City officials in Fort Lauderdale, Florida, are trying to decide whether to evacuate coastal residents in anticipation of a major hurricane that my make landfall near their city within the next 48 hours. Based on previous studies, it is estimated that it will cost approximately $1 million to evaluate the residents living among the coast of this major metropolitan area. However, if city officials choose not to evaluate their residents and the storm strikes Fort Lauderdale, there would likely be some deaths as a result of the hurricane's storm surge along the coast. Although city officials are reluctant to place an economic value on the loss of human life resulting from such a storm, they realize that it may ultimately be necessary to do so to make a sound judgment in this situation. Prior to making the evacuation decision, city officials consult hurricane experts at the National Hurricane Center in Coral Gables regarding the accuracy of past predictions. They learn that in similar past cases, hurricanes that were predicted to make landfall near a particular coastal location actually did so 60% of the time. Moreover, they learn that in past similar cases hurricanes that were predicted not to make landfall near a particular coastal location actually did so 20% of the time. Finally, in response to similar threats in the past, weather forecasters have issued predictions of a major hurricane making landfall near a particular coastal location 40% of the time.
a. Let L be the economic valuation of the loss of human life resulting from a coastal strike by the hurricane. Employ a decision tree to help these city officials make a decision that minimizes the expected cost of responding to the threat of the impending storm as a function of L. To proceed, you might begin by choosing an initial value of L (pick approximate figure to start) and then perform sensitivity analysis on the optimal decision by varying this model parameter. Summarize your findings.
b. For which value of L will these city officials always choose to evaluate the coastal residents, regardless of the Hurricane Center's prediction?