Decision Analysis and Risk Management : Payoff, Oppprtunity
Loss and Minimax Regret
3-19
Mickey Lawson is considering investing some money that he
inherited. The following payoff table gives the profits that would be realized
during the next year for each of the three investment alternatives Mickey is
considering:
a. What
decision would maximize expected profile?
b. What is
the maximum amount that should be paid for a perfect forecast of the economy?
State of Nature
Decision Alternative Good
Economy Bad Economy
Stock market 80,000
(20,000)
Bonds 30,000 20,000
CD’s 23,000
23,000
Probability 0.5 0.5
3-23
Today’s electronics specializes in manufacturing modern
electronic components. It also builds the equipment that produces the
components. Phyllis Weinberger, who is responsible for advising the president
of Today’s Electronics on electronic manufacturing equipment, has developed the
following table concerning a proposed facility:
a. develop
an opportunity loss table
b. what is
the minmax regret decision?
Profit ($)
Strong Market Fair
Market Poor Market
Large facility 550,000
110,000 (310,000)
Medium sized facility 30,000
129,000 (10,000)
Samll facility 20,000
10,000 (32,000)
No facility 0
0 0
3-32
Bill Holiday is not sure what he should do. He can either build
a quadplex, build a duplex, gather additional information, or simply do
nothing. If he gathers additional information, the results could be either
favorable or unfavorable, but it would cost him $3,000 to gather the
information. Bill believes that there is a 50-50 chance that the information
will be favorable. If the rental market is favorable, Bill will $15,000 with
the quadplex or $5,000 with the duplex. Bill doesn’t have the financial
resources to do both. With an unfavorable rental market, however, Bill could
lose $20,000 with the quadplex or $10,000 with the duplex. Without gathering
additional information, Bill estimates that the probability of a favorable
rental market is .7. A favorable report from the study would increase the
probability of a favorable rental market to .9. Furthermore, an unfavorable
report from the additional information would decrease the probability of a
favorable rental market to .4. Of course, Bill could forget all of these
numbers and do nothing. What is your advice to Bill?
3-42
In the past few years, the traffic problems in Lynn McKell’s
hometown have gotten worse. Now, Broad Street is congested about half the time.
The normal travel time to work for Lynn is only 15 minutes when Broad Street is
used and there is no congestion. With congestion, however, it takes Lynn 40
minutes to get to work. If Lynn decides to take the expressway, it will take 30
minutes regardless of the traffic conditions. Lynn’s utility for travel time
is:
U(15 minutes) = .9
U(30 minutes) = .7
U(40 minutes) = .2
a. Which
route will minimize Lynn’s expected travel time?
b. Which
route will maximize Lynn’s utility?
c. When it
comes to travel time, is Lynn a risk seeker or risk avoider?
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