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1 Chapter 5 There is no more miserable human being than one in whom nothing is habitual but indecision.—William James Decision-Making Concepts

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2 Elements of Decisions Every decision has acts. These are the possible choices. Outcomes are the consequences. Decisions made under uncertainty involve events. When there is uncertainty, outcomes are determined partly by choice (acts) and partly by chance (events). Decisions are portrayed: With a decision table or a payoff table. Or by a decision tree.

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3 The Payoff Table The payoff table has a column for each act and a row for each event. The payoff value expresses how closely an outcome brings the decision maker to his or her goal.

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4 The Decision Tree The decision tree shows acts and events on separate forks, sequenced chronologically. Each outcome has a path.

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5 Payoffs and Probabilities Here the payoffs for outcomes are found adding partial cash flows on branches. Event branches have probabilities.

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6 Making the Decision Using a Payoff Table Decision makers want to maximize payoff. But, the outcome is uncertain. Various criteria exist for making the choice. Maximizing expected payoff is commonly used to make choices. First, compute expected payoff for each act. An act’s expected payoff is the weighted average value for its column found by multiplying payoffs by the row’s probability and summing the products. Second, choose the act having the maximum.

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7 Computing Expected Payoffs The Tippi-Toes expected payoffs are: For simplicity, the pneumatic movement act was first eliminated. It is an inadmissible act because it is dominated by one or more acts. Inadmissible acts will never be selected because there is a single act that is always at least as good and in one case strictly better. Weights and pulleys (see previous slide) dominates pneumatic.

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8 Maximizing Expected Payoff is the Bayes Decision Rule It is not a perfect criterion because it can lead to the less preferred choice. Consider the Far-Fetched Lottery decision: Would you gamble? EVENTS Proba- bility ACTS GambleDon’t Gamble Head.5+$10,000$0 Tail.5 5,000 0

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9 The Far-Fetched Lottery Decision The expected payoffs are: Most people prefer not to gamble! That violates the Bayes decision rule. But the rule often indicates preferred choices even though it is not perfect. EVENTS Proba- bility ACTS GambleDon’t Gamble Payoff × Prob.Payoff × Prob Head.5+$5,000$0 Tail.5 2,500 0 Expected Payoff: $2,500$0

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10 Other Decision Criteria Maximin Payoff: Choose best of possible worsts (take MAXImum of MINimums). Way too conservative for business decisions. Focuses totally on downside. Ignores upside. Uses less information than Bayes decision rule.

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11 Other Decision Criteria Maximum Likelihood: Identify most likely event, ignore others, and pick act with greatest payoff. Personal decisions often made that way. Collectively, other events may be more likely. Ignores lots of information.

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12 Decision Tree Analysis Each node is evaluated in terms of its expected payoff. Event forks: expected payoffs are computed. Act forks: the greatest value is brought back. The decision tree is folded back by maximizing expected payoff. Inferior acts are pruned from the tree. The pruned tree indicates the best course of action, the one maximizing expected payoff. The process works backward in time.

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13 Folding Back the Decision Tree

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14 Opportunity Loss Another perspective on decision making is provided by the opportunity loss. It is the reduction in payoff between the best outcome and what would be achieved.

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15 Using Opportunity Loss Criteria may be based on opportunity loss, which is a measure of regret. It is a quantity to be minimized. Choosing the act minimizing expected opportunity loss is the preferred criterion. It is equivalent to Bayes decision rule. This sometimes involves easier calculations.

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16 Expected Value of Perfect Information Although perfect information is an ideal, it says a lot about less-than-perfect predictors. EVPI = Expected payoff under certainty Maximum Exp. Payoff (no Info.) The expected payoff under certainty is computed assuming best act will be chosen regardless of the event that occurs.

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17 Expected Value of Perfect Information The expected payoff under certainty is just an ideal. (Perfect predictors are unrealistic.) For Tippi-Toes, the maximum expected payoff (no information) is $455,000 and EVPI = $460,500 455,000 = $5,500 The above expresses “on the average” how much better we are with the information. We should reject less-than-perfect predict- ors (real ones) costing more than the EVPI.

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18 Templates and Software Payoff Table templates Palisade Decision Tools PrecisionTree 1.0

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19 Simple Payoff Table for Exchecker Decision (Figure 5-2) 1. Enter problem name in B3. 3. If more events or acts are required, expand the table by inserting additional rows and/or columns. Make sure the formulas for the Expected Payoffs in the last row include all the rows of the expanded table. 2. Enter data in B9:F12 and labels in A9:A12 and C8:F8. 4. Expected payoffs

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20 Expanded Payoff Table for Exchecker Decision (Figure 5-3) 1. Enter problem name in B3. 2. Enter data in B9:F12 and labels in A9:A12 and C8:F8. 3. If more events or acts are required, expand the table by inserting additional rows and/or columns. Make sure the formulas in the Act Summary table include all the rows of the expanded table. Make sure that the formulas in D23:E24 include all the columns in the expanded table. 4. Answers : exp. payoff, exp. opportunity loss, max. exp. payoff, min. exp. opportunity loss, EVPI.

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21 Palisade Decision Tools PrecisionTree The PrecisionTree 1.0 software program on the CD-ROM accompanying this book is an Excel Add-In that solves decision trees. It has a number of options for analyzing and graphing results.

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22 PrecisionTree To start PrecisionTree, click on the Windows Start button, select Programs, Palisade Decision Tools, then PrecisionTree 1.0 for Excel Both Excel and PrecisionTree will open. You will see the normal Excel screen with two new tool bars, one for Palisade Decision Tools and the other for PrecisionTree, as shown next.

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23 The PrecisionTree Tool Bar The PrecisionTree tool bar will show along with the Excel tool bars. Click on the New Tree icon and click in a cell in the spreadsheet to start a new tree. Or click on PrecisionTree on the menu bar, select the Create New option, and click on Tree.

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24 Initial PrecisionTree Decision Tree Clicking in cell A1 yield this initial tree. Figure 5-8 To name the tree, click in the tree #1 box. This brings to the screen the Tree Settings dialog box shown next.

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25 Tree Settings Dialog Box for Naming Decision Tree (Figure 5-9 ) Enter the name Ponderosa Record Company in the Tree Name line and click OK.

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26 Initial Ponderosa Record Co. Decision Tree (Figure 5-10) To expand the decision tree move the cursor over the end nod and click. This yields the Nodes Settings dialog boxes shown next.

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27 Node Settings Dialog Box (Figure 5-11) Under node type click on the decision node. The Node Settings dialog box changes to that shown on the right. There enter 2 in the # of Branches line and click OK.

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28 Extended PrecisionTree Decision (Figure 5-12) The costs associated with the branches are entered directly onto the spreadsheet, $15,000 in cell B2 and $0 in cell B6. To name the branches click inside one of the boxes named branch. This brings to the screen the Branch Settings dialog box shown next.

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29 Branch Settings Dialog Box for Naming Decision Branches (Figure 5-13 ) Enter the name of the branch in the Branch Name line and click OK.

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30 Extended Decision Tree with Decisions and Partial Cash Flows (Figure 5-14 ) Clicking on the end node in cell C1:C2 continues the tree expansion. The Node Settings dialog box appears as previously. Only this time under Node Type select the chance button. The 1 and 0 in C1 and C5 are the probabilities and the $15,000 and $0 in C2 and C6 are the net payoffs for the respective branches. The $15,000 in B4 is the expected payoff for the decision.

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31 Second Expanded Decision Tree (Figure 5-15) The tree has two new branches, Favorable and Unfavorable. Probabilities of 50% and 0% are in C1 and C5. Partial cash flows, both $0, appear in C2 and C6. Expanding the tree once more yields the next tree.

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32 Third Expanded Decision Tree (Figure 5-16) Two new branches, Market nationally and Abort, have been added to the tree. Their respective cash flows, -$50,000 and $0, are in D2 and D6. Continuing to add branches yields the final tree shown next.

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33 Final Decision Tree (Figure 5-17) TRUE on a branch indicates a branch is selected and FALSE means it is not. The optimal strategy is: 1. Test market 2. If the test market is successful, market nationally. 3. If the test market is not successful, abort. 4. The expected payoff is $1,000 (cell B24). The optimal strategy is: 1. Test market 2. If the test market is successful, market nationally. 3. If the test market is not successful, abort. 4. The expected payoff is $1,000 (cell B24).

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34 Risk Profile Clicking on the Decision Analysis icon gives the risk profile. The risk profile is the probability distribution of the possible outcomes if the optimal strategy is followed.

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35 Risk Profile for Ponderosa Record Co. (Figure 5-18)

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36 Sensitivity Analysis Determining Important Factors The optimal solution depends on many factors. Which is the most important? A sensitivity analysis answers this question. To perform a sensitivity analysis, click on the Sensitivity Analysis icon.

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37 Sensitivity Analysis Determining Important Factors How does the $1,000 payoff change if ±10% changes occur in: the $90,000 partial cash flow in cell E2 the 0.80 success probability in cell E1 the $15,000 test marketing cost in cell B12 Clicking on the Sensitivity Analysis Icon yields the Sensitivity Analysis dialog box shown next.

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38 Sensitivity Analysis Dialog Box (Figure 5-19) 1. In the Cell to Analyze line enter B24, the location of the $1,000 expected payoff 2. Under the Input Editor section, input E2 in the Cell line as the location of the $90,000 partial cash flow. 3. Click the Suggest Values button and enter the ±10% variation and click on the Add button and Success/Ponderosa !$E$2 (-10%,90000, 10%) appears in the first line in the Cells to Vary box. 4. Repeat these steps for the other items to vary. 5. Click on the Run Analysis button.

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39 Tornado Diagram (Figure 5-20) Each horizontal bar shows the effect on the $1,000 expected payoff of a ±10% change in original levels of (1) $90,000 successful sales outcome, (2) 0.80 success probability, (3) the $15,000 test marketing cost.

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40 Spider Graph (Figure 5-21) 1. The steeper the slope of the line, the larger the effect of a factor on the $1,000 expected payoff. 2. The success probability and sales lines coincide indicating that they have equal effects on the $1,000 expected payoff.

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Decision Theory McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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