Decision Analysis: A Guide to Effective Decision Making

Decision Analysis

Key Concepts

Decision Alternatives: Options available to the decision maker.

Chance Event: An uncertain future event affecting the consequence, or payoff, associated with a decision.

Consequence: The result obtained when a decision alternative is chosen and a chance event occurs. A measure of the consequence is often called a payoff.

States of Nature: The possible outcomes for chance events that affect the payoff associated with a decision alternative.

Influence Diagram: A graphical device that shows the relationship among decisions, chance events, and consequences for a decision problem.

Node: An intersection or junction point of an influence diagram or a decision tree.

• Decision Nodes: Nodes indicating points where a decision is made.
• Chance Nodes: Nodes indicating points where an uncertain event will occur.
• Consequence Nodes: Nodes indicating points where a payoff is received.

Payoff: A measure of the consequence of a decision, such as profit, cost, or time. Each combination of a decision alternative and a state of nature has an associated payoff (consequence).

Payoff Table: A tabular representation of the payoffs for a decision problem.

Decision Tree: A graphical representation of the decision problem that shows the sequential nature of the decision-making process.

Branch: Lines showing the alternatives from decision nodes and the outcomes from chance nodes.

Decision-Making Approaches

Optimistic Approach: For a maximization problem, it leads to choosing the decision alternative corresponding to the largest payoff; for a minimization problem, it leads to choosing the decision alternative corresponding to the smallest payoff.

Conservative Approach: For a maximization problem, it leads to choosing the decision alternative that maximizes the minimum payoff; for a minimization problem, it leads to choosing the decision alternative that minimizes the maximum payoff.

Opportunity Loss (Regret): The amount of loss (lower profit or higher cost) from not making the best decision for each state of nature.

Minimax Regret Approach: For each alternative, the maximum regret is computed, which leads to choosing the decision alternative that minimizes the maximum regret.

Expected Value Approach: An approach based on the expected value of each decision alternative. The recommended decision alternative is the one that provides the best expected value.

Expected Value (EV): For a chance node, it is the weighted average of the payoffs. The weights are the state-of-nature probabilities.

Expected Value of Perfect Information (EVPI): The expected value of information that would tell the decision maker exactly which state of nature is going to occur.

Risk Analysis: The study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy.

Sensitivity Analysis: The study of how changes in the probability assessments for states of nature or changes in the payoffs affect the recommended decision alternative.

Risk Profile: The probability distribution of the possible payoffs associated with a decision alternative or decision strategy.

Prior Probabilities: The probabilities of the states of nature prior to obtaining sample information.

Sample Information: New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities.

Posterior (Revised) Probabilities: The probabilities of the states of nature after revising prior probabilities based on sample information.

Decision Strategy: A strategy involving a sequence of decisions and chance outcomes to provide the optimal solution to a decision problem.

Expected Value of Sample Information (EVSI): The difference between the expected value of an optimal strategy based on sample information and the “best” expected value without any sample information.

Efficiency: The ratio of EVSI to EVPI as a percentage.

Bayes’ Theorem: A theorem that enables the use of sample information to revise prior probabilities.

Conditional Probabilities: The probability of one event given the known outcome of a (possibly) related event.

Joint Probabilities: The probabilities of both sample information and a particular state occurring simultaneously.