1. Consider the following project network and activity times (in weeks):
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
|
Time
|
5
|
3
|
7
|
6
|
7
|
3
|
10
|
8
|
a. Identify the critical path.
b. How much time will be needed to complete this project?
c. Can activity D be delayed without delaying the entire project? If so, by how many weeks?
d. Can activity C be delayed without delaying the entire project? If so, by how many weeks?
e. What is the schedule for activity E?
2. Davison Construction Company is building a luxury lakefront home in the Finger Lakes region of New York. Coordination of the architect and subcontractors will require a major effort to meet the 44-week (approximately 10-month) completion date requested by the owner. The Davison project manager prepared the following project network:
Estimates of the optimistic, most probable, and pessimistic times (in weeks) for the activities are as follows:
|
Activity
|
Optimistic
|
Most Probable
|
Pessimistic
|
|
A
|
4
|
8
|
12
|
|
B
|
6
|
7
|
8
|
|
C
|
6
|
12
|
18
|
|
D
|
3
|
5
|
7
|
|
E
|
6
|
9
|
18
|
|
F
|
5
|
8
|
17
|
|
G
|
10
|
15
|
20
|
|
H
|
5
|
6
|
13
|
a. Find the critical path.
b. What is the expected project completion time?
c. Based only on the critical path, what is the estimated probability the project can be completed in the 44 weeks as requested by the owner?
d. Based only on the critical path, what is the estimated probability the building project could run more than 3 months late? Use 57 weeks for this calculation.
e. What should the construction company tell the owner?
3. Embassy Club Condominium, located on the west coast of Florida, is undertaking a summer renovation of its main building. The project is scheduled to begin May 1, and a September 1 (17-week) completion date is desired. The condominium manager identified the following renovation activities and their estimated times:
|
Activity
|
Immediate Predecessor
|
Time
|
|
A
|
-
|
3
|
|
B
|
-
|
1
|
|
C
|
-
|
2
|
|
D
|
A, B, C
|
4
|
|
E
|
C, D
|
5
|
|
F
|
A
|
3
|
|
G
|
D, F
|
6
|
|
H
|
E
|
4
|
a. Draw a project network.
b. What are the critical activities?
c. What activity has the most slack time?
d. Will the project be completed by September 1?
4. At a local university, the Student Commission on Programming and Entertainment (SCOPE) is preparing to host its first rock concert of the school year. To successfully pro¬duce this rock concert, SCOPE has listed the requisite activities and related information in the following table (duration estimates measured in days).
|
Activity
|
Immediate Predecessor(s)
|
Optimistic
|
Most Probable
|
Pessimistic
|
|
A: Negotiate contract with selected musicians
|
-
|
8
|
10
|
15
|
|
B: Reserve site
|
-
|
7
|
8
|
9
|
|
C: Manage travel logistics for music group
|
A
|
5
|
6
|
10
|
|
D: Screen & hire security personnel
|
B
|
3
|
3
|
3
|
|
E: Arrange advertising
|
B, C
|
1
|
5
|
9
|
|
F: Hire parking staff
|
D
|
4
|
7
|
10
|
|
G: Arrange concession sales
|
E
|
3
|
8
|
10
|
a. Draw the project network.
b. Compute the expected duration and variance of each activity.
c. Determine the critical path in the project network.
d. What is the expected duration and variance of the critical path?
e. What is the likelihood that the project will be completed within 30 days?
f. If activity B is delayed by six days beyond its early start time, how does this affect the expected project duration?
5. The manager of the Oak Hills Swimming Club is planning the club's swimming team program. The first team practice is scheduled for May 1. The activities, their immediate predecessors, and the activity time estimates (in weeks) are as follows:
| Activity |
Description |
Immediate Predecessor |
Optimistic |
Time (weeks) Most Probable |
Pessimistic |
| A |
Meet with board |
- |
1 |
1 |
2 |
| B |
Hire coaches |
A |
4 |
6 |
8 |
| C |
Reserve pool |
A |
2 |
4 |
6 |
| D |
Announce program |
B. C |
1 |
2 |
3 |
| E |
Meet with coaches |
B |
2 |
3 |
4 |
| F |
Order team suits |
A |
1 |
2 |
3 |
| G |
Register swimmers |
D |
1 |
2 |
3 |
| H |
Collect fees |
G |
1 |
2 |
3 |
| I |
Plan first practice |
E, H, F |
1 |
1 |
1 |
a. Draw a project network.
b. Develop an activity schedule.
c. What are the critical activities, what is the expected project completion time?
d. If the club manager plans to start the project on February 1, what is the probability the swimming program will be ready by the scheduled May 1 date (13 weeks)? Should the manager begin planning the swimming program before February 1?
6. The product development group at Landon Corporation has been working on a new computer software product that has the potential to capture a large market share. Through outside sources, Landon's management learned that a competitor is working to introduce a similar product. As a result, Landon's top management increased its pressure on the product development group.
The group's leader turned to PERT/CPM as an aid to scheduling the activities remaining before the new product can be brought to the market. The project network is as follows:
The activity time estimates (in weeks) are as follows:
| Activity |
Optimistic |
Most Probable |
Pessimistic |
| A |
3 |
4 |
5 |
| B |
3 |
3.5 |
7 |
| C |
4 |
5 |
6 |
| D |
2 |
3 |
4 |
| E |
6 |
10 |
14 |
| F |
7.5 |
8.5 |
12.5 |
| G |
4.5 |
6 |
7.5 |
7.
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
|
Time
|
5
|
3
|
7
|
6
|
7
|
3
|
10
|
8
|
The crashing data for this project are as follows:
| |
Time (days) |
Cost ($) |
| Activity |
Normal |
Crash |
Normal |
Crash |
| A |
3 |
2 |
800 |
1400 |
| B |
2 |
1 |
1200 |
1900 |
| C |
5 |
3 |
2000 |
2800 |
| D |
5 |
3 |
1500 |
2300 |
| E |
6 |
4 |
1800 |
2800 |
| F |
2 |
1 |
600 |
1000 |
| G |
2 |
1 |
500 |
1000 |
a. Find the critical path and the expected project completion time.
b. What is the total project cost using the normal times?
8. Consider the following project network and activity times (in weeks):
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
|
Time
|
5
|
3
|
7
|
6
|
7
|
3
|
10
|
8
|
The crashing data for this project are as follows:
| |
Time (days) |
Cost ($) |
| Activity |
Normal |
Crash |
Normal |
Crash |
| A |
3 |
2 |
800 |
1400 |
| B |
2 |
1 |
1200 |
1900 |
| C |
5 |
3 |
2000 |
2800 |
| D |
5 |
3 |
1500 |
2300 |
| E |
6 |
4 |
1800 |
2800 |
| F |
2 |
1 |
600 |
1000 |
| G |
2 |
1 |
500 |
1000 |
9. Refer to Problem 8. Assume that management desires a 12-day project completion time.
a. Formulate a linear programming model that can be used to assist with the crashing Dicisions.
b. What activities should be crashed
c. What is the total project cost for the 12-day completion time?
10. Office Automation, Inc., developed a proposal for introducing a new computerized office system that will standardize the electronic archiving of invoices for a particular company. Contained in the proposal is a list of activities that must be accomplished to complete the new office system project. Use the following relevant information about the activities:
| |
|
|
Time (weeks) |
Cost ($1000s) |
| Activity |
Description |
Immediate Predecessor |
Normal |
Crash |
Normal |
Crash |
| A |
Plan needs |
_ |
10 |
8 |
30 |
70 |
| B |
Order equipment |
A |
8 |
6 |
120 |
150 |
| C |
Install equipment |
B |
10 |
7 |
100 |
160 |
| D |
Set up training lab |
A |
7 |
6 |
40 |
50 |
| E |
Conduct training course |
D |
10 |
8 |
50 |
75 |
| F |
Test system |
C, E |
3 |
3 |
60 |
_ |
a.Develop an activity network.
b.Develop an activity schedule.
c.What are the critical activities, and what is the expected project completion time?
d.Assume that the company wants to complete the project in six months or 26 weeks. What crashing decisions do you recommend to meet the desired completion time at the least possible cost? Work through the network and attempt to make the crashing decisions by inspection.
e.Develop an activity schedule for the crashed project.
f.What added project cost is required to meet the six-month completion time?