11.1 Decision Trees and Influence Diagrams

Decision trees and influence diagrams are powerful tools for modeling complex decisions. They help visualize choices, uncertainties, and outcomes, enabling managers to make informed decisions based on expected values and risk preferences.

These techniques are crucial in prescriptive analytics, guiding optimal decision-making. By breaking down problems into manageable components, they allow for systematic analysis of alternatives, consideration of probabilities, and evaluation of potential outcomes in various business scenarios.

Decision trees for modeling

Constructing decision trees

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• Decision trees are graphical representations of decision-making processes that illustrate a sequence of decisions, chance events, and outcomes
• The main components of a decision tree include:
  • Decision nodes (squares) represent points where a decision must be made
  • Chance nodes (circles) represent uncertain events or outcomes
  • Branches emanating from decision nodes represent available options or choices
  • Branches from chance nodes represent possible outcomes and their associated probabilities
  • Terminal nodes (triangles) represent the final outcomes or payoffs resulting from the sequence of decisions and chance events
• Constructing a decision tree involves:
  • Identifying the main decision problem
  • Determining the sequence of decisions and uncertainties
  • Estimating probabilities and payoffs for each possible outcome
• Example: A company deciding whether to launch a new product (decision node) with uncertain market demand (chance node) and potential profit or loss (terminal nodes)

Analyzing decision trees

• Rollback analysis is used to solve decision trees by working backward from the terminal nodes, calculating expected values at chance nodes, and selecting the optimal decision at each decision node
• Sensitivity analysis can be performed on decision trees to assess the impact of changes in probabilities or payoffs on the optimal decision path
• Example: Analyzing the decision tree for the product launch to determine the expected value of launching or not launching the product, and testing the sensitivity of the decision to changes in market demand probabilities

Interpreting decision trees

Optimal decision paths

• The optimal decision path in a decision tree is the sequence of decisions that maximizes the expected value or utility of the outcomes
• To determine the optimal decision path:
  • Calculate the expected value (EV) or expected monetary value (EMV) at each chance node by multiplying the probability of each outcome by its corresponding payoff and summing the results
  • At decision nodes, select the alternative with the highest EV or EMV as the optimal choice, considering the subsequent chance events and outcomes
• The certain equivalent (CE) is the guaranteed amount that a decision-maker would accept in lieu of the uncertain outcomes in a decision tree
  • It can be used to compare the value of different decision paths
• Example: Choosing the optimal path in the product launch decision tree based on the highest expected monetary value

Value of information and risk preferences

• Value of information (VOI) analysis can be conducted to determine the potential benefit of gathering additional information before making a decision
  • Compare the expected value with and without the information
• Risk preferences and utility functions can be incorporated into decision tree analysis to account for a decision-maker's attitude towards risk and the diminishing marginal utility of outcomes
• Example: Conducting a VOI analysis to determine if market research would be beneficial before deciding on the product launch, and adjusting the decision based on the company's risk tolerance

Influence diagrams for visualization

Elements of influence diagrams

• Influence diagrams are graphical representations of decision problems that show the relationships between decisions, uncertainties, and outcomes in a compact and intuitive format
• The main elements of an influence diagram include:
  • Decision nodes (rectangles) represent choices available to the decision-maker
  • Chance nodes (ovals) represent uncertain variables or events
  • Value nodes (diamonds) represent the objectives or criteria used to evaluate the outcomes, such as profit, cost, or utility
  • Arcs (arrows) indicate the dependencies and information flow between nodes, with the direction of the arc signifying the direction of influence

Constructing and using influence diagrams

• Constructing an influence diagram involves:
  • Identifying the relevant decisions, uncertainties, and outcomes
  • Determining their relationships and dependencies
• Influence diagrams can be transformed into decision trees for analysis by expanding the nodes and adding branches to represent the possible outcomes and their probabilities
• Influence diagrams can be used to:
  • Communicate the structure of a decision problem to stakeholders
  • Facilitate discussion and collaboration in the decision-making process
• Example: Creating an influence diagram for a company's marketing strategy decision, including decision nodes (target market, promotional channels), chance nodes (competitor actions, economic conditions), and a value node (market share)

Decision analysis in business

Applying decision trees and influence diagrams

• Decision trees and influence diagrams can be applied to a wide range of business problems:
  • Investment decisions
  • Product development
  • Marketing strategies
  • Resource allocation
• When applying these techniques:
  • Clearly define the decision problem
  • Identify the relevant variables and outcomes
  • Gather reliable data on probabilities and payoffs
• Sensitivity analysis should be conducted to:
  • Assess the robustness of the recommended decision
  • Identify critical uncertainties that may require further investigation or risk mitigation strategies
• Example: Using a decision tree to evaluate investment options for a company, considering factors such as initial costs, potential returns, and market risks

Communication and integration with other tools

• The results of the analysis should be communicated effectively to decision-makers, highlighting the key insights, assumptions, and limitations of the model
• Decision trees and influence diagrams can be combined with other decision-making tools for a more comprehensive analysis of complex business problems:
  • Multi-criteria decision analysis
  • Simulation
• It is important to consider the organizational context, stakeholder preferences, and ethical implications when applying these techniques to real-world business decisions
• Example: Presenting the findings of a product development decision analysis to executives, emphasizing the expected values, risks, and trade-offs associated with each option, and discussing how the results align with the company's strategic goals and values