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1 Decision-Making Under Uncertainty Lesson 12 LECTURE TWELVE Decision -Making UNDER UNCERTAINITY

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2 Decision-Making Under Uncertainty Lesson 12 Introduction Decision analysis provides a framework and methodology for rational decision making when the outcomes are uncertain. Example: A company plans to determine the best location to startup a new plant from a choice of several locations. Each location offers a different cost scenario. Decision Analysis techniques can be used to determine the best decision.

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3 Decision-Making Under Uncertainty Lesson 12 Payoff Table States of Nature States of Nature s 1 s 2 s 3 s 1 s 2 s 3 d d Decisions d Decisions d d d States of Nature refer to future events which may occur and the values in a Payoff Table refer to either Profit or Cost. Example: s1, s2 & s3 could refer to possible scenarios (i.e. Moderate, Strong & Weak market demand)

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4 Decision-Making Under Uncertainty Lesson 12 Simple Decision Making without Probabilities Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are: Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are: – the Optimistic approach (Maximax or Minimin) – the Conservative approach (Maximin or Minimax) – the Minimax Regret approach.

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5 Decision-Making Under Uncertainty Lesson 12 Optimistic Approach The optimistic approach would be used by an optimistic decision maker. The optimistic approach would be used by an optimistic decision maker. The decision with the largest possible payoff is chosen. The decision with the largest possible payoff is chosen. If the payoff table was in terms of costs, the decision with the lowest cost would be chosen. If the payoff table was in terms of costs, the decision with the lowest cost would be chosen.

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6 Decision-Making Under Uncertainty Lesson 12 Example: Optimistic Approach Consider the following problem with three decision alternatives and three states of nature with the following payoff table representing profits: States of Nature States of Nature s 1 s 2 s 3 s 1 s 2 s 3 d d Decisions d Decisions d d d

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7 Decision-Making Under Uncertainty Lesson 12 Example: Optimistic Approach Formula Spreadsheet Formula Spreadsheet The Optimistic Approach is to make decision based on the maximum of the largest profits. For each decision, d, the largest profits are identified (i.e. 4, -1 & 5)

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8 Decision-Making Under Uncertainty Lesson 12 Example: Optimistic Approach Solution Spreadsheet Solution Spreadsheet

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9 Decision-Making Under Uncertainty Lesson 12 Conservative Approach The conservative approach would be used by a conservative decision maker. The conservative approach would be used by a conservative decision maker. For each decision the minimum payoff is listed and then the decision corresponding to the maximum of these minimum payoffs is selected. For each decision the minimum payoff is listed and then the decision corresponding to the maximum of these minimum payoffs is selected. If the payoff was in terms of costs, the maximum costs would be determined for each decision and then the decision corresponding to the minimum of these maximum costs is selected. If the payoff was in terms of costs, the maximum costs would be determined for each decision and then the decision corresponding to the minimum of these maximum costs is selected.

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10 Decision-Making Under Uncertainty Lesson 12 Example: Conservative Approach Based on the same table with three decision alternatives and three states of nature with the following payoff table representing profits: States of Nature States of Nature s 1 s 2 s 3 s 1 s 2 s 3 d d Decisions d Decisions d d d

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11 Decision-Making Under Uncertainty Lesson 12 Example: Conservative Approach Formula Spreadsheet Formula Spreadsheet

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12 Decision-Making Under Uncertainty Lesson 12 Example: Conservative Approach Solution Spreadsheet Solution Spreadsheet

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13 Decision-Making Under Uncertainty Lesson 12 Minimax Regret Approach The minimax regret approach requires the construction of a regret table or an opportunity loss table. The minimax regret approach requires the construction of a regret table or an opportunity loss table. This is done by calculating for each state of nature the difference between each payoff and the largest payoff for that state of nature. This is done by calculating for each state of nature the difference between each payoff and the largest payoff for that state of nature. Then, using this regret table, the maximum regret for each possible decision is listed. Then, using this regret table, the maximum regret for each possible decision is listed. The decision chosen is the one corresponding to the minimum of the maximum regrets. The decision chosen is the one corresponding to the minimum of the maximum regrets.

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14 Decision-Making Under Uncertainty Lesson 12 Example: 4, 0, 1 is subtracted by 4 giving OL 0, 4, 3, etc. Compute a regret table by subtracting each payoff in a column from the largest payoff in that column. Add a Max Regret Col and make decision based on the Minimum of Maximum Regret. Example: 4, 0, 1 is subtracted by 4 giving OL 0, 4, 3, etc. OLOLOL Max Regret s 1 OL s 2 OL s 3 OL Max Regret 0111 d d d Example: Minimax Regret Approach

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15 Decision-Making Under Uncertainty Lesson 12 Example: Minimax Regret Approach Formula Spreadsheet Formula Spreadsheet

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16 Decision-Making Under Uncertainty Lesson 12 Solution Spreadsheet Example: Minimax Regret Approach

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17 Decision-Making Under Uncertainty Lesson 12 Expected Value Approach – If probabilities regarding the states of nature is available, we may use the expected value (EV) approach. Decision is based on maximising EV. – The expected value (EV) of decision alternative d i is defined as: where: N = the number of states of nature P ( s j ) = the probability of state of nature s j P ( s j ) = the probability of state of nature s j V ij = the payoff corresponding to decision alternative d i and state of nature s j V ij = the payoff corresponding to decision alternative d i and state of nature s j Decision Making with Probabilities

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18 Decision-Making Under Uncertainty Lesson 12 ABC Restaurant Average Number of Customers Per Hour Average Number of Customers Per Hour s 1 = 80 s 2 = 100 s 3 = 120 s 1 = 80 s 2 = 100 s 3 = 120 Model A $10,000 $15,000 $14,000 Model A $10,000 $15,000 $14,000 Model B $ 8,000 $18,000 $12,000 Model B $ 8,000 $18,000 $12,000 Model C $ 6,000 $16,000 $21,000 Model C $ 6,000 $16,000 $21,000 Probability Probability Given s1, s2 & s3 have the probabilities: 0.4, 0.2 & 0.4 Example: Expected Value Approach

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19 Decision-Making Under Uncertainty Lesson 12 Example: Expected Value Approach Formula Spreadsheet

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20 Decision-Making Under Uncertainty Lesson 12 Solution Spreadsheet Example: Expected Value Approach

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21 Decision-Making Under Uncertainty Lesson 12 Expected Value of Perfect Information The expected value of perfect information (EVPI) is the increase in the expected profit that would result if one knew with certainty which state of nature would occur. The expected value of perfect information (EVPI) is the increase in the expected profit that would result if one knew with certainty which state of nature would occur. EVPI = EVwPI – Max EV where EVwPI = ∑ Pi * Max Vi where Vi is the payoffs and EVwPI = Expected Value with Perfect Information EVPI = EVwPI – Max EV where EVwPI = ∑ Pi * Max Vi where Vi is the payoffs and EVwPI = Expected Value with Perfect Information

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22 Decision-Making Under Uncertainty Lesson 12 Spreadsheet Expected Value of Perfect Information

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23 Decision-Making Under Uncertainty Lesson 12 Decision Tree d1d1d1d1 d2d2d2d2 d3d3d3d3 s1s1s1s1 s1s1s1s1 s1s1s1s1 s2s2s2s2 s3s3s3s3 s2s2s2s2 s2s2s2s2 s3s3s3s3 s3s3s3s3 Payoffs 10,000 15,000 14,000 8,000 18,000 12,000 6,000 16,000 21, Average Number of Customers Per Hour s 1 = 80 s 2 = 100 s 3 = 120 s 1 = 80 s 2 = 100 s 3 = 120 Model A $10,000 $15,000 $14,000 Model B $ 8,000 $18,000 $12,000 Model C $ 6,000 $16,000 $21,000 Probabilities

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24 Decision-Making Under Uncertainty Lesson 12 Decision Tree Choose the model with largest EV, Model C. 33 d1d1d1d1 d2d2d2d2 d3d3d3d3 EMV =.4(10,000) +.2(15,000) +.4(14,000) = $12,600 = $12,600 EMV =.4(8,000) +.2(18,000) +.4(12,000) = $11,600 = $11,600 EMV =.4(6,000) +.2(16,000) +.4(21,000) = $14,000 = $14,000 Model A Model B Model C

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25 Decision-Making Under Uncertainty Lesson 12 Decision Tree with Tree Plan Open ‘tree164e.xla’ and enable Macro first.

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26 Decision-Making Under Uncertainty Lesson 12 Decision Tree with Tree Plan

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27 Decision-Making Under Uncertainty Lesson 12 Decision Tree with Tree Plan

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28 Decision-Making Under Uncertainty Lesson 12 Decision Tree with Tree Plan

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29 Decision-Making Under Uncertainty Lesson 12 TOM BROWN INVESTMENT DECISION Tom Brown has inherited $1000. He has to decide how to invest the money for one year. A broker has suggested five potential investments. – Gold – Junk Bond – Growth Stock – Certificate of Deposit – Stock Option Hedge

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30 Decision-Making Under Uncertainty Lesson 12 The return on each investment depends on the (uncertain) market behavior during the year. Tom would build a payoff table to help make the investment decision TOM BROWN

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31 Decision-Making Under Uncertainty Lesson 12 The Payoff Table DJA is down more than 800 points DJA is down [-300, -800] DJA moves within [-300,+300] DJA is up [+300, ] DJA is up more than1000 points

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32 Decision-Making Under Uncertainty Lesson 12 Task Evaluate each investment alternative using: Maximax approach Maximin approach Minimax Regret approach EV approach And construct Decision Tree for EV approach Calculate EVPI

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33 Decision-Making Under Uncertainty Lesson 12 QUESTIONS

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34 Decision-Making Under Uncertainty Lesson 12 Review Questions: 1. What is meant by ‘decision-making under uncertainty’? 2. Why should sequential decisions be considered differently from a series of separate decisions? 3. How can you identify the best decisions in a decision tree?

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