To prepare for disasters such as hurricanes, organizations such as the Red Cross must make decisions about when and wher

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To prepare for disasters such as hurricanes, organizations suchas the Red Cross must make decisions about when and where topreposition relief supplies such as water, food, and medicalsupplies. Suppose that the Red Cross can choose to stock suppliesfor a possible hurricane that hits Florida either in a centraldistribution center that is protected from possible hurricanedisaster or in regional distribution centers that are closer towhere damage is expected but run the risk of being destroyed bysevere hurricanes. The following table displays the costs (in $millions) of the different decision alternatives under threepossible states of nature: no hurricane landfall, moderatehurricane landfall, and severe hurricane landfall. Note thatbecause these values represent costs, they are all displayed asnegative values.
s1
s2
s3
d1
−25
−13
−60
d2
−10
−40
−50
The probabilities for the states of nature are
P(s1) = 0.23, P(s2) =0.48, P(s3) = 0.29.
The Red Cross can also wait an additional 48 hours duringwhich time an additional "hurricane hunter" flight will collectadditional data on the hurricane. By waiting, the Red Cross gathersadditional sample data on whether the hurricane will make a turntoward or away from Florida. The probabilities associated withthese are:
P(Toward Florida) = 0.8
P(Away From Florida) = 0.2
P(s1|Toward Florida) = 0.1
P(s2|Toward Florida) = 0.55
P(s3|Toward Florida) = 0.35
P(s1|Away From Florida) = 0.75
P(s2|Away From Florida) = 0.2
P(s3|Away From Florida) = 0.05
(a)
Construct a decision tree for this problem.
(b)
What is the recommended decision if the Red Cross does not waitto make a decision?
What is the expected value of this decision?
(c)
What is the optimal decision strategy if the Red Cross waits anadditional 48 hours?
What is the expected value of this decision?
(d)
What is the expected value of the sample data?