Exercises in Unit 6
1. Greentrop Pharmaceutical Products is the world leader in the area of sleep aids. Its major product is
“Dozealot.” The Research-and-Development Division has defined two alternatives to improve the quality
of the product. These alternatives are simple reformulations of the product to minimize the side effects
and to improve the product efficacy. To conduct an analysis, management has decided to consider the
possible demands for the drug under each alternative. The following payoff table shows the projected
profit in millions of dollars.
Decision Alternatives
Demand
Medium
$320
Low
$290
d1
d2
P
High
$525
$275
$350
$765
.3
.5
.2
a. Construct a decision tree for this problem.
b. What is the recommended decision using the optimistic, conservative, minimax regret approaches,
criterion of realism (using alpha = .8) and Laplace criterion?
c. If the probabilities for low, medium and high demands are .3, .5, .2, respectively, what is the decision
using the EV approach?
2. ABC airlines decided to offer direct service from point A to point B. Management must decide between
full-price service using a company’s new fleet of jet aircraft and a discount-service using smaller capacity
commuter planes. Management developed estimates of the contribution to profit for each type of service
based upon two possible levels of demand for service on point B: high, moderate, and low. The following
table shows the estimated quarterly profits (in thousands of dollars):
Service
Full Price
Discount
Demand for service
High
Medium
900
760
710
650
Low
–430
350
What is the best decision using the 5 approaches? If the probabilities for High, Medium and Low are
available, what is the best decision using the EV approach?
3. The following payoff table shows the profit for a decision problem with three states of nature and three
decision alternatives:
d1
State of Nature
s1
s2
7
3
s3
4
d2
2
4
5
d3
8
2
3
Decision
Alternative
What is the best decision using the 5 approaches? If the probabilities for s1, s2, and s3 are available, what
is the best decision using the EV approach?
4. Visual Park is considering marketing one of its two television models for the coming Christmas season:
Model A or Model B. Model A is a unique featured television and appears to have no competition.
Estimated profits (in thousands of dollars) under high, medium, and low demand are given below:
Model A
Profit
Probability
High
1200
0.2
Demand
Medium
900
0.6
Low
500
0.2
Visual Park is optimistic about the TV Model B. However, the concern is that profitability will be
affected if a competitor launches a TV model which has similar features as Model B. Estimated profits (in
thousands of dollars) with and without competition is as follows:
Model B
With competition
Profit
Probability
High
1,200
0.2
Demand
Medium
900
0.3
Low
500
0.5
Model B
Without competition
Profit
Probability
High
1,600
0.6
Demand
Medium
1,100
0.2
Low
700
0.2
a. Develop a decision tree for the Visual Park problem.
b. For planning purposes, Visual Park believes there is a 0.7 probability that its competitor will launch a
TV model similar to Model B. Given this probability of competition, the director of planning
recommends marketing the Model A. Using expected value, what is your recommended decision?
c. Show a risk profile for your recommended decision.
d. Use sensitivity analysis to determine what the probability of competition for Model B would have to be
for you to change your recommended decision alternative.
5. The Golden Jill Mining Company is interested in procuring 10,000 acres of coal mines in Powder River
Basin. The mining company is considering two payment-plan options to buy the mines:
I. 100% Payment
II. Installment-Payment
The payoff received will be based on the quality of coal obtained from the mines which has been
categorized as High, Normal, and Poor Quality as well as the payment plan. The profit payoff in millions
of dollars resulting from the various combinations of options and quality are provided below:
Payment-Plan Options
100% Payment
Installment-Payment
High
Quality
Normal
Poor
450
320
–250
350
300
–110
a. What is the decision to be made, what is the chance event, and what is the consequence for this
problem? How many decision alternatives are there? How many outcomes are there 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?
6. The Golden Jill Mining Company is interested in procuring 10,000 acres of coal mines in Powder River
Basin. The mining company is considering two payment-plan options to buy the mines:
I. 100% Payment
II. Installment-Payment
The payoff received will be based on the quality of coal obtained from the mines, which has been
categorized as High, Normal, and Poor Quality, as well as the payment plan. The profit payoff in millions
of dollars resulting from the various combinations of options and quality are provided below:
PaymentPlan
Options
100%
Payment
InstallmentPayment
Quality
High
Normal
Poor
450
320
–250
350
300
–110
a. Suppose that management believes that the probability of obtaining High Quality coal is 0.55,
probability of Normal Quality Coal is 0.35, and probability of Poor Quality Coal is 0.1. Use the expected
value approach to determine an optimal decision.
b. Suppose that management believes that the probability of High Quality coal is 0.25, probability of
Normal Quality Coal is 0.4, and probability of Poor Quality Coal is 0.35. What is the optimal decision
using the expected value approach?
7. Meega airlines decided to offer direct service from Akron to Clearwater Beach, Florida. Management
must decide between full-price service using a company’s new fleet of jet aircraft and a discount-service
using smaller capacity commuter planes. Management developed estimates of the contribution to profit
for each type of service based upon two possible levels of demand for service on Clearwater Beach: high,
moderate, and low. The following table shows the estimated quarterly profits (in thousands of dollars).
Service
Full price
Discount
Demand for service
High Medium Low
900
760
–430
710
650
350
The probabilities for the demand is P(High) = 0.3, P(Medium) = 0.5, and P(Low) = 0.2, respectively.
a. What is the optimal decision strategy if perfect information were available?
b. What is the expected value for the decision strategy developed in part a?
c. Using the expected value approach, what is the recommended decision without perfect information?
What is its expected value?
d. What is the expected value of perfect information?