Alternative 1: You can create the chance using the techniques you learned in handout 1.

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1 DECISION ANALYSIS MODELS AND APPLICATIONS Precision Tree handout Part 2 DECISION TREES Open the DT Texaco handout 2 excel file. There is a missing chance node Final Court Decision in the Refuse 3$ Billion branch. There are three possibilities for completing this part of the tree. Alternative 1: You can create the chance using the techniques you learned in handout 1. Alternative 2: You can copy and paste the chance node by following these steps: A2.1: Click with the right button of the mouse on the Final Court Decision node. A2.2: Select the Copy subtree button. A2.3: Now click on the right button of the mouse over the end node (blue triangle) of the Refuse $3 Billion branch, and select Paste subtree. PrecisionTree will re create the Final Court Decision at the end of the branch. Alternative 3: The third possibility is to use the existing Final Court Decision node as a Reference node. In this case, you are instructing PrecisionTree to refer back to the Final Court Decision chance node (and all of its subsequent structure) at the end of the Refuses Counteroffer branch. To do this: A3.1: Click on the end note of the Refuse $3 Billion branch and select the Reference Node option (gray diamond) A3.2: In the name box, type Final Court Reaction. A3.3: Click in the entry box that is situated to the right of the option button labelled node of this tree. Move the cursor to outside the dialog box to the spreadsheet and click in the cell below the name Final Court Decision (Figure 1, cell D15). (Be sure to point to the cell D15, which contains the value of the chance node, not the cell D14, which contains the name of the node.) A3.4: Click Ok. Mónica Oliveira, RPEM 2009/2010 1

2 Figure 1: Texaco Pennzoil decision tree 1. Step 1: 1.1. Click on the Decision Analysis button In the Decision Analysis dialog box that appears (Figure 2), choose the Risk Profile option. Afterwards choose the Policy suggestion option within the Decision Analysis button and choose the Entire model option. Figure 2: Decision Analysis dialog box 1.3. Click OK. Mónica Oliveira, RPEM 2009/2010 2

3 Figure 3: Policy Suggestions for Texaco Pennzoil problem Figure 4: Cumulative risk profiles for the Accept $2 billion and the counteroffer $5 billion alternatives INFLUENCE DIAGRAMS Please construct the Influence Diagram presented in Figure 5. Mónica Oliveira, RPEM 2009/2010 3

4 Figure 5: Influence diagram for Texaco versus Pennzoil 2. Step 2: As a general rule, numbers are added to a node of an influence diagram by clicking on the name of the node, clicking the exit to value table button, and entering the appropriate numbers in the Influence Value Editor dialog box. Remember to hit the Return button after each value is specified Enter the numerical values and probabilities for the nodes Accept $2 billion?, Texaco Response and Final Court Decision using Figure 6 as a guide. For example, for the values of the Accept $2 billion? node, enter 2 if accepted and enter 0 if $5 billion is counteroffered. Similarly, enter 5 if Texaco s response is to accept the $5 billion counteroffer and 0 if they refuse or counteroffer $3 billion. Enter 0 for Value if skipped for three nodes. Figure 6 : Decision Tree for Texaco 2.2. Click on the decision node name Pennzoil Reaction and click on the Values button. A spreadsheet pops up titled Influence Value Editor, in which we use the entries on the right Mónica Oliveira, RPEM 2009/2010 4

5 to specify the values in the Value column (Figure 7). Essentially, the Influence Value Editor is a consequence table similar to table 1 except the columns are read from right to left. Figure 7: Influence Value Editor for Pennzoil Reaction decision node Mónica Oliveira, RPEM 2009/2010 5

6 Table 1: Outcomes table 2.3. Start by typing 0 in the first row (Value when skipped) and hit Enter. Mónica Oliveira, RPEM 2009/2010 6

7 2.4. Type the equals sign (=) in the second row. For this row the alternative we are entering is found by reading the rightmost entry accept the $2 billion offer. Hence its value is 2, which is accessed by clicking on the first Accept 2 in the column below the Accept $2 Billion heading. Row 2 should now read: =E4. Hit Enter The next five entries also involve accepting the $2 billion, so repeat Step 2.4 five times, and for each row click on the corresponding Accept 2 in the rightmost column. Alternatively, because this is an Excel spreadsheet, you can use the fill down command. As a guide in completing this node, we have outlined the outcomes that you are to reference with boxes in figure Continuing onto rows 7 12, the rightmost alternative is to counteroffer $5 billion. Since Pennzoil has counteroffered, the values are now determined by Texaco s response. Specify the appropriate value by clicking on the corresponding row under the Texaco Response heading Click OK when your Influence Value Editor matches Figure Following the same procedure, open the Influence Value Editor for Settlement Amount and enter the appropriate values as you read from left to right. Figure 8 highlight the cells to click on. Figure 8: Settlement Amount Values dialog box for Texaco Pennzoil model 3. Step 3: 3.1. Click on the name of the influence diagram Texaco versus Pennzoil with the right button of the mouse Select Model and Convert to Decision Tree. 4. Step 4: The procedure for analyzing an influence diagram is the same as analyzing a decision tree Click on the Decision Analysis button and click OK to one of the options. Mónica Oliveira, RPEM 2009/2010 7

8 5. Step 5: 5.1. Build the decision tree, as shown is Figure 9, using the given probabilities. Leave the values (the numbers below the branches) temporarily at zero. Figure 9: Modeling multiattribute decisions using the spreadsheet for calculations 6. Step 6: 6.1. Create the weights table by typing 0.6 in cell B3 and =1 B3 in cell C3. 7. Step 7: 7.1. Create the consequence table by entering the appropriate scale salary and scale fun scores corresponding to the branch values in columns F and G, as shown in Figure Compute the weighted scores for the top branch by clicking in cell E5 and type =$B$3*F5+$C$3*G5. A score of 88.6 should appear in E Click on cell E5 and copy (either Ctrl C or Edit Copy) 7.4. Click into cell E7 and paste. A score of 84.6 should appear in E7. Continue pasting the formula into the cells corresponding to each of the branches. You can streamline the process by copying the formula once, then holding down the control Key while highlighting each cell into which you want to past the formula. Now choose paste, and the formula is inserted into each highlighted cell. The weighted scores should be the same as those in Figure Step 8: 8.1. We now place the weighted scores into the decision tree. Click in cell C5 and type =E Copy the contents of C5 and paste into the cells below each branch of the decision tree. At this point, your tree should be identical to the one in Figure 9. Mónica Oliveira, RPEM 2009/2010 8

9 9. Step 9: 9.1. Construct the Mail order decision tree as shown is figure 10 and name the tree Linked Tree. You should note that this is a minimizing problem. Figure 10: A decision tree linked to a table that computes the end node value 10. Step 10: Next, we construct the table as shown at the top of Figure In cell C6, we put C4*C In cell C8, we put C4 C6+C Step 11: Now that we have build the tree and the table, we will link the tree Click directly in the tree s name: Mail oder Under the Calculation heading in the dialog box, choose the Link to spreadsheet Model option button in the Path Payoff Calculation and choose the Automatically Update Link box, using a default cell C One by one, click in each end node of the Mail order tree (as shown in Figure 10) and choose the correct Link Branch Value as indicated in the Figure. 12. Step 12: We have now to fill the values of the branches of the tree with the values that will be replaced in the link. And after we can perform analysis to the linked tree. Mónica Oliveira, RPEM 2009/2010 9