Decision trees and Influence Diagram -Problems
3.10 When patients suffered from hemorrhagic fever, M*A*S*H doctors replaced lost sodium by
administering a saline solution intravenously. However, headquarters (HQ) sent a treatment
change disallowing the saline solution. With a patient in shock and near death from a
disastrously low sodium level, B. J. Hunnicut wanted to administer a low-sodium-concentration
saline solution as a last-ditch attempt to save the patient. Colonel Potter looked at B. J. and
Hawkeye and summed up the situation. "O.K., let's get this straight. If we go by the new
directive from HQ and don't administer saline to replace the sodium, our boy will die for sure. If
we try B. J.'s idea, then he may survive, and we'll know how to treat the next two patients who
are getting worse. If we try it and he doesn't make it, we're in trouble with HQ and may get
court-martialed. I say we have no choice. Let's try it” (Source:" Mr. and Mrs. Who." Written by
Ronny Graham, directed by Burt Metcalfe, 1980.) Construct a decision tree and an influence
diagram
3.16 In the spring of 1987 Gary Hart, the leading Democratic presidential candidate, told the
news media that he was more than willing to have his private life scrutinized carefully. A few
weeks later, the Miami Herald reported that a woman, Donna Rice, had been seen entering his
Washington townhouse on a Friday evening but not leaving until Saturday evening. The result
was a typical political scandal, with Hart contending that Rice had left Friday evening by a back
door that the reporter on the scene was not watching. The result was that Hart's credibility as a
candidate was severely damaged, thus reducing his chance of winning both the Democratic
nomination and the election. The decision he had to make was whether to continue the campaign
or to drop out. Compounding the issue was a heavy debt burden that was left over from his
unsuccessful 1984 presidential bid. Using both an influence diagram and a decision tree,
structure Hart's decision.
4.14 A real-estate investor has the opportunity to purchase an apartment complex. The apartment
complex costs $400,000 and is expected to generate net revenue (net after all operating and
finance costs) of $6000 per month. Of course, the revenue could vary because the occupancy rate
is uncertain. Considering the uncertainty, the revenue could vary from a low of -$1000 to a high
of $10,000 per month. Assume that the investor's objective is to maximize the value of the
investment at the end of l0 years.
a Do you think the investor should buy the apartment complex or invest the $400,000 in a 10year certificate of deposit earning at 9.5%?Why?
b The city council is currently considering an application to rezone a nearby empty parcel of
land. The owner of that land wants to build a small electronics-assembly plant. The proposed
plant does not really conflict with the city's overall land use plan, but it may have a substantial
long-term negative effect on the value of the nearby residential district in which the apartment
complex is located. Because the city council currently is divided on the issue and will not make a
decision until next month, the real estate investor is thinking about waiting until the city council
makes its decision. If the investor waits, what could happen? What are the trade-offs that the
investor has to make in deciding whether to wait or to purchase the complex now?
c Suppose the investor could pay the seller $ 1000 in earnest money now, specifying i n
the purchase agreement that if the council's decision is to approve the rezoning, the
investor can forfeit the $1000 and forego the purchase. Draw the decision tree
showing the investor's three options.
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