TUTORIAL BSc (Hons) Construction Management Construction Systems and Analysis (BCM524)

Answer all of the questions.

1. Fauziah & Co. Is going to introduce one of the three new product: Fauziah Weatherbond, Fauziah

Sheer Finish or Fauziah Clean Matte paint. As the market conditions (favourable, stable or

unfavourable) affect the payoffs of the products, the company estimates the following payoffs:

Table 1

Product Market Condition

Favourable Stable Unfavourable

Weatherbond 18 000 9 000 - 5 000

Sheer Finish 12 000 7 000 2 000

Clean Matte 11 000 10 000 -6 000

a) Maximax

b) Maximin

c) Hurwicz with k =0.7

d) Laplace

e) Minimax Regret

2. Gapurna Company is considering several alternative development projects. The financial success

of these projects depends on the interest rates movements in the next four years. The projects and

their three-year financial returns (in Millions) with the possible given interest rates decline, remain

stable or increase are shown in the table below.

Table 2

Project Interest Rate

Decline Stable Increase

Shops 36 22 15

Mall 53 39 25

Condominium 35 17 4

Warehouse 16 15 10

Determine the investment using the following decision criteria :

a) Maximax

b) Maximin

c) Hurwicz with k =0.8

d) Laplace

e) Minimax Regret

3. The payoff table below indicates the returns (in RM thousands) of an investment.

Table 3

Type of investment

Economic Situation

Good Stable Poor

Stock 150 60 -30

Bond 50 40 36

Fixed Deposit 45 45 45

Determine the best course of action using:

a) Maximax

b) Maximin

c) Hurwicz criterion with k=0.8

d) Laplaces equally likely criterion

e) Minimax regret criterion

4. Fauziah & Co. Is going to introduce one of the three new product: Fauziah Weatherbond, Fauziah

Sheer Finish or Fauziah Clean Matte paint. As the market conditions (favourable, stable or

unfavourable) affect the payoffs of the products, the company estimates the following payoffs:

Table 4

Product Market Condition

Favourable Stable Unfavourable

Weatherbond 18 000 9 000 - 5 000

Sheer Finish 12 000 7 000 2 000

Clean Matte 11 000 10 000 -6 000

Not introducing 0 0 0

Probability 0.3 0.5 0.2

a) What is the decision under risk using the EMV method

b) Shafie Market Research Co approached Fauziah & Co to help in decision making. Shafie is able

to tell Fauziah with certainty whether the market is favourable, stable or unfavourable by market

technical analysis. This will prevent Fauziah & Co from making an expensive mistake by

choosing the wrong product. Thus the maximum amount of money that Fauziah is willing to pay

for the market research (EVPI).

Find the amount of money Fauziah & Co is willing to splurge.

c) Using minimizing expected opportunity loss method, determine which product Fauziah & Co

should produce.

5. Salma Electro specializes in manufacturing electronic components. It is considering building a new

facility either large, medium, or small, to produce the components. The following table shows the

payoffs (in RM Thousands) for a proposed facility under three market conditions (strong, fair, and

poor markets)

Table 5

Product Market Condition

Favourable Stable Unfavourable

Large Facility 85 60 25

Medium Facility 60 50 45

Small Facility 40 40 35

Probability 0.3 0.6 0.1

a) What decision would maximize the expected payoff

b) Construct an opportunity loss table and determine the best decision by minimizing expected

opportunity loss

c) Determine the expected value with perfect information (EVWPI) and expected value of

perfect information (EVPI)

6. You are trying to determine what stock to invest in. The wisdom of your decision depends on the

state KLSE in one year. There are three possible states of nature; the market could go down, stay

about the same, or it would go up. You have narrowed your investment choices to four stocks. The

payoffs for the various combinations of investment choices and market conditions are shown in the

following table.

Table 6

Alternative State of Nature

Market is Up Market is unchanged Market is Down

Stock A 20,000 5,000 -15,000

Stock B 10,000 8,000 0

Stock C 100,000 0 -50,000

Stock D 15,000 5,000 -10,000

What are the correct investment choices given in the following decision- making criteria?

a) Laplace

b) Maximin

c) Hurwicz k=0.4

d) Minimax Regret

7. A farmer is undecided whether to plant yam or tapioca. If he plants yam and the weather is wet, he earns RM 8000 and if it is dry, he earns RM 5000. On the other hand, if he plant tapioca and the weather is wet, he earns RM7000 and if it is dry, he earns RM6500. In the past, he realizes that 30% of the previous years have been wet and 70% have been dry. Before planting, the farmer considers hiring an expert in weather forecast at the cost of RM500. There is a 40% chance that the expert will predict a wet year ahead but if the forecast is wet weather, there is a 90% chance that the weather will be wet while if the forecast is dry weather, there is a 70% chance that the weather will be dry.

a) Construct a decision tree for the above situation. b) Advise the farmer for the best decision.

8. A company is deciding whether to develop and launch a new product. Research and development

costs are expected to be $400,000 and there is a 70% chance that the product launch will be

successful, and a 30% chance that it will fail. If it is successful, the levels of expected profits and the

probability of each occurring have been estimated as follows, depending on whether the products

popularity is high, medium or low:

Table 7

Probability Profits

High 0.2 $500,000 per annum for two years

Medium 0.5 $400,000 per annum for two years

Low 0.3 $300,000 per annum for two years

If it is a failure, there is a 0.6 probability that the research and development work can be sold for

$50,000 and a 0.4 probability that it will be worth nothing at all.

9. En. Hashim is not sure what he should do. He can either build a quadplex (that is, a building with

four apartments), a duplex, gather additional information, or simply do nothing. If he gathers

additional information, the results could be either favorable or unfavorable, but it would cost him RM

3,000 to gather the information. En Hashim believes that there is a 50-50 chance that the

information will be favorable. If the rental market is favorable he will earn RM 15,000 with the

quadplex or RM 5,000 with the duplex. En. Hashim doesn't have the financial resources to do both.

With an unfavorable rental market, however, he could lose RM 20,000 with the quadplex or RM

10,000 with the duplex.

Without gathering additional information En. Hashim estimates that the probability of a favorable

rental market is 0.7. A favorable report from the study would increase the probability of a favorable

rental market to 0.9. Furthermore, an unfavorable report from the additional information would

decrease the probability of a favorable rental market to 0.4. Of course, En. Hashim could forget all

of these numbers and do nothing.

Use decision tree method to advice En. Hashim.

10. Mr. Ismail, the Fund Manager of the CIMB investment, must decide on investment of theirs fund. He

can choose strategy A, strategy B or not to invest. The profit (RM) from each alternative depends on

the economic conditions as given in the following table:

Table 8

Alternative Economic Condition

Good condition Poor Condition

Strategy A 365 000 35 000

Strategy B 450 000 -60 000

No to invest 0 0

Mr. Ismail estimates the probability of a good economy without performing a survey is 0.5. As he is

still uncomfortable with his personal assessment, he would like to hire an economist to survey the

future economic condition. This will cost RM20 000. Furthermore, the probability of a positive result

from market survey is 0.6 and there is a 70% chance that the economy will be good given a positive

survey result. However, if the survey result is negative, the chance of a good economy will be

reduced 30%.

Draw a tree diagram to illustrate the problem. Calculate all the expected monetary values and make

a recommendation to Mr. Ismail.

11. A group of school teachers is considering the construction of a tuition centre. If the demand is high, the teachers could realize a net profit of RM80,000. If the market is not favourable, they could lose RM30,000. Of course, they do not have to proceed at all, in which case there is no cost. In the absence of any market data, the best the teachers can guess is that there is a 60% chance the tuition centre will be successful. The teachers were approached by a market research firm that offers to perform a study of the market at a fee of RM1000. The market researchers claim their experience enables them to make the following statements of probability as stated in Table 1.

Table 9

Probability of a favourable market given a favourable study 0.82

Probability of an unfavourable market given a favourable study 0.18

Probability of a favourable market given an unfavourable study 0.11

Probability of an unfavourable market given an unfavourable study 0.89

Probability of a favourable research study 0.55

Probability of an unfavourable research study 0.45

a) Develop a new decision tree for the teachers to reflect the options with the market study. b) Determine the expected value of sample information and the maximum amount the

teachers are willing to pay for a market study.

12. A building contractor is submitting a bid for a construction project. The project would cost him

RM400,000 and he must decide on how much to bid. He is considering bids at RM500,000,

RM525,000, RM550,000 and RM575,000 and thinks that with the lowest bid he stands 0.4 chance

of getting the project. The other bids have chances of 0.35, 0.25 and 0.10 respectively of being

successful. No cost is involved in submitting an unsuccessful bid.

Construct a decision tree for this problem, and find the optimal bid and optimal expected profit.

13. Siti Saerah has enjoyed sailing small boats since she was 7 years old, when her mother started

sailing with her. Today, Siti is considering the possibility of starting a company to produce small

sailboats for the recreational market. Unlike other mass produced sailboats, however, these boats

will be made specifically for children between the ages of 10 and 15. The boats will be of the highest

quality, and extremely stable, and the sail size will be reduced to prevent problems of capsizing.

Because of the expense involved in developing the initial moulds and acquiring the necessary

equipment to produce fibreglass sailboats for young children, Siti has decided to conduct a pilot

study to make sure that the market for the sailboats will be adequate. She estimates that the pilot

study will cost her RM10,000. Furthermore, the pilot study can be either successful or not

successful. Her basic decisions are to build a large manufacturing facility, a small manufacturing

facility, or no facility at all. With a favourable market, Siti can expect to make RM 90,000 from the

large facility or RM 60,000 from the smaller facility. If the market is unfavourable, however, Siti

estimates that she would lose RM 30,000 with a large facility, while she would lose only RM 20,000

with the small facility. Siti estimates that the probability of a favourable market given a successful

pilot study is 0.8. The probability of an unfavourable market given an unsuccessful pilot study is

estimated to be 0.9. Siti feels that there is a 50-50 chance that the pilot study will be successful. Of

course, Siti could bypass the pilot study and simply make the decision as to whether to build a large

plant, small plant or no facility at all. Without doing any testing in a pilot study, she estimates that

the probability of a successful market is 0.6.

Give recommendation on the best decision Siti Saerah should take by conducting a decision tree.

GOOD LUCK!!