Decision Making and Posterior Probabilities

Topics: Decision theory, Game theory, Decision making Pages: 5 (1171 words) Published: April 19, 2015
Decision Making and Posterior Probabilities

Question 1

A manager is faced with three decision alternatives and three states of nature. He prepares the following payoff table representing profits ($):

Decision
Alternative
State of Nature

s1
s2
s3
d1
28,000
20,000
10,000
d2
18,000
20,000
22,000
d3
16,000
22,000
26,000

(a) What is the optimal decision if the manager uses the conservative approach? (b) What is the optimal decision if the manager uses the optimistic approach? (c) What is the optimal decision if the manager uses the minimax regret approach? (d) Construct a decision tree and find the optimal decision alternative using the expected value approach if P(s1) = 0.20, P(s2) = 0.45 P(s3) = 0.35 (e) Using the probabilities in part (d), calculate the expected value of perfect information (EVPI). Interpret the calculated value of EVPI. (f) Draw the risk profiles for d2 and d3 decision alternatives. Comment on them from the manager’s point of view.

Question 3

Due to increase in gold prices, many people in Australia are now digging for gold. A gold digger can employ a consultant at a cost of $22,000, or go looking for gold himself. The cost of the gold digging is not known with certainty but could be $16,000 (with a probability of 0.3), $22,000 (with a probability of 0.3) or $28,000, depending on the underground rock structure and depth of the gold reserve.

A gold digger can hire a local geographical survey company to do on-site tests. For a cost of $300, he will give either a favourable or an unfavourable report on the chances of easily finding gold. The reliability of this report, phrased in terms of the probability of a favourable report given the drilling cost will be low, etc. is given in the following table:

Digging costs

$16,000
$22,000
$28,000
Favourable report
0.8
0.6
0.2
Unfavourable report
0.2
0.4
0.8

(a) Complete the Posterior Probabilities tables for both the favourable and unfavourable reports:

(b)

Favourable Report Probabilities
Cost
Prior
Conditional
Joint
Posterior
$16,000

$22,000

$28,000

Total

Unfavourable Report Probabilities
Cost
Prior
Conditional
Joint
Posterior
$16,000

$22,000

$28,000

Total

(b)Using the information from part (a), draw a decision tree. (c)Advise the farmer on the best option and the expected cost.

Question 4

A bus company decided to offer a direct service from Sengkang to Shenton Way. Management must decide between a full-price service using the company’s new fleet of double-deck buses and a discount service using smaller capacity single deck buses. The best choice depends on the market reaction to the service offered. The estimates of profit for each type of service are based on two types of demands – strong and weak. The following table shows the estimated annual profits (in thousands of dollars):

Service
Demand for Service

Strong
Weak

S1
S2
Full price, d1
$960
-$490
Discount, d2
$670
$320

a) i)What is the decision to be made?
ii) What is the chance event?
iii) What is the consequence for this problem?
iv) List the decision alternatives.
v) List the outcomes for the chance event.

b) If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative and minimax regret approaches?

c) Suppose that management of the bus company believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach to determine an optimal decision.

d) Suppose that the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What is the optimal decision using the expected value approach?

Question 7

A toy manufacturer makes stuffed kittens and puppies which have relatively lifelike motions. There are three...
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