Lecture Notes: Chapter 15 - Decision Analysis

Introduction to Decision Analysis

• Focus on making better decisions in business analytics.
• Decision analysis helps develop an optimal strategy when facing several decision alternatives and uncertain future events.
• Example: North Carolina's use of decision analysis for medical screening tests.

Key Concepts

• Risk Analysis: Provides probability information about favorable and unfavorable outcomes.
• Payoff Tables and Decision Trees: Tools used in decision analysis.
• Sensitivity Analysis and Bayes’ Theorem: Topics covered in decision analysis.

Decision Analysis Process

Problem Formulation

• Involves identifying decision alternatives, chance events, and outcomes.
• Example: Pittsburgh Development Corporation's decision on condominium project size.
  • Decision alternatives: Small (30 units), Medium (60 units), Large (90 units).
  • States of nature: Strong demand or weak demand for condominiums.

Payoff Tables

• Payoff: Outcome from a specific combination of decision alternative and state of nature.
• Example: Payoff table showing millions of dollars in outcomes for different project sizes and demand levels.

Decision Trees

• Graphical representation of decision-making processes.
• Nodes represent decisions and chance events using squares and circles respectively.
• Branches connect nodes and indicate states of nature.

Decision Analysis Without Probabilities

• Optimistic Approach: Evaluates alternatives based on best possible payoffs.
• Conservative Approach: Focuses on worst-case outcomes to minimize potential losses.
• Min-Max Regret Approach: Aims to minimize the maximum regret possible over all states of nature.

Decision Analysis With Probabilities

• Expected Value Approach: Calculates the weighted sum of payoffs for decision alternatives.
• Use of historical data for estimating probabilities of states of nature.
• Risk profiles illustrate potential payoffs and associated probabilities.

Sensitivity Analysis

• Determines impact of changes in probabilities and payoffs on decision alternatives.
• Helps identify critical inputs affecting the choice of the best decision alternative.

Sample Information and Decision Making

Additional Information

• Collecting sample information helps refine understanding of states of nature.
• Prior vs. Posterior probabilities: Adjustments made after obtaining additional information.

Decision Strategy

• Sequence of decisions and chance outcomes dependent on chance event results.

Expected Value of Sample Information (EVSI)

• Measures the value of additional sample information in influencing decision outcomes.

Expected Value of Perfect Information (EVPI)

• Compares decisions with and without perfect information to determine value of information.

Bayes’ Theorem

• Used to compute branch probabilities for decision trees.
• Rearranges conditional probabilities to update beliefs based on new information.

Utility Theory

• Addresses scenarios where monetary value is not the sole decision-making criterion.
• Utility: Total worth or desirability of an outcome.
• Decision maker attitudes categorized as risk-averse, risk-neutral, or risk-taking.
• Exponential utility functions represent varying risk tolerances and attitudes.

Conclusion

• Utility theory provides additional insights but is not heavily focused in this course.
• Final lectures conclude the course; focus shifts to final projects.
• Congratulations on course completion and best wishes for future endeavors.