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166 Decision trees and influence diagrams
machine in 5 days. However, if at the end of 5 days the attempted
repair has not been successful he will have to decide whether to
call in the local engineering company or to make a second attempt
at repair by investigating a different part of the mechanism. This
would take 2 further days, and he estimates that there is a 25%
chance that this second attempt would be successful. If he fails
at the second attempt, he will have no alternative other than to
call in the local engineering company. It can be assumed that the
probability distribution for the local engineering company’s repair
time will be unaffected by any work which the factory engineer has
carried out.
Assuming that the engineer’s objective is to minimize expected
costs, what course(s) of action should he take?
(3) Westward Magazine Publishers are thinking of launching a new
fashion magazine for women in the under-25 age group. Their
original plans were to launch in April of next year, but information
has been received that a rival publisher is planning a
similar magazine. Westward now have to decide whether to bring
their launch forward to January of next year, though this would
cost an additional $500 000. If the launch is brought forward it
is estimated that the chances of launching before the rival are
about 80%. However, if the launch is not brought forward it is
thought that there is only a 30% chance of launching before the
rival.
For simplicity, the management of Westward have assumed that
the circulation of the magazine throughout its life will be either
high or low. If Westward launch before the rival, it is thought that
there is a 75% chance of a high circulation. However, if the rival
launches first, this probability is estimated to be only 50%.
If the rival does launch first then Westward could try to boost
sales by increasing their level of advertising. This would cost an
extra $200 000, but it is thought that it would increase the probability
of a high circulation to 70%. This increased advertising expenditure
would not be considered if Westward’s magazine was launched
first. Westward’s accountants have estimated that a high circulation
would generate a gross profit over the magazine’s lifetime of
$4 million. A low circulation would bring a gross profit of about
$1 million. It is important to note, however, that these gross profits
do not take into account additional expenditure caused by bringing
the launch forward or by increased advertising.
(a) Draw a decision tree to represent Westward’s problem.