QuestionCase Study: The Hartland River A

Case Study: The Hartland River Authority
The risk of the flooding in land adjacent to the River Nudd has recently increased. This
is because of a combination of high spring tides and the development by farmers of
more efficient drainage systems in the nearby hills which means that, after heavy
rainfall, water enters the river more quickly. A tidal barrier is being constructed at the
mouth of the river, but the Hartland River Authority has to decide how to provide flood
protection in the two years before the barrier is completed. Flooding is only likely to
occur during the spring high tide period and the height of the river at this time cannot be
predicted with any certainty. In the event of flooding occurring in anyone year the
Authority will have to pay out compensation of about £2 million. Currently, the Authority
is considering three options. First, it could do nothing and hope that flooding will not
occur in either of the next two years. The river’s natural banks will stop flooding as long
as the height of the water is less than 9.5 feet. It is estimated that there is a probability
of 0.37 that the height of the river will exceed this figure in any one year.
Alternatively, the Authority could erect a cheap temporary barrier to a height of 11feet.
This barrier would cost £0.9 million to erect and it is thought that there is a probability of
only 0.09 that the height of the river would exceed this barrier. However, if the water did
rise above the barrier in the first year, it is thought that there is a 30% chance that the
barrier would be damaged, rendering it totally ineffective for the second year. The
Authority would then have to decide whether to effect repairs to the barrier at a cost of
£0.7 million or whether to leave the river unprotected for the second year. The third
option would involve erecting a more expensive barrier. The fixed cost of erecting this
type of barrier would be £0.4 million and there would be an additional cost of £0.1 million
for each foot in the barrier’s height. For technical reasons the height of this barrier would
be either 11 or 13 feet and it is thought that there would be no chance of the barrier
being damaged if flooding did occur. The probability of the river’s height exceeding the
13 feet barrier in anyone year is estimated to be only0.004.
a) Draw a decision tree to represent the River Authority’s problem.
b) Determine the optimum policy for the Authority, assuming that their objective is to
minimize expected costs. (For simplicity you should ignore time preferences for money).

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