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1 BA 555 Practical Business Analysis Decision Analysis PrecisionTree Agenda

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2 Decision-making under Certainty Decision-making under certainty entails the selection of a course of action when we know the results that each alternative action will yield. This type of decision problems can be solved by linear/integer programming technique. Example: A company produces two different auto parts A and B. Part A (B) requires 2 (2) hours of grinding and 2 (4) hours of finishing. The company has two grinders and three finishers, each of which works 40 hours per week. Each Part A (B) brings a profit of $3 ($4). How many items of each part should be manufactured per week?

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3 Decision-making under Uncertainty Decision-making under uncertainty entails the selection of a course of action when we do not know with certainty the results that each alternative action will yield. This type of decision problems can be solved by statistical techniques along with good judgment and experience. Example 1 (p.105). McCovery Development Co. has purchased land in Texas, on the shore of the Gulf of Mexico, and is attempting to determine the size of the condominium complex it should build. Three sizes are being considered: small, medium, and large. Management also contemplates three possible levels of demand: low, medium, and high, each equally probable. (1). If the demand is high, McCovey will make $900K if they build the large complex, $600K if they build the medium complex, and $400K if they build the small complex. (2). If the demand is medium, McCovey will make $300K if they build the large complex, $600K if they build the medium complex, and $400K if they build the small complex. (3). If the demand is low, McCovery will lose $300K if they build the large complex, will make $100K if they build the medium complex, and will make $400K if they build the small complex. What is the optimal strategy of the company?

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4 Elements of a Decision Analysis (p.106) Alternative/Action: An alternative (or action) is a course of action intended to solve a problem. Build a small size of condominium complex Build a medium size of condominium complex Build a large size of condominium complex State of Nature and Probabilities: The uncontrollable future events that affect the payoff associated with a decision alternative. Low demand (1/3) Medium demand (1/3) High demand (1/3) Payoff: The outcome measure, such as profit or cost. Each combination of a decision alternative and a state of nature has an associated payoff. If the demand is high, McCovey will make $900K if they build the large complex. If the demand is low, McCovery will lose $300K if they build the large complex. Payoff Matrix: A tabular representation of the payoffs for a decision problem. The rows of the matrix correspond to the decision alternatives, and the columns of the matrix correspond to the possible states of nature.

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5 Decision Rules for Single-Stage Decision Problems The Maximax Decision Rule The Maximin Decision Rule The Minimax Regret Decision Rule The Expected Monetary Value Decision Rule The Expected Regret Decision Rule

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6 The Maximax Decision Rule

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7 The Maximin Decision Rule

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8 The Minimax Regret Decision Rule Regret Matrix: a table summarizes the possible opportunity losses that could result from each decision alternative under each state of nature. Each entry in the regret matrix shows the difference between the maximum payoff that can occur under a given state of nature and the payoff that would be realized from each alternative under the same state of nature.

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9 The EMV Decision Rule Expected Monetary Value (EMV): the weighted average of the payoffs, with weights given by the probabilities of the different states of nature. This rule selects the decision alternative with the largest expected monetary value.

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10 The Expected Opportunity Loss Decision Rule

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11 Decision Tree Using the EMV Rule Read the tree from left to right Solve the tree from right to left At a box, choose the branch with the best EMV. At a chance node (circle), computer the EMV. Decision Tree is a graphical representation of the decision problem that shows the sequential nature of the decision-making process. In a decision tree, decisions are denoted by boxes. random (uncertain) outcomes are denoted by circles.

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12 Solving Multi-Stage Decision Problems – Decision Tree Oilco must determine whether or not to drill for oil in the South China Sea. It costs $1M and if oil is found the value is estimated to be $6M. At present, Oilco believes there is a 45% chance that the field contains oil. Before drilling, Oilco can hire (for $100K) a geology firm to obtain more information about the likelihood that the field will contain oil. Oilco believes there is a 50% chance that the geologist will issue a favorable report, and a 50% chance of an unfavorable report. Given a favorable report, there is a 80% chance that the field contains oil. Given an unfavorable report, there is a 10% chance that the field contains oil. Construct a decision tree to identify Oilco’s possible actions. Clearly label each node and provide sufficient information (e.g., payoff, probability) on each node and branch.

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13 Example 2

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14 Expected Value of Perfect Information Expected Value of Sample Information EVPI = EMV free perfect information – EMV with no information How much would you pay for perfect information? EVSI = EMV with free sample information – EMV with no information Suppose a market research shows that the probabilities of having a low, med., high demand are 0.25, 0.50, How much would you pay for sample information (e.g., market research)?

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