Assignment:
A food company runs a computerized processing plant and needsto formulate a series of decision rules to advise its managers on242 Revising judgments in the light of new informationhow they should react if the control panel indicates particularproblems with the system. Because there is always a possibilitythat an indicated problem is in fact caused by a fault in thecontrol panel itself, there is some concern that unnecessary losseswill be incurred if production is halted because of a non-existentproblem. Light number 131 will illuminate on the panel if the computerdetects that packs of a frozen food are being filled to below the legalweight.
However, it is known that there is a 0.15 probability that thislight will give a false alarm. In the event of this light illuminating,the manager would have to decide whether or not to gather furtherinformation before making a decision on whether to stop productionimmediately. Any stoppage would cost an estimated $150 000, buta decision to ignore the light would lead to losses of $300 000 ifthe bags being filled on the automatic production line really wereunderweight.If the manager decides to gather further information before takingthe decision on whether to stop production then this will involvetaking a sample from output and weighing the selected packs.
Thiswill render the sampled packs unsaleable and cost the company$5000. The sample will indicate whether or not there is a fault inproduction, but there is a 0.2 probability that it will give misleadingresults. Despite this it has always been company policy to takea sample because of the small cost of sampling relative to theother costs.
(a) If the company's objective is to minimize expected costs, formulatea decision rule which will tell the duty manager how toreact when light 131 illuminates.
(b) Explain the rationale behind your recommended decision rulein non-technical terms.
(c) Explain the role which sensitivity analysis could have inthis problem.