Question

1. The SPEA’s administration was concerned about the potential loss that might occur in the event of a power failure. The school estimated that the loss from one of these incidents could be as much as

$10 million, including losses due to interrupted student service and potential loss of data collected for years in NSF and DoD sponsored projects. One alternative the school is considering is the installation of an emergency power generator. The cost of the emergency generator is

$80,000, and if it is installed, no losses from this type of incident will be incurred. However, if the generator is not installed, there is a 12% chance that a power outage will occur during a year. If there is an outage, there is a .07 probability that the resulting losses will be very large, or approximately $7 million in net aggregated loss. Alternatively, it is estimated that there is a .93 probability of only slight losses of around $1 million.

Using decision tree analysis, determine whether the SPEA should have install the new power generator. What considerations may change your decision?

Answer 1

The decision Tree can be drawn as follows

Total potential losses of not installing a generator = (7,000,000 * 0.07 + 1,000,000 * 0.93) * 0.12 = 1,420,000 * 0.12 = 170,400

Total expense in installing a generator = $80,000

Since the cost of installing a generator is less than the potential losses of not installing, so it is better to install the generator.

If the probability of a power outage was less than 80,000 / 1,420,000 or less than 5.6%, then it would not have made sense to install the generator.
Basically if the total potential losses of not installing the generator was lesser than the cost to install a generator, then the generator will not be installed. This can happen in either or all of the following ways

1) The cost of Heavy Damage is lower

2) The potential of a power outage is much lower

3) The cost of installing the generator is higher

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