ADDITIONAL PROBLEMS OF CHAPTER 3-LMS
1. Mr. Minh is a securities investor considering two options with a capital of $ 10,000: (1) Deposit money
in the bank at an interest rate of 8% and (2) continue to invest in securities with interest (calculated as%
of capital) according to the market situation as follows: if the market is good, it will gain 20%, if the
market average 8%, if the bad market loses 10% Mr. Minh estimates that the probability of a good market
is 0.4, average market is 0.4 and bad market is 0.2. Make a payoff table and identify a good option.
2. Mr. Binh is the owner of oil and gas company X.O To enhance his competitiveness, Mr. Binh bought
more equipment with the following options:
Equipment
Good market
Bad market
Sub 100
$ 300000
- $ 200000
Oiler J
$ 250000
- $ 100000
Texan
$ 75000
- $ 18000
A chemical magazine has forecast the probability of a good market at 70% and a bad market at 30%. Mr.
Binh wants to use this information to make a decision.
a) What kind of decision making environment is this problem?
b) What is the optimal solution?
c) Mr. Binh believes that the profit margin of $ 300,000 for the Sub 100 equipment in the good market is
too high. Therefore, which value of Sub 100’ profit margin will he change the decision made in question
b)
3. Mr. Thang, director of 3T Company, is considering building another factory in Tay Ninh with the
decision shown in the payoff table:
Good Market
Bad market
Big factory
$ 400000
- $ 100000
Small factories
$ 100,000
- $ 40000
Do nothing
$0
$0
Probability
0.4
0.6
a) Formulate a regret table
b) Determine the EOL and optimal solution
c) Calculate EVPI
Senior Lecturer: Hai Thanh Doan
4. Ms. Hang plans to invest in building a private hospital in a central province with two options: a large
hospital and a small hospital. If the population grows, the large hospital will have annual profits of $
200,000 and a small hospital $ 80000. When the population doesn't increase, the big hospital will lose $
50,000 a year and the small hospital will lose $ 30,000. Unfortunately, Ms. Hang has no information
about the future population.
a) What is this decision making environment?
b) Make a payoff table.
c) Use the criteria of equally likely to choose the best option.
d) If Ms. Hang is a risk avoider, which option will she choose?
5. Mr. Son is Ms. Hang's boss, who does not accept Ms. Hang's decision-making criteria. He thinks that
the actual coefficient (Herwicz) of 0.75 should be used to choose the plan.
a) Make a payoff table in this case.
b) Use Herwicz criteria to find the best option.
c) Are there differences between Ms. Hang's and Mr. Son's plans?
6. Mr. Kim decided to invest in a gas station with 4 different levels. The results of annual profits (USD)
for each petrol station in each market condition are shown in the following table.
The size of the gas station
Good market
Average market
Bad market
Small
50000
20000
-10000
Medium
80000
30000
-20000
Large
130000
35000
-40000
Very large
300000
25000
-180000
Please choose the option according to:
f) Maximax (optimistic)
g) Maximin (conservative)
h) Laplace criterion
i) Herwicz criterion with coefficient α = 0.4
j) Minimax regret
7. If Mr. Kim thinks that the probability of a good market, average market and bad market is 0.4, 0.4 and
0.2, respectively.
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a) Which gas station will Mr. Kim decide to invest in? What is the EV value of that decision?
b) Draw a decision tree for this case.
c) If someone sold information to Mr. Kim about the future of the market, what maximum price would he
buy?
d) When the probability of a good market is constant, what is the probability that a bad market will allow
Mr. Kim to change his mind in question a)?
8. A company that manufactures X chemicals. X is no value more than 1 month. This chemical is
produced in batches of 500l, 1000l, 1500l and 2000l. In the past, the probability of selling these batches
was 0.2, 0.3, 0.4 and 0.1, respectively. Production cost is $ 15 / l, administration fee is $ 3 / l, inventory
fee is $ 5 / l, selling price is $ 30 / l. After 1 month, there is still inventory, X will only sell scraps at a
price of $ 12 / l. In addition, if there is not enough stock, the company has to buy at another place with
price $ 28 / l for resale to customers.
a) Build up the company's payoff table
b) Draw the company's decision tree and indicate how many liters the company should choose to produce
batches.
c) Find the expected value of perfect information.
9. Mr. Vinh has three routes to the office. The time on each route varies depending on the level of traffic
jam as shown in the following table: (unit: minutes)
Route
No traffic jam
Moderate trafic jam
Serious traffic jam
LT1
15
30
45
LT2
20
25
40
LT3
30
30
35
In the past two months, according to Mr. Vinh's observations, there have been 10 days of serious traffic
jams and 20 days of moderate traffic jam.
a) Set up a payoff table for this problem.
b) Which option should Mr. Vinh choose? Calculate EOL and compare results
c) If Mr. Vinh does not have data on traffic jam, what criteria can he decide to choose? What are the
options corresponding to these decisions? (for α = 0.7)
d) If Mr. Vinh buys a radio, he can know information about traffic jam in advance. So how much time
would he save on average if he has a radio?
10. Mr. A is considering two plans to buy an apartment for rent at 1200 million dong or to buy land for
400 million dong. Population situation influences decision making results. With the decision to buy an
Senior Lecturer: Hai Thanh Doan
apartment after two years, if the population will increase (60%), he will get 2 billion when selling the
apartment, in contrast if the population will be unchanged (40%), he can only get 900 million. With the
decision to buy land, when the population will increase (60%), after a year he will decide to sell the land
or build a villa. If he sells the land he will earn 600 million, if he builds a villa at a cost of 2 billion within
the next year if the population will increase (80%), when selling the villa he will earn VND 4 billion. The
population will not increase (20%), when selling the villa, he earned 2 billion VND. With the decision to
buy land and the population will not increased (40%), after 3 years he will be facing the decision to sell
land or build a warehouse. If he sell the land he would get 350 million. If building a warehouse at a cost
of 600 million and in the following year, if the population will increase (70%) when selling the
warehouse, he will get 2.3 billion, otherwise if the population will not increase (30%) ), when he sell the
warehouse he will earn 1200 million. Draw a decision tree to analyze Mr. A's decision.
11. A hotel manager intend to buy fire insurance for the following year. The property of the hotel is 30
billion, the probability of a fire happening next year is 2%. A fire has a 50% chance of losing 20% of
hotel’s properties, a 30% chance of losing 40% of hotel’s properties and a 20% chance of losing a 60% of
hotel’s properties. The hotel manager is considering buying insurance at 3 companies A, B, and C. The
premium of company A is 250 million with full compensation. Company B's insurance premium is 150
million with the compensation rate for the hotel damages only 50 million in the case of a fire. The
premium of company C is 75 million with a compensation of 40% of damage.
Draw a decision tree related to the hotel manager’s decision: should he/she buy insurance? If buying,
which company to be chosen?
12. Company A considers to invest in project X. If the market is good (40%), the company get a profit of
1,200 million VND, if the market is normal (30%), it will gain 400 million VND and if the market is bad,
the company will lost 500 million VND.
a) Should the company invest in project X?
b) Before making the above decision, company A intends to hire a market research company B to provide
market forecast information at a cost of VND 100 million. The results of B's 200 previous surveys are
shown in the following table:
Good market S1
Average market S2
Bad market S3
Good forecast
94
42
4
Bad forecast
8
4
48
Draw the decision tree and decide which option Company A will choose? How much can a company pay
up to market research?
Senior Lecturer: Hai Thanh Doan