Given the information below:

Activity

Immediate Predecessor(s)

Pessimistic

Probable

Optimistic

A

--

13

8

6

B

--

7

3

1

C

A

15

11

7

D

A, B

9

4

2

E

C

7

5

3

F

D

10

7

5

Draw a network diagram; what is the critical path? (5 marks)

Calculate the expected duration of each activity; remember to show your formulas and calculations. (15 marks)

Activity

Expected Time

Variance of time

Standard Deviation

ES

EF

LS

LF

Slack

A

B

C

D

E

F

Calculate the expected duration and variance of the critical path, and the standard deviation; remember to show your formulas and calculations. (5 marks)

Use exponential smoothing with trend adjustment to forecast deliveries for period 4. Let alpha = 0.4, beta = 0.2, and let the initial trend value be 4 and the initial forecast be 200. Remember to show your formula and calculations. (5 marks)

Period

Actual

Demand

Forecast

Trend

FIT

1

200

2

212

3

214

4

222

A swim club is designing a new pool to replace its old pool. The new pool would need to last for 10 years since the club is planning on relocating after 10 years. A concrete shell would cost $100,000 and last for all 10 years. Another option is to install a vinyl liner that would cost only $90,000 to install. However, the vinyl is not guaranteed to last for all 10 years and has a 60% chance of breaking down. Repair of the vinyl would cost $40,000 and would extend the life of the vinyl liner to the 10-year mark. If both options are acceptable to the swim club, which one minimizes their cost?

Draw a decision tree. (5 marks)

Calculate the EMV(s); which one should they choose? (5 marks)