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(Solved) MGMT 2012- Introduction to Quantitative Method s- Individual Assignment -Graded Assignment Two S2- 2016-17- Due April 15th - 10 percent Final Grade


MGMT 2012- Introduction to Quantitative Method

s-

Individual Assignment -Graded Assignment Two S2-

2016-17- Due April 15th – 10

percent Final Grade

Students should note that this assignment should su

bmitted in a Word document.

Question 1A

Assume the following payoffs are

profits

.

Payoffs

states of nature

Decision

alternatives

1

2

3

A

50

75

30

B

35

55

60

C


40

50

(a)

Which alternative should the firm choose under the

maximax criterion?

(1 mark)

(b)

Which option should the firm choose under the maxim

in criterion?

(1 mark)

(c)

Which option should the firm choose under the LaPla

ce criterion?

(2 marks)

(d)

Which option should the firm choose with the Hurwic

z criterion with

α

= 0.4?

(2 marks)

(e)

Using a minimax regret approach, what alternative s

hould the firm choose?

(4 marks)

(f)

Probabilities of 0.25, 0.35, and 0.40 have been ass

igned

.

Using expected monetary

values, what option should be chosen and what is th

at optimal expected value?

(4

marks)

(g)

What is the most that the firm should be willing

to pay for additional information? Use

Expected Regret

(3 marks)

(h)

Use the alternative method to verify EVPI

(3 marks)

Question 1B

Assume now that the pay offs are

costs

answer the following

:

(a)

Using an optimistic approach (maximax), which optio

n would you choose? 1 mark

(b)

Using a pessimistic approach (maximin), which optio

n would you choose?1 mark

(c)

If you are a LaPlace decision maker, which option w

ould you choose? 2 marks

(d)

If you are a Hurwicz decision maker, which option w

ould you choose with

α

= 0.4?1

mark

(e)

Using a minimax regret approach, which option would

you choose? 4 marks

(f)

Using the same probabilities of 0.25, 0.35, and 0

.40 for possible states of nature

respectively

,

which decision alternative will

minimise

the expected

costs?

What are the

expected annual costs associated with that recommen

dation? 4 marks

g) What is the most the firm should be wil

ling to pay to obtain further (perfect)

information (EVPI)? 3 marks

h) Use the alternative method to verify EVP

I

(3 marks

Question 2

A farmer in the Blue Mountains area of Jamaica want

s to decide on the crop to plant next season.

He wants to plant either ganja or coffee for export

to the USA but need some help. He knows

that if he plants ganja and the weather in the USA

is predominantly cold he earns $10,000(US

per month. If the weather is warm he earns $16,000.

If he plants coffee and the weather is cold

he earns 13,000 and if the weather is warm he earns

$14000. In 40% of the years, the weather

was cold and in 60 % the weather was warm.

For $600, he could buy an expert weather forecast f

rom CWD consulting.

States of Nature with Profits ($)

Does not include forecast cost

Decision

Alternatives

Warm

weather(W)

Cold weather (C)

Ganja

$16,000

$10,000

Coffee

$14,000

$13000

Prior Probabilities

P(W) = 0.60

P(C) = .40

Conditional probability for a given state of nature

where forecasts are either Good (G) or bad

(B): That is: P (G|W) = 0.80; P (B|W) = 0.20;

P (G|

C) = 0.10;

P (B|C) = 0.90

After you have computed the revised probabilities r

ound to two decimal places

a)

Construct the appropriate decision tree to help the

farmer make the appropriate decisions.

This tree must be constructed in logical order with

labels and net payoffs

(5 marks

). It

also includes the revised probabilities (

5 marks

) (

10 marks

)

b)

Fold back the decision tree

(5 marks

) to determine the best strategy for the farmer; yo

u

must state this strategy (

1 mark

). What is the final expected profit?(

1 mark)(7 marks

)

c)

What is the expected value of sample information(EV

SI)- the most that should be paid to

seismic testing firm for the test?(

1 mark

)

d)

Calculate the expected value of perfect information

(EVPI)- the most that should be paid

CWD for prediction of the uncertain outcomes.(

1 mark

)

e)

What is the efficiency of sample information?(

1 mark

)

Question 3

Data collected on the yearly demand for 50-pound ba

gs of fertilizer at Wallace Garden Supply

are shown in the following table.

a)Estimate demand with a weighted moving average i

n which sales in the most recent year, next

most recent , most distant are given weights of 3,

2 and 1 respectively . Compute the MAD,

MSE and MPE for this method.(

six marks

)

b)Use exponential smoothing with a smoothing consta

nt of 0.2 to forecast the demand for

fertilizer. Assume that last period’s forecast for

year 1 is 5,000 bags to begin the procedure.

Which method do you think is best?. Is this an impr

ovement over the weighted average- use

MAD alone( Six

marks)

c) Use regression analysis to estimate the line of

best fit(

eight marks

). Forecast the demand for

years 12 and 13.

Question four

A new project is to be completed. The following ac

tivities need to be completed in the order

shown, where times are in weeks.

Activity

Immediate

predecessors

Optimistic

time

Most

likely

time

Most

pessimistic

time

Variance

A

-

2

3

4

0.11111

B

-

2

4

6

0.44444

C

A,B

1

2

3

0.11111

D

B

1

3

5

0.44444

E

A

2

3

4

0.11111

F

C

1

4

7

1

G

E,F

2

2

2

0

H

D,F

2

5

8

1

I

G,H

1

3

5

0.44444

J

I

2

3

4

0.11111

You must use two decimal places at all times for ex

pected times when they are not integer

(you are not permitted to round off to integers).

(a)

Draw the activity network for this problem

(6 marks)

(b)

Determine the Expected Times.

(1 mark)

(c)

Determine the activity schedule (ES, EF, LS, and LF

) as well as slack.

(7 marks)

(d)

Determine and state the critical path for this proj

ect.

(1 mark)

(e)

What are the expected time and the variance of the

project?

(2 marks)

(f)

What is the probability that the project is complet

ed in 22 or fewer weeks

(1 mark)

(g)

What date should be set su

 


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