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What date should be set such that there is a 94% chance of completion within that time?

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

 Question 1 

A the new project is to be completed. The following activities need to be completed in the order shown, where times are in weeks. 

Activity

Immediate

predecessor

Optimistic

Time (a)

Most Likely

Time (m)

Pessimistic

time (b)

Variance

A

-

6

8

9

.25

B

-

9

12

15

1.00

C

A,B

4

6

11

1.36

D

B

3

4.5

6

.25

E

A

1

2

3

.11

F

C

1

3

5

.44

G

E,F

5

6

10

.69

H

D,F

2

3

4

.11

I

G,H

1

1

1

.00

J

I

2

3

7

.69

 You must use two decimal places at all times for expected 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 project. (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 completed in 32 or fewer weeks? (1 mark)

(g) What date should be set such that there is a 94% chance of completion within that time? (2 marks)

The table of normal distribution on page 5 can be used when answering this question.

 

 Question 2

The Boss Furniture Company is a furniture manufacturer and has a base in Grenada. The company sells furniture to different countries in the Caribbean but wants to employ a shipping company that has the capability to ship their products to several countries in North America. The company is considering three shipping companies, but several factors must be considered before the choice can be made. One such factor is the number of products the shipping company can ship to North America to meet the demand for Boss furniture in those countries. This will determine the amount of profit that the Boss Furniture Company can earn from each shipment. The Payoff table below shows the decision alternatives, states of nature (level of demand) and the payoffs (profits) that can be used to inform the decision process.  

 

Payoff (profit 000)

 

Alternatives

states of nature

Option

Low

Moderate

High

Antros

$1500

$5,500

$13,000

Bracos

-$250.00

$8,250

$13,500

Cargo

-$100

$7,400

$13,800

 

 

 

 

   (a) Which alternative should the manager choose under the maximax criterion? (1 mark)


(b) Which option should the manager choose under the maximin criterion? (1 mark)

(c) Which option should the manager choose under the LaPlace criterion? (2 marks)

(d) Which option should the manager choose with the Hurwicz criterion with α = 0.7?(2 marks)

(e) Using a minimax regret approach, what alternative should be chosen? (4 marks)

(f) After reading about economic predictions, the manager has assigned the probability of low, moderate or high at 35%, 25% and 40% respectively. Using expected monetary values, what option should be chosen and what is the optimal expected value?(4 marks)

(g) What is the most that should be paid for additional information? Use Expected Regret.(3 marks)

(h) Use the alternative method to verify EVPI (3 marks)

 

 Question 3

 During the past five months the emergency room at the new district Hospital has observed the number of patients during the weekend (Friday through Sunday). They typically experience greater patient traffic on weekends than during the week.

 

Week

No of Patients

1

105

2

119

3

122

4

128

5

117

6

136

7

141

8

126

9

143

10

140

 

 a) Compute a weighted three-period moving average forecast, using weights of 3, 2, and 1 for the most recent, next recent, and most distant data. (4 marks)

 b) What are the MAD, MSE and the MPE for this method? (6 marks)

 c) If the company decided to forecast using exponential smoothing with value of alpha =.3, what is the forecast in month 11? (use 2 decimal places) (4 marks)

 d) Using the MAD, is the exponential method an improvement over the previous method? (2 marks)

Compute the linear regression equation given the following: ƩX=55.0, ƩY=1277, ƩXY=7304, ƩX2=385 and forecast sales for month.
(5/5)
Attachments:
Instructions Files

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