9.1 Define the following terms:

a. Path

b. Activity

c. Early start

d. Early finish

e. Late start

f. Late finish

g. Forward pass

h. Backward pass

i. Node

j. AON

k. Float or Slack

l. Critical path

m. PERT

9.2 Distinguish between serial activities and concurrent activities. Why do we seek to use concurrent activities as a way to shorten a project’s length?

9.3 List three methods for deriving duration estimates for project activities. What are the strengths and weaknesses associated with each method?

9.4 In your opinion, what are the chief benefits and drawbacks of using beta distribution calculations (based on PERT techniques) to derive activity duration estimates?

9.5 “The shortest total length of a project is determined by the longest path through the network.” Explain the concept behind this statement. Why does the longest path determine the shortest project length?

9.6 The float associated with each project task can only be derived following the completion of the forward and backward passes. Explain why this is true.

9.7 Consider a project such as moving to a new neighborhood, completing a long-term school assignment, or even cleaning your bedroom. Develop a set of activities necessary to accomplish that project, and then order them in a precedence manner to create sequential logic. Explain and defend the number of steps you identified and the order in which you placed those steps for the best completion of the project.

9.8 What is the time estimate of an activity in which the optimistic estimate is 4 days, the pessimistic is 12 days, and most likely is 5 days? Show your work.

9.9 What is the time estimate of an activity in which the optimistic time is 5 days, the likely time is 8 days, and the pessimistic time is 14 days? Show your work.

9.10 Using the following information, develop an activity network for Project Alpha:

Activity Preceding Activities

A —

B A

C A

D B, C

E B

F D

G C

H E, F, G

9.11 Construct a network activity diagram based on the following information:

Activity Preceding Activities

A —

B A

C A

D A

E B

F C, D

G E, F

H F

I

J

G, H

I

9.12 You have a partial network for your project, and you are about to conduct a forward pass through it. Explain why the early start (ES) for activity G is 23 days, not 19 days.

Remember, activity G is a merge activity.

16 E

7

23

14 F

5

19

G

4

9.13 Referring to the figure in Problem 9.12, suppose that Activity G was the last activity in the network and you were about to start a backward pass.

a. What is the project’s duration? (Hint: complete the forward pass)

b. What are the late finish (LF) and late start (LS) values for activities E, F, and G?

c. Which activity has slack time? How many days?

9.14 Referring to the figure shown below, suppose that Activity O was the last activity in the network and you were about to start a backward pass.

a. What is the project’s duration? (Hint: complete the forward pass)

b. What are the late finish (LF) and late start (LS) values for activities L, M, N, and O?

c. Which activities have slack time? How many days?

10 L

7

17

13 M

5

18 0

4

14 N

2

16

9.15 Your university is holding a fund-raiser and will be hiring a band to entertain spectators. You have been selected to serve as the event project manager and have created a Work Breakdown Structure and duration estimates for the activities involved in site preparation for the event. Construct a network activity diagram based on the following information:

Activity Description Predecessors

Duration

(Days)

A Site selection None 4

B Buy concessions A 4

C Rent facilities A 2

D Build stands A 5

E Generator & wiring installation C 2

F Security B 4

G Lighting installation E 2

H Sound system installation E, F 2

I Stage construction D 3

J Tear down G, H, I 4

a. Conduct both a forward and backward pass using AON notation. What is the estimated total duration for the project?

b. Identify all paths through the network. Which is the critical path?

c. Which activities have slack time?

d. Identify all burst activities and merge activities.

9.16 Consider the following project tasks and their identified best, likely, and worst-case estimates of task duration. Assume the organization you work for computes TE based on the standard beta distribution formula. Calculate the TE for each of the following tasks (round to the nearest integer):

Activity Best Likely Worst TE

A 5 5 20

B 3 5 9

C 7 21 26

D 4 4 4

E 10 20 44

F 3 15 15

G 6 9 11

H 32 44 75

I 12 17 31

J 2 8 10

9.17 Consider the following project tasks and their identified best, likely, and worst-case estimates of task duration. Assume the organization you work for computes TE based on the standard beta distribution formula. Calculate the TE for each of the following tasks (round to the nearest integer):

Activity Best Likely Worst TE

A 4 5 10

B 4 6 9

C 2 5 8

D 5 8 10

E 12 16 20

F 6 10 12

G 5 9 14

H 14 16 22

I 10 14 20

J 1 2 5

9.18 Using the information from the following table, create an AON network activity diagram:

a. Calculate each activity TE (rounding to the nearest integer), the total duration of the project, its early start, early finish, late start, and late finish times, and the slack for each activity. Finally, show the project’s critical path.

b. Now, assume that activity E has taken 10 days past its anticipated duration to complete. What happens to the project’s schedule? Has the duration changed? Is there a new critical path? Show your conclusions.

Activity

Preceding

Activities Best Likely Worst

A — 12 15 25

B A 4 6 11

C — 12 12 30

D B, C 8 15 20

E A 7 12 15

F E 9 9 42

G D, E 13 17 19

H F 5 10 15

I G 11 13 20

J G, H 2 3 6

K J, I 8 12 22

9.19 An advertising project manager has developed a program for a new advertising campaign. In addition, the manager has gathered the time information for each activity as shown in the following table:

Time Estimates (week)

Activity Optimistic

Most Likely Pessimistic

Immediate Predecessor(s)

A 1 4 7 —

B 2 6 10 —

C 3 3 9 B

D 6 13 14 A

E 4 6 14 A, C

F 6 8 16 B

G 2 5 8 D, E, F

a. Calculate the expected activity times (round to the nearest integer).

b. Calculate the activity slacks. What is the total project length? Make sure you fully label all nodes in the network.

c. Identify the critical path. What are the alternative paths, and how much slack time is associated with each noncritical path?

d. Identify the burst activities and the merge activities.

e. Given the activity variances, what is the likelihood of the project finishing on week 24?

f. Suppose you wanted to have 99% confidence in the project finishing on time. How many additional weeks would your project team need to negotiate for in order to gain this 99% likelihood?

9.20 Consider a project with the following information:

Activity Duration Predecessors

A 3 —

B 5 A

C 7 A

D 3 B, C

E 5 B

F 4 D

G 2 C

H 5 E, F, G

Activity Duration ES EF LS LF Slack

A 3 0 3 0 3 —

B 5 3 8 8 13 5

C 7 3 10 3 10 —

D 3 10 13 10 13 —

E 5 8 12 13 17 5

F 4 13 17 13 17 —

G 2 10 12 15 17 5

H 5 17 22 17 22 —

a. Construct the project activity network using AON methodology and label each node.

b. Identify the critical path and other paths through the network.

9.21 Use the following information to determine the probability of this project finishing within 34 weeks of its scheduled completion date. Assume activities A – B – D – F – G are the project’s critical path:

Activity Optimistic Likely Pessimistic

Expected

Time Variance

A 1 4 8

B 3 5 9

C 4 6 10

D 3 7 15

E 5 10 16

F 3 6 15

G 4 7 12

a. Calculate the expected durations for each activity.

b. Calculate individual task variances and overall project variance.

c. The company must file a permit request with the local government within a narrow time frame after the project is expected to be completed. What is the likelihood that the project will be finished by week 34?

d. If we wanted to be 99% confident of the on-time delivery of the project, how much additional time would we need to add to the project’s expected delivery time?