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556 CHAPTER 13 DECISION ANALYSIS

NOTES AND COMMENTS

1 Some decision analysis software automatically to determine the value of the optimal solution. By
provides the risk profiles for the optimal decision varying each input over its range of values, we
alternative. These packages also allow the user obtain information about how each input affects
to obtain the risk profiles for other decision the value of the optimal solution. To display this
alternatives. After comparing the risk profiles, a information, a bar is constructed for the input with
decision maker may decide to select a decision the width of the bar showing how the input affects
alternative with a good risk profile even though the value of the optimal solution. The widest bar
the expected value of the decision alternative is corresponds to the input that is most sensitive.
not as good as the optimal decision alternative. The bars are arranged in a graph with the widest
2 A tornado diagram, a graphical display, is bar at the top, resulting in a graph that has the
particularly helpful when several inputs combine appearance of a tornado.

13.5 Decision Analysis with Sample Information

In applying the expected value approach, we showed how probability information
about the states of nature affects the expected value calculations and thus the
decision recommendation. Frequently, decision makers have preliminary or prior
probability assessments for the states of nature that are the best probability values
available at that time. However, to make the best possible decision, the decision
maker may want to seek additional information about the states of nature. This new
information can be used to revise or update the prior probabilities so that the final
decision is based on more accurate probabilities for the states of nature. Most often,
additional information is obtained through experiments designed to provide sample
information about the states of nature. Raw material sampling, product testing and
market research studies are examples of experiments (or studies) that may enable
management to revise or update the state-of-nature probabilities. These revised
probabilities are called posterior probabilities.
Let us return to the PDC problem and assume that management is considering a
six-month market research study designed to learn more about potential market
acceptance of the PDC project. Management anticipates that the market research
study will provide one of the following two results:
1 Favourable report: A significant number of the individuals contacted express
interest in purchasing or leasing a PDC unit.
2 Unfavourable report: Very few of the individuals contacted express interest in
purchasing or leasing a PDC unit.

Decision Tree

The decision tree for the PDC problem with sample information shows the logical
sequence for the decisions and the chance events in Figure 13.6.
First, PDC’s management must decide whether the market research should be
conducted. If it is conducted, PDC’s management must be prepared to make a
decision about the size of the project if the market research report is favourable
and, possibly, a different decision about the size of the project if the market research
report is unfavourable. In Figure 13.6, the squares are decision nodes and the circles

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