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242 Revising judgments in the light of new information
how they should react if the control panel indicates particular
problems with the system. Because there is always a possibility
that an indicated problem is in fact caused by a fault in the
control panel itself, there is some concern that unnecessary losses
will be incurred if production is halted because of a non-existent
problem.
Light number 131 will illuminate on the panel if the computer
detects that packs of a frozen food are being filled to below the legal
weight. However, it is known that there is a 0.15 probability that this
light will give a false alarm. In the event of this light illuminating,
the manager would have to decide whether or not to gather further
information before making a decision on whether to stop production
immediately. Any stoppage would cost an estimated $150 000, but
a decision to ignore the light would lead to losses of $300 000 if
the bags being filled on the automatic production line really were
underweight.
If the manager decides to gather further information before taking
the decision on whether to stop production then this will involve
taking a sample from output and weighing the selected packs. This
will render the sampled packs unsaleable and cost the company
$5000. The sample will indicate whether or not there is a fault in
production, but there is a 0.2 probability that it will give misleading
results. Despite this it has always been company policy to take
a sample because of the small cost of sampling relative to the
other costs.
(a) If the company’s objective is to minimize expected costs, formulate
a decision rule which will tell the duty manager how to
react when light 131 illuminates.
(b) Explain the rationale behind your recommended decision rule
in non-technical terms.
(c) Explain the role which sensitivity analysis could have in
this problem.
(10) When the demand for electricity exceeds a particular level the
Central Electricity Company has to bring an additional power
station on line at a fixed cost of $10 000. Excessive demand only
occurs on cold winter weekdays between 4.30 and 5.30 pm.
To try to avoid bringing the additional station on line Central
has made a deal with its largest industrial customer. According to
the deal the customer will reduce its electricity usage by an agreed
amount between 4.30 and 5.30 pm on any day that they receive a
request from Central. In return they will receive a reduction in their