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560 CHAPTER 13 DECISION ANALYSIS

Figure 13.8 PDC Decision Tree After Calculating Expected Values at Chance Nodes
6to14

Small (d ) 6 EV = 7.94
1

Favourable Medium (d )
2
Report 0.77 3 7 EV = 13.46

Large (d )
3
8 EV = 18.26
Market Research
Study 2
Small (d 1 )
9 EV = 7.35

Unfavourable Medium (d )
2
1 Report 0.23 4 10 EV = 8.15

Large (d )
3
11 EV = 1.15

Small (d 1 )
12 EV = 7.80

No Market Research Medium (d )
2
5 13 EV = 12.20
Study

Large (d )
3
14 EV = 14.20

For node 4, we select the best expected value from nodes 9, 10 and 11. The best
decision alternative is the medium complex branch that provides EV(Node 4) ¼ 8.15.
For node 5, we select the best expected value from nodes 12, 13 and 14. The best
decision alternative is the large complex branch that provides EV(Node 5) ¼ 14.20.
Figure 13.9 shows the reduced decision tree after choosing the best decisions at
nodes 3, 4 and 5.
The expected value at chance node 2 can now be calculated as follows:
EVðNode2Þ¼ 0:77EVðNode3Þþ 0:23EVðNode4Þ
¼ 0:77ð18:26Þþ 0:23ð8:15Þ¼ 15:93

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