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Lecture 2 S11 - L ecture2 Decision Analysis Source/1...

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Lecture 2 Decision Analysis Source: /1 / D.R.Anderson, D.J.Sweeney, T.A.Williams. Quantitative Methods for Business, South- Western College Publishing, 11-th edition. Chapter 4. Contents: 2.1 Problem formulation 2.2 Decision making without probabilities 2.3 Introduction to probabilities 2.4 Decision making with probabilities Decision analysis can be used to develop an optimal strategy when a decision maker is faced with several decision alternatives and uncertain future events. We begin the decision analysis process with problem formulation. 2.1 Problem formulation Problem formulation includes the following four parts: Part1. Statement of the problem Part2 . Identification the decision alternatives Part3. Identification the uncertain future events or chance events outcomes, referred to as the states of nature Part4. Identification the consequences associated with each decision alternative and each chance event outcome. Example 2.1 of problem formulation. Part 1. Statement of the problem: Pittsburgh Development Corporation (PDC) is attempting to determine the size of the new condominium project that will lead to the largest profit. The profit of the project depends upon the size of the condominium complex and the chance event concerning the demand for the condominiums. Part 2. Identification the decision alternatives: PDC has the following three decision alternatives: d 1 = to build a small complex with 30 condominiums d 2 = to build a medium complex with 60 condominiums d 3 = to build a large complex with 90 condominiums. Part 3. Identification the states of nature: PDC's president decided to consider two possible chance event outcomes (states of nature ) : s 1 = strong demand for the condominiums s 2 = weak demand for the condominiums. Part 4. Identification the consequences: The consequence is PDC's profit. Influence Diagrams 1
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An influence diagram is a graphical representation of the relationships among the decisions, the chance events, and the consequences for a decision problem. Example 2.2 of influence diagram. Figure 2.1 shows the influence diagram for the PDC problem. Figure 2.1 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 The consequence resulting from a specific combination of a decision alternative and a state of nature is a payoff. A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table. Example 2.3 of payoff table. The payoff table for the PDC condominium project with profits expressed in millions of dollars is shown in Table 2.1 Decision Alternatives States of Nature Strong Demand s 1 Weak demand s 2 Small complex, d 1 8 7 Medium complex, d 2 14 5 Large complex, d 3 20 -9 Note, for example, that if a medium complex is built and demand turns out to be strong, a profit of $14 million will be realized. We will use the notation ij V to denote the payoff 2
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associated with decision alternative i and state of nature j .
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