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Decision trees and utility 149
successful, and so on. Moreover, if the company chooses to develop
its knowledge of gas, rather than electric, technology, this may restrict
its options in the long term. However, any attempt to formulate a tree
which represents every possible consequence and decision which may
arise over a period stretching into the distant future would clearly lead
to a model which was so complex that it would be intractable. Judgment
is therefore needed to determine where the tree should end.
Clearly, the calculations involved in analyzing a large decision tree can
be rather tedious. Because of this, a number of computer packages have
been developed which will display and analyze decision trees and allow
them to be easily modified. For example, DPL, produced by Standard &
Poor’s Applied Decision Analysis (ADA) (Menlo Park, California), is a
Microsoft® Windows® application, while PRECISION TREE, produced
by the Palisade Corporation (Newfield, New York), allows decision
trees to be developed in Microsoft Excel spreadsheets. Both packages
also allow users to draw influence diagrams to represent the decision
(see later in this chapter) and then to convert these automatically into
decision trees.
Decision trees and utility
In the previous section we made the assumption that the decision maker
was neutral to risk. Let us now suppose that the engineer is concerned
that his career prospects will be blighted if the development of the
processor leads to a great loss of money for the company. He is therefore
risk averse, and his utility function for the monetary sums involved in
this problem is shown in Figure 6.4.
The procedure for analyzing the tree when utilities are involved is
exactly the same as that which we used for the EMV criterion. Figure 6.5
shows the decision tree, with the utilities replacing the monetary values.
After applying the rollback method it can be seen that now the optimum
policy is to develop the electric-powered design and, if it fails, to abandon
the project. Note, however, that the closeness of the expected utilities
suggests that sensitivity analysis should be applied to the tree before a
firm decision is made.
If the engineer had wished to include other attributes besides money
in his decision model then multi-attribute utilities would have appeared
at the ends of the tree. However, the rollback procedure would still have
been applied in the same way. This would also be the case if the payoffs
on the tree had been represented as net present values (see Chapter 7).