notes Ch 130 - CHAPTER 13 Decision Analysis Pittsburgh...

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CHAPTER 13 Decision Analysis Pittsburgh Development Corporation (PDC) purchased land that will be the site of a new luxury condominium complex. PDC commissioned drawings for three different projects: one with 30 condominiums, one with 60 condominiums, and one with 90 condominiums. The financial success of the project depends upon the size of the condominium complex and the chance event concerning the demand for the condominiums. The statement of the PDC problem is to select the size of the new luxury condominium project that will lead to the largest profit given the uncertainty concerning the demand for the condominiums The payoff table is given below. Payoff Table [in $ millions] Decision Alternative State 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 13.1 Problem Formulation States of nature are the possible outcomes. An influence diagram shows the relationships among the decisions, the chance events, and the consequences for a decision problem. Rectangles depict decision nodes, circles or ovals depict chance nodes, and diamonds 1
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depict consequence nodes (see below). A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table (see below). For example, if a small complex is developed and the demand turns out to be strong, the payoff will be 8 million. Influence Diagram A decision tree provides a graphical representation of the decision-making process. 13.2 Decision Making Without Probabilities The optimistic approach evaluates each decision alternative in terms of the best payoff that can occur. For the PDC example, first identify the maximum payoff for each decision alternative (8, 14, 20); then select the decision alternative that provides the overall maximum payoff (large complex, $20 million). The conservative approach evaluates each alternative in terms of the worst payoff can occur, and recommends the one that provides the best of the worst possible payoffs. For the PDC example, identify the minimum payoff for each of the decision alternatives (7, 5, and -9), then select the decision alternative that maximizes the minimum payoff (small complex, $7 million). In a minimization problem, the optimistic approach will be the one with the minimum payoff and the conservative approach will take the alternative that will minimize the maximum payoff. Comple x size Dema nd Pro fit States of Nature Strong (s 1 ) Decision: Complex size Dema nd Strong (s 1 ) Weak (s 2 ) 8 7 Dema nd Strong (s 1 ) Weak (s 2 ) 14 5 Dema nd Strong (s 1 ) Weak (s 2 ) 20 -9 Small Medium Large 2
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The minimax regret approach is neither purely optimistic nor conservative. In the left table below, we compute the absolute difference between each alternative and the best payoff for each column. These differences represent the opportunity loss (or regret). For
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