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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
Decision analysis can be used to determine an optimal strategy when a decision maker is faced with several decision alternatives and an uncertain or risk-filled pattern of future events. For example, a global manufacturer might be interested in determining the best location for a new plant. Suppose that the manufacturer has identified five decision alternatives corresponding to five plant locations in different countries. Making the plant location decision is complicated by factors such as the world economy, demand in various regions of the world, labor availability, raw material costs, transportation costs, and so on. In such a problem, several scenarios could be developed to describe how the various factors combine to form the possible uncertain future events. Then probabilities can be assigned to the events. Using profit or cost as a measure of the consequence for each decision alternative and each future event combination, the best plant location can be selected. Even when a careful decision analysis has been conducted, the uncertain future events make the final consequence uncertain. In some cases, the selected decision alternative may provide good or excellent results. In other cases, a relatively unlikely future event may occur causing the selected decision alternative to provide only fair or even poor results. The risk associated with any decision alternative is a direct result of the uncertainty associated with the final consequence. A good decision analysis
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includes risk analysis. Through risk analysis the decision maker is provided with probability information about the favorable as well as the unfavorable consequences that may occur. We begin the study of decision analysis by considering problems having reasonably few decision alternatives and reasonably few possible future events. Influence diagrams and payoff tables are introduced to provide a structure for the decision problem and to illustrate the fundamentals of decision analysis. We then introduce decision trees to show the sequential nature of decision problems. Decision trees are used to analyze more complex problems and to identify an optimal sequence of decisions, referred to as an optimal decision strategy. Sensitivity analysis shows how changes in various aspects of the problem affect the recommended decision alternative.
The first step in the decision analysis process is problem formulation. We begin with a verbal statement of the problem. We then identify the decision alternatives, the uncertain future events, referred to as chance events, and the consequences associated with each decision alternative and each chance event outcome. Let us begin by considering a construction project of the Pittsburgh Development Corporation. Pittsburgh Development Corporation (PDC) has purchased land, which will be the site of a new luxury condominium complex. The location provides a spectacular view of downtown Pittsburgh and the Golden Triangle where the Allegheny and Monongahela rivers meet to form the Ohio River. PDC plans to price the individual condominium units between $300,000 and $1,400,000. PDC has preliminary architectural drawings for three different-sized projects: one with 30 condominiums, one with...
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