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Constructing a decision tree 145
because each branch emanating from this node presents an option, the
decision maker can choose which branch to follow. A circle, on the
other hand, is used to represent a chance node. The branches which
stem from this sort of node represent the possible outcomes of a given
course of action and the branch which is followed will be determined,
not by the decision maker, but by circumstances which lie beyond his or
her control. The branches emanating from a circle are therefore labeled
with probabilities which represent the decision maker’s estimate of the
probability that a particular branch will be followed. Obviously, it is not
sensible to attach probabilities to the branches which stem from a square.
The following example will be used to demonstrate how a decision
tree can be used in the analysis of a multi-stage problem. An engineer
who works for a company which produces equipment for the foodprocessing
industry has been asked to consider the development of a
new type of processor and to make a recommendation to the company’s
board. Two alternative power sources could be used for the processor,
namely gas and electricity, but for technical reasons each power source
would require a fundamentally different design. Resource constraints
mean that the company will only be able to pursue one of the designs,
and because the processor would be more advanced than others which
have been developed it is by no means certain that either design would
be a success. The engineer estimates that there is a 75% chance that the
electricity-powered design would be successful and only a 60% chance
that the gas-powered design would be a success.
Figure 6.1 shows an initial decision tree for the problem with estimated
payoffs in millions of dollars. After considering this tree the engineer
realizes that if either design failed then the company would still consider
modifying the design, though this would involve more investment and
would still not guarantee success. He estimates that the probability that
the electrical design could be successfully modified is only 30%, though
the gas design would have an 80% chance of being modified successfully.
This leads to the new tree which is shown in Figure 6.2. Note that the
decision problem is now perceived to have two stages. At stage one
a decision has to be made between the designs or not developing the
problem at all. At stage two a decision may have to be made on whether
thedesignshouldbemodified.
After some reflection, the engineer agrees that this tree is a satisfactory
representation of the options facing the company. Other alternatives
such as switching to the development of a gas-powered design if the
electrical design is not successful are not considered to be feasible, given
the resources available to the company.