Network Analysis

ECTION A …10 marks

Instruction: Highlight the correct answer

1.

7

2. Of all the paths through a network, the critical path has the _________.

A. maximum actual time

B. maximum expected time

C. minimum actual time

D. minimum expected time

3. Which of the following statements best describe the way in which the critical path may be determined?

A. The earliest start time equals the latest start time

B. The pessimistic time is the least in minutes

C. Milestones are equal in length

D. Variance

4. A dummy activity is referred to as:

A. an activity on a node

B. a milestone

C. an activity to cover more than one predecessors

D. an activity to identify those milestones where the earliest start time is later than the latest start time

5. In the forward pass through a CPM network, the EFT for an activity is computed by:

A. adding the EST to the LST

B. subtracting the EST from the LST

C. adding the activity time to the EST

D. adding slack values to the activity time

6. The earliest starting time for an activity leaving a node:

A. is the maximum of the earliest finish time for all activities leaving the node

B. is equal to the earliest finish time for the same activity minus its expected activity time

C. depends on all paths leading from the starting to the finishing node

D. depends on the earliest finish and the latest start

7. The latest starting time for an activity leaving a node:

A. is equal to the maximum of the latest start time for all activities leaving the node

B. depends on the latest finish time for the project

C. is equal to the latest finish time minus the activity time for the same activity

D. depends on the earliest finish and the latest start

8.

For a given activity K, . What is the expected time of the activity?
A.
B.
C.
D.

Use the scenario below to answer questions 8 – 13

Activity

Predecessors

Duration (weeks)

A

 

5

B

 

6

C

A

4

D

A

3

E

A

1

F

E

4

G

D , F

14

H

B , C

12

I

G , H

2

9. Which of the following is the critical path for the network?
A.
B.
C.
D.

10. The earliest starting time for activity F is after:
A.
B.
C.
D.

11. The earliest finish time for activity D is:
A.
B.
C.
D.

12. What is the project’s expected completion date?
A.
B.
C.
D.

13. What activities are considered to be non-critical activities?
A.
B.
C.
D.

14. Which activities have their latest finish time equal to their earliest finish time?
A.
B.
C.
D.

15. In calculating the expected activity time using the PERT method, what three (3) parameters must be known?
A. Optimistic time, LST and standard deviation
B. Standard deviation, most probable time and pessimistic time
C. Optimistic time, most probable time and pessimistic time
D. Probability, standard deviation and most probable time
16. The slack of an activity is given by:
A.
B.
C.
D.

17. The use of a dummy activity in drawing network diagram is to_______.
A. maintain the appropriate relationship in the diagram
B. show that time and resources are used up
C. indicate the critical path
D. enable the ease of calculation of activity time
18.
For a given activity G, . What is the variance of the activity?
A.
B.
C.
D.

19. What is the purpose of using Critical Path Method in business?
A. To create a formula based upon the most likely time and least likely time.
B. To find the shortest time to complete the project.
C. To find out faults in the system.
D. A method of mapping out the plan for a particular activity

Use the scenario below to answer questions 19– 21

The following information has been computed for a project.

Expected completion time,

Variance,
20. What is the standard deviation of the project?
A.
B.
C.
D.

21. If the desired completion time is 44 weeks, then the standardize variable z is?
A.
B.
C.
D.

22. What is the probability that the project will be completed in less than 44 weeks?
A.
B.
C.
D.

23. The total slack of the critical path is:
A. -3
B. 0
C. 1
D. ∞
24. In calculating the probability that a project will be completed within a specified period, based on the PERT analysis, which of the following is a correct assumption?
A. The actual times are normally distributed.
B. The estimated activity times follow a normal distribution.
C. The times along the critical path follows a Student-t distribution.
D. The expected completion times follow a normal distribution.
25.
If for activity C, , determine the variance of the expected time of the activity.
A. 0.028
B. 0.167
C. 0.660
D. 1.5

26. On the forward pass if two (2) or more activities precede an activity then the EST of the present activity is equal to:
A. largest EST of the immediate predecessors
B. largest EFT of the immediate predecessors
C. smallest EFT of the immediate predecessors
D. smallest EST of the immediate predecessors

27. The expected completion time for a project is 70 days and the variance is 49. Calculate the probability that the project will be completed in less than 80 days.
A. 0.0928
B. 0.1764
C. 0.5971
D. 0.9236
28. Which of the following statement(s) is/are TRUE?
I. the critical path is the shortest sequence of consecutive activities through a network.
II. the critical path is the longest sequence of consecutive activities through a network
III. the earliest time and latest time are equal for each event on the critical path
A. I only
B. II only
C. I and III only
D. II and III only

29. Which of the following rules for the construction of a PERT diagram is INCORRECT?
A. No activity can start until its tail event is reached
B. Loops are allowable in the network
C. An event is not complete until all activities leading into it are complete
D. A network should have only one entry event and one exit event
30. What is the difference between the EST and the LST for an event in a network?
A. Slack
B. Float
C. Free time
D. Lead time

31. The diagram shows an event in a network. Which of the following is TRUE?

Event Earliest Latest
number time time
A. 3 4 5
B. 5 3 4
C. 4 5 3
D. 4 3 5

32. If the project completion time is normally distributed and the due date for the project is greater than the expected completion time, then the probability that the project will be finished by the due date is:
A. less than 0.5
B. greater than 0.5
C. equal to 0.5
D. undeterminable without more information
33. The latest finish time for an activity is found during the backward pass through the network. The latest finish time is equal to the:
A. largest LF of the activities for which it is an immediate predecessor.
B. smallest LF of the activities for which it is an immediate predecessor.
C. largest LS of the activities for which it is an immediate predecessor.
D. smallest LS of the activities for which it is an immediate predecessor.

34. Given an activity’s optimistic, most likely and pessimistic time estimates of 4, 6 and 14 days respectively, compute the PERT expected activity time for this activity.
A. 8
B. 6
C. 7
D. 9
35. The amount of extra time an activity can take before it affects a following activity in a PERT network is referred to as the:
critical time
lead time
float time
slack time

36. For the given network, the critical path is:

SECTION B…30 marks

Instruction: Answer ALL questions. ALL working must be CLEARLY shown.

The owner of a chain of fast food restaurants is considering a new computer system for an accounting and inventory control. A computer company sent the following information about the system installation.

Activity

Immediate Predecessor

Most Optimistic

Most Likely

Most Pessimistic

A

— 

2

4

6

B

A

3

6

9

C

A

1

2

3

D

B

2

4

6

E

B

2

3

4

F

B , C

4

5

6

G

B

2

3

4

H

F

2

3

4

I

F, H

4

1.5

2

J

I

2

3

4

K

D , E

4

7

10

(i). Determine the expected time and variance for each activity (4 marks)
(ii). Draw the activity network for this project. (11 marks)
(iii). Show the activity schedule (ES, EF, LS and LF) as well as slack (in table) (3 marks)
(iv). Determine and state the critical path for the project. (2 marks)
(v). What are the expected time and variance of the project? (2 marks)
(vi). What is the probability that the project will be completed in 25 days? (4 marks)
(vii). What due date has a 95% chance of being met? (4 marks)
2.7
0.1894
0.9172
0.9773
2,3and2.5
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ACHI
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5
weeks
6
weeks
10
weeks
24
weeks
5
weeks
7
weeks
8
weeks
10
weeks
20
weeks
23
weeks
24
weeks
26
weeks
,,,
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LFTLST
–
LSTEST
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EFTEST
–
7,11and4
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0.44
0.67
1.17
1.36
62
Cweeks
=
5,8and3
abm
===
(
)
81
VCweeks
=
4.4
weeks
7.9
weeks
9
weeks
12
weeks
4.11
–
2
–
0.22
–
1.31
0.0227