Texts: Prepositioning Supplies for Hurricane Response. In 2017, the American Red Cross had to make decisions related to preparations for Hurricane Irma, which was threatening the United States, including the state of Florida, Puerto Rico, and the U.S. Virgin Islands. To prepare for such disasters, organizations such as the Red Cross must make decisions about when and where to preposition relief supplies such as water, food, and medical supplies. Suppose that the Red Cross can choose to stock from possible hurricane disaster or in regional distribution centers that are closer to where damage is expected but run the risk of being destroyed by severe hurricanes. The following table displays the costs (in $ millions) of the different decision alternatives under three possible states of nature: no hurricane landfall, moderate hurricane landfall, and severe hurricane landfall. Note that because these values represent costs, they are all displayed as negative values.
State of Nature Moderate Severe No Landfall, s Landfall, s Landfall, s
-30 -18 -65
Decision Alternatives
Stock Centralized Distribution Center, d Stock Regional Distribution Centers, d
-15 -40 -50
The probabilities for the states of nature are P(s) = 0.5, P(s) = 0.35, P(s) = 0.15. The Red Cross can also wait an additional 48 hours during which time an additional "hurricane hunter" flight will collect additional data on the hurricane. By waiting, the Red Cross gathers additional sample data on whether the hurricane will make a turn toward or away from Florida. The probabilities associated with these are:
P(Toward Florida) = 0.6
P(s|Toward Florida) = 0.2
P(s|Away From Florida) = 0.75
P(Away From Florida) = 0.4
P(s|Toward Florida) = 0.55
P(s|Away From Florida) = 0.2
P(s|Toward Florida) = 0.35
P(s|Away From Florida) = 0.5
a. Construct a decision tree for this problem.
b. What is the recommended decision if the Red Cross does not wait to make a decision? What is the expected value of this decision?
c. What is the optimal decision strategy if the Red Cross waits an additional 48 hours? What is the expected value of this decision?
d. What is the expected value of the sample data?
