Chapter 4

DECISION ANALYSIS

CONTENTS 4.1 PROBLEM FORMULATION Influence Diagrams Payoff Tables Decision Trees DECISION MAKING WITHOUT PROBABILITIES Optimistic Approach Conservative Approach Minimax Regret Approach DECISION MAKING WITH PROBABILITIES Expected Value of Perfect Information RISK ANALYSIS AND SENSITIVITY ANALYSIS Risk Analysis Sensitivity Analysis DECISION ANALYSIS WITH SAMPLE INFORMATION An Influence Diagram A Decision Tree Decision Strategy Risk Profile Expected Value of Sample Information Efficiency of Sample Information COMPUTING BRANCH PROBABILITIES

4.2

4.3 4.4

4.5

4.6

Decision analysis can be used to determine an optimal strategy when a decision maker is faced

*…show more content…*

98

QUANTITATIVE METHODS FOR BUSINESS

Influence Diagrams

An influence diagram is a graphical device that shows the relationships among the decisions, the chance events, and the consequences for a decision problem. The nodes in an influence diagram are used to represent the decisions, chance events, and consequences. Rectangles or squares are used to depict decision nodes, circles or ovals are used to depict chance nodes, and diamonds are used to depict consequence nodes. The lines connecting the nodes, referred to as arcs, show the direction of influence that the nodes have on one another. Figure 4.1 shows the influence diagram for the PDC problem. The complex size is the decision node, demand is the chance node, and profit is the consequence node. The arcs connecting the nodes show that both the complex size and the demand influence PDC’s profit.

Payoff Tables

Given the three decision alternatives and the two states of nature, which complex size should PDC choose? To answer this question, PDC will need to know the consequence associated with each decision alternative and each state of nature. In decision analysis, we refer to the consequence resulting from a specific combination of a decision alternative and a state of nature as a payoff. A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table. Because PDC wants to select the complex size that provides the largest