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Determining the optimal policy 147
Determining the optimal policy
It can be seen that our decision tree consists of a set of policies. A policy
is a plan of action stating which option is to be chosen at each decision
node that might be reached under that policy. For example, one policy
would be: choose the electrical design; if it fails, modify the design.
Another policy would be: choose the electrical design; if it fails, abandon
the project.
We will now show how the decision tree can be used to identify
the optimal policy. For simplicity, we will assume that the engineer
considers that monetary return is the only attribute which is relevant
to the decision, and we will also assume that, because the company is
involved in a large number of projects, it is neutral to the risk involved
in this development and therefore the expected monetary value (EMV)
criterion is appropriate. Considerations of the timing of the cash flows
and the relative preference for receiving cash flows at different points in
time will also be excluded from our analysis (this issue is dealt with in
Chapter 7).
The technique for determining the optimal policy in a decision tree
is known as the rollback method. To apply this method, we analyze
the tree from right to left by considering the later decisions first. The
process is illustrated in Figure 6.3. Thus if the company chose the
electrical design and it failed (i.e. if the decision node labeled with an A
was reached), what would be the best course of action? Modifying the
design would lead to an expected return of (0.3 × $6 m) + (0.7 ×−$7 m),
which equals −$3.1 m. Since this is worse than the −$3 m payoff that
would be achieved if the design was abandoned, abandoning the design
would be the best course of action. Two bars are therefore placed
over the inferior branch and the ‘winning’ payoff is moved back to
the decision node where it is now treated as a payoff for the ‘failure’
branch. This means that the expected payoff of the electrical design is
(0.75 × $10 m) + (0.25 ×−$3 m), which equals $6.75 m.
The same analysis is applied to the section of the tree that represents
the gas-powered design. It can be seen that if this design fails the best
option is to modify it. Hence the expected payoff of the gas design is
$11.24 m. This exceeds the expected payoff of the electrical design and
the $0 payoff of not proceeding with the development. Two bars are
therefore placed over the branches representing these options and the
$11.24 m is moved back to the initial decision node. The optimum policy
is therefore to develop the gas-powered design and, if it fails, to modify
the design.