting the payoffs from different decisions given the various
states of nature.
Payoff Table
Types of Decision-Making Environments
• Type 1: Decision-making under certainty
– decision-maker knows with certainty the consequences of
every alternative or decision choice
• Decision-making under uncertainty (without probability)
– The decision-maker does not know the probabilities of the
various outcomes
• Type 2: Decision-making under risk (with probability)
– The decision-maker does know the probabilities of the
various outcomes
Decision Analysis
Decision Making without Probabilities
Decision situation: An investor wants to decide which of the three property to buy.
Payoff Table for the Real Estate Investments
Decision-Making Criteria:
Maximax, Maximin, Minimax, Minimax Regret, Hurwicz,
Equal Likelihood (Laplace)
Decision Making without Probabilities
The Maximax Criterion
In the maximax criterion the decision maker selects the decision that
will result in the maximum of maximum payoffs; an optimistic
criterion.
Payoff Table Illustrating a Maximax Decision
Decision Making without Probabilities
The Maximin Criterion
In the maximin criterion the decision maker selects the decision that
will reflect the maximum of the minimum payoffs; a pessimistic
criterion.
Payoff Table Illustrating a Maximin Decision
Decision Making without Probabilities
The Minimax Regret Criterion
Regret is the difference between the payoff from the best decision and all
other decision payoffs.
The decision maker attempts to avoid regret by selecting the decision
alternative that minimizes the maximum regret.
Regret Table Illustrating the Minimax Regret Decision
Decision Making without Probabilities
The Hurwicz Criterion
- The Hurwicz criterion is a compromise between the maximax and maximin criterion.
- A coefficient of optimism, , is a measure of the decision maker’s optimism.
- The Hurwicz criterion multiplies the best payoff by  and the worst payoff by 1- .,
for each decision, and the best result is selected.
Decision
Values
Apartment building
$50,000(.4) + 30,000(.6) = 38,000
Office building
$100,000(.4) - 40,000(.6) = 16,000
Warehouse
$30,000(.4) + 10,000(.6) = 18,000
Decision Making without Probabilities
The Equal Likelihood Criterion
- The equal likelihood ( or Laplace) criterion multiplies the decision payoff for each
state of nature by an equal weight, thus assuming that the states of nature are equally
likely to occur.
Decision
Values
Apartment building
$50,000(.5) + 30,000(.5) = 40,000
Office building
$100,000(.5) - 40,000(.5) = 30,000
Warehouse
$30,000(.5) + 10,000(.5) = 20,000
Decision Making without Probabilities
Summary of Criteria Results
- A dominant decision is one that has a better payoff than another decision under each
state of nature.
- The appropriate criterion is dependent on the “risk” personality and philosophy of the
decision maker.
Criterion
Decision (Purchase)
Maximax
Office building
Maximin
Apartment building
Minimax regret
Apartment building
Hurwicz
Apartment building
Equal liklihood
Apartment building
Decision Making without Probabilities
Solutions with QM for Windows (1 of 2)
Decision Making without Probabilities
Solutions with QM for Windows (2 of 2)
Decision Making under Risk (with Probabilities)
Expected Value
Expected value is computed by multiplying each decision outcome under
each state of nature by the probability of its occurrence.
EV(Apartment) = $50,000(.6) + 30,000(.4) = 42,000
EV(Office) = $100,000(.6) - 40,000(.4) = 44,000
EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000
Decision Making with Probabilities
Expected Opportunity Loss
The expected opportunity loss is the expected value of the regret for
each decision.
The expected value and expected opportunity loss criterion result in the
same decision.
EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000
EOL(Office) = $0(.6) + 70,000(.4) = 28,000
EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000
Decision Making with Probabilities
Solution of Expected Value Problems with QM for Windows
Decision Making with Probabilities
Expected Value of Perfect Information
• The expected value of perfect information (EVPI) is the maximum
amount a decision maker would pay for additional information.
• EVPI equals the expected value given perfect information minus
the expected value without perfect information.
• EVPI equals the expected opportunity loss (EOL) for the best
decision.
Decision Making with Probabilities
EVPI Example
Decision with perfect information: $100,000(.60) + 30,000(.40) = $72,000
Decision without perfect information: EV(office) = $100,000(.60) - 40,000(.40) = $44,000
EVPI = $72,000 - 44,000 = $28,000
EOL(office) = $0(.60) + 70,000(.4) = $28,000
Decision Making with Probabilities
EVPI with QM for Windows
Decision Making with Probabilities
Decision Trees
A decision tree is a diagram consisting of decision nodes
(represented as squares), probability nodes (circles), and decision
alternatives (branches).