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I. Multiple choice
1. The options from which a decision maker chooses a course of action are
a. called the decision alternatives.
b. under the control of the decision maker.
c. not the same as the states of nature.
d. each of the above is true.
2. States of nature
a. can describe uncontrollable natural events such as floods or freezing temperatures.
b. can be selected by the decision maker.
c. cannot be enumerated by the decision maker.
d. each of the above is true.
3. When consequences are measured on a scale that reflects a decision maker's attitude toward profit, loss, and risk, payoffs are replaced by
a. utility.
b. multicriteria measures.
c. sample information.
d. opportunity loss.
4. The expected utility approach
a. does not require probabilities.
b. leads to the same decision as the expected value approach.
c. is most useful when excessively large or small payoffs are possible.
d. requires a decision tree.
5. Utility reflects the decision maker’s attitude toward
a. probability and profit
b. profit, loss, and risk
c. risk and regret
d. probability and regret
6. If the payoff from outcome A is twice the payoff from outcome B, then the ratio of these utilities will be
a. 2 to 1.
b. less than 2 to 1.
c. more than 2 to 1.
d. unknown without further information.
7. A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(-25000) + (1-p)(5000). If the utility of -25,000 is 0 and of 5000 is 1, then the utility of -10,000 is
a. .5
b. .6
c. .4
d. 4
8. A decision maker whose utility function graphs as a straight line is
a. conservative.
b. risk neutral.
c. a risk taker.
d. a risk avoider.
II - Math Problems
1.
Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores. Information on pricing, sales, and inventory costs has led to the following payoff table, in thousands.
DemandOrder Size / Low / Medium / High
1 lot / 12 / 15 / 15
2 lots / 9 / 25 / 35
3 lots / 6 / 35 / 60
a. What decision should be made by the optimist?
b. What decision should be made by the conservative?
c. What decision should be made using minimax regret?
(a) The optimist uses the maximax criterion.
DemandOrder Size / Low / Medium / High / maximum
1 lot / 12 / 15 / 15 / 15
2 lots / 9 / 25 / 35 / 35
3 lots / 6 / 35 / 60 / 60
Maximum / 60
The maximum of the row maximums is 60. It is achieved by ordering 3 lots.
The optimist will order 3 lots.
(b) The conservative will use the maximin criterion
DemandOrder Size / Low / Medium / High / minimum
1 lot / 12 / 15 / 15 / 12
2 lots / 9 / 25 / 35 / 9
3 lots / 6 / 35 / 60 / 6
Maximum / 12
The maximum of the row minimums is 12. It is achieved by ordering 1 lot.
The conservative will order 1 lot
(c )
Regret table
.
DemandOrder Size / Low / Medium / High / maximum
1 lot / 0 / 20 / 45 / 45
2 lots / 3 / 10 / 25 / 25
3 lots / 6 / 0 / 0 / 6
Minimum / 6
The regret table is prepared by subtracting each entry in the payoff table from the column maximum.
The minimum of the maximum regret is 6. It is achieved for 3 lots. The minimax regret criterion chooses 3 lots.
2.
If p is the probability of Event 1 and (1-p) is the probability of Event 2, based on the expected returns, for what values of p would you choose A? B? C? Values in the table are payoffs.
A / 0 / 20
B / 4 / 16
C / 8 / 0
(Here are some hints for solving this question, since it's somewhat challenging:o first derive the expected returns, as a function of p, for each of the three choices, A, B, C.o then compare the expected returns in pairs to see for what ranges of p:
(1) A's return exceeds B's and vice versa
(2) A's return exceeds C's and vice versa
(3) B's return exceeds C's and vice versa
This should give you enough information to answer the question.It might also help to graph each return function against p. Remember that since p is a probability, it can only take on values between 0 and 1.)
and
and
and
3.
For the payoff table below, the decision maker will use P(s1) = .15, P(s2) = .5, and P(s3) = .35.
d1 / -5000 / 1000 / 10,000
d2 / -15,000 / -2000 / 40,000
a. What alternative would be chosen according to expected value?
Expected value of decision d1 =
Expected value of decision d2 =
Decision d2 is having the maximum expected value. So decision d2 is taken according to expected value.
b. For a lottery having a payoff of 40,000 with probability p and -15,000 with probability (1-p), the decision maker expressed the following indifference probabilities.
Payoff Probability
10,000 .85
1000 .60
-2000 .53
-5000 .50
Let U(40,000) = 10 and U(-15,000) = 0 and find the utility value for each payoff.
c. What alternative would be chosen according to expected utility?
Utilities
s1 / s2 / s3d1 / 5 / 6 / 8.5
d2 / 0 / 5.3 / 10
Expected utility of decision d1 =
Expected utility of decision d2 =
Decision d1 is having the maximum expected utility. So decision d1 is taken according to expected utility.