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Practical considerations 235
information was estimated to be $11 million, which was high enough to
suggest that the decision should be postponed until more information
could be gathered. The value of having perfect information on particular
aspects of the problem was also assessed. For example, one area of
uncertainty was the amount of a valuable by-product which would
be produced. The value of perfect information on this variable was
estimated to be $6.2 million. In contrast, it was thought to be worth
paying only $0.3 million to have perfect information on raw material
costs. By comparing the value of perfect information for the different
areas of uncertainty it was possible to identify those areas where the
gathering of more information would be most useful.
As we saw in the previous section, assessing the expected value of
imperfect information requires the decision maker to judge how reliable
the information will be in order to obtain the conditional probabilities for
the Bayes’ theorem calculations. In some circumstances this assessment
can be made on the basis of statistical theory. Consider, for example, a
quality control problem where random sampling is being used to provide
information on the proportion of a batch of components which are
defective. It is possible to use elementary statistical methods to calculate
the probability of a random sample of five components containing two
defectives when, in reality, only 10% are defective. The track record of an
information source can also be useful when estimating the conditional
probabilities. For example, past records might suggest that on 20% of
days when it rained the local weatherman had forecast fine weather.
Similarly, experience with standard market tests leads to a common
assumption that there is an 85% probability that they will give a correct
indication (Scanlon 2 ).
In most cases, however, the assessment of the reliability of the information
will ultimately be based on the decision maker’s subjective
judgment. For example, Schell 3 used the expected value of imperfect
information concept to assess the value of proposed information systems
at a foods corporation, before a commitment was made to allocate
personnel and other resources to the system. As part of the analysis,
managers were asked to estimate the accuracy of proposed systems.
Thus in the case of a sales forecasting system they would be asked
to estimate the percentage of occasions that the system would predict
a decrease in sales when sales would actually increase. The analysis
acted as an initial screening process, leading to the early rejection of a
number of projects and enabling the corporation to focus only on those
which had a good potential for generating economic gains. Because the
managerial and other inputs to the model were ‘soft’, Schell stressed