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148 Decision trees and influence diagrams
$11.24 m
Develop electric-powered design
Develop gas-powered design
Do not develop the product
$0
$6.75 m
$11.24 m
Success
0.75 −$3 m
Failure
0.25
Success
Failure
Figure 6.3 – Rolling back the decision tree
0.4
$10 m
A
$15 m
$5.6 m
0.6
Modify design
Abandon project
Modify design
Abandon project
−$3.1 m
$5.6 m
Success
−$3 m
−$7 m
Failure
Success
Failure
0.3
0.7
0.8
0.2
$6 m
−$7 m
$10 m
−$12 m
It can be seen that the rollback method allows a complex decision
problem to be analyzed as a series of smaller decision problems. We
should, of course, now apply sensitivity analysis to the probabilities
and payoffs using the method we introduced in the previous chapter.
For brevity, this analysis will not be carried out here. It should also
be pointed out that the decision tree suggests the best policy based
on the information which is available at the time it is constructed. By
the time the engineer knows whether or not the gas-powered design
is successful his perception of the problem may have changed and he
would then, of course, be advised to review the decision. For example, if
the design fails, the knowledge he has gained in attempting to develop
the equipment may lead him to conclude that modification would be
unlikely to succeed and he might then recommend abandonment of
the project.
Note also that the planning period which the tree represents is arbitrary.
Even if a successful gas design is developed this surely will not
be the end of the story, since this choice of design is bound to have
ramifications in the future. For example, any money earned from the
design may well be reinvested in research and development for future
products and the developments of these products may or may not be