Page 306 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 14: Decision-making

States of Nature Notes
Alternative X Y Z
A 4 3 3
B 5 2 5
C 5 6 2
D 6 1 4
(a) Draw a decision tree for the above payoff table.

(b) If the probability of the states of nature is 0.3, 0.4 and 0.3 for the states X, Y and Z
respectively, find out the optimum decision.
(c) Assume that the payoff table provides cost rather than profit payoffs. What is the
recommended decision now if the probabilities given in the option (b) still holds?
3. Which action would an optimal Decision Theoretic Agent take in the following situation?
Utility of Resulting State Probability
Action 1 10 0.2
Action 2 10000 0.001
Action 3 5 0.799

4. After your yearly checkup, the doctor has bad news and good news. The bad news is that
you tested positive for a serious disease, and that the test is 99% accurate (i.e. the probability
of testing positive given that you have the disease is 0.99, as is the probability of testing
negative given you don't have the disease). The good news is that this is a rare disease,
striking only 1 in 10,000 people. Why is it good news that the disease is rare? What are the
chances that you actually have the disease?
5. John's monthly consumption:
(a) X1 = £4000 if he does not get ill

(b) X2 = £500 if he gets ill (so he cannot work)
(c) Probability of illness 0.25
(d) Consequently, probability of no illness = 1 – 0.25 = 0.75
What will be the expected value?

Answers: Self Assessment

1. Certainty, Risk and uncertainty 2. Cognition
3. Inertia and impatience 4. Decision-making under certainty

5. True 6. False
7. True 8. probabilistic
9. expected

10. Expected Value of Perfect Information (EVPI)
11. decision tree 12. pessimistic decision
13. one and only one consequence 14. intellectual

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