An engineer should design a new levee along the Snake River to protect households, infrastructure, and
potato crops against floods. Based on the FEMA (Federal Emergency Management Agency) national flood
maps, two levee designs are considered: (a) a levee with the height of 8’ and (b) a levee with the height of
10’. The engineer has a long experience with levees in Washington State. Based on his/her experience and
historical data, he/she divides the states of nature into three flood levels and assigns the annual probabilities
of occurrence to the different flood heights as follows:
θ1 = {h < 8’} P’[θ1] = 0.65
θ2 = {8’ ≤ h < 10’} P’[θ2] = 0.25
θ3 = {10’ ≤ h} P’[θ3] = 0.10
If the 8’ levee is designed and the flood exceeds 8’ but is less than 10’, the losses of households and other
infrastructure are estimated to be $300M and the loss from damage to potato crop is an additional $50M. If
the 8’ levee is designed and the flood exceeds 10’, the estimated losses of households and other
infrastructure will be $500M and the loss from damage to potato crop is $75M.
The 10’ levee requires additional $200M. If there is a flood, however, the losses of households and other
infrastructure are estimated to be $200M and the loss to potato crop will be $40M.
The engineer has a risk-neutral attitude and makes a decision based on expected losses.
The engineer is willing to spend up-front money to investigate and review the probabilities of flood heights.
The initial probabilities do not include data from the past 10 years. This process will add another $25M
since it will require review of flood levels in the past 10 years, estimation of the flooded area and averaged
flood heights across the flooded area, which should be based on GIS mapping and repeated analysis for
inundation. The possible outcomes from this flood model are (a) z1 = {h < 8’}, (b) z2 = {8’ ≤ h < 10’}, and
(c) z3 = {10’ ≤ h} and the reliability of this model is shown in the table below.
Table 1. Sample Likelihood function
θ1 θ2 θ3
z1 0.80 0.20 0.15
z2 0.15 0.70 0.20
z3 0.05 0.10 0.65
CE 405/505 Fall 2020 Lee
- You have performed additional analysis and have found that the flood level will be higher than 10’. What
is your recommendation for levee height? Show all the posterior probabilities and monetary consequences
in your decision tree. - If the cost of perfect test is $50M, what is the Value of Perfect Information? Is the perfect test worth it?
Show your decision tree. - What is the Value of Information? Is the test worth it? Show your decision tree.