Project Management Final Exam
Instructions: Please use a word document to show all work.
Q1. A project includes the following activities. Also listed below are the predecessor-successor relationship for the activities and the duration of each activity.
|
Activity
|
Duration (Days)
|
Immediate Predecessors
|
|
A
|
2
|
-
|
|
B
|
5
|
A
|
|
C
|
3
|
A
|
|
D
|
2
|
B, C
|
|
E
|
1
|
C
|
|
F
|
4
|
D
|
|
G
|
3
|
E
|
|
H
|
6
|
F, G
|
A. Draw the project network diagram.
B. Calculate the early and late start and finish times for each activity.
C. What is the critical path?
D. Due to an unforeseen weather delay, activity C's duration has doubled from 3 to 6 days. What are the effects of this delay?
Q2. The project network and activity durations for a maintenance of a computer network, including backups, reformatting the hard drive, etc. are listed below on the activity-on-node network diagram for the project.
A. Compute the early and fate start schedules. What is the critical path? What is the duration of the critical path?
B. How much can activity G be delayed without delaying the project?
C. How much can activity B be delayed without delaying the project? Without delaying another activity.
Q3. You are a member of a team that has been assigned the task of implementing a new Reservations System for the Best Eastern Hotel system, where you work. You have been assigned the job of developing a project network diagram to aid in planning, scheduling and controlling the project. You have interviewed your colleagues on the development team and determined that there are 10 primary activities that must be performed. After reviewing your notes, you have arrived at the following summary regarding the relationships among the ten activities, which you have labeled A through J: The project begins with activity A, which precedes B, C and D. A and B precede E and F. E precedes H, I and J. F precedes I, while I precedes J. G and J can begin after C and D are completed. D and G precede I. H immediately precedes J. J can begin after all other activities are complete.
A. List the precedence relationships in the matrix below, then eliminate all redundant relationships so that only immediate predecessor-successor relationships are listed.
B. Draw an activity-on-node project network diagram for the project.
C. Given the following duration estimates for each activity, find the early and late start schedule for the project.
|
Activity
|
Duration
|
Activity
|
Duration
|
|
A
|
1
|
F
|
2
|
|
B
|
3
|
G
|
4
|
|
C
|
5
|
H
|
5
|
|
D
|
3
|
I
|
3
|
|
E
|
4
|
J
|
2
|
Q4. Given the following project network and activity durations, answer the questions below:
A. Find the early and late start activity start and finish times.
B. What is the critical path?
C. Can activity B be delayed without delaying the project? By how much?
D. Can activity E be delayed without delaying the project? By how much?
Q5. The following project network was developed by a quality improvement team at WordPro, a major word processing software company. The team is describing the plan for their activities for finding the sources of poor quality in providing telephone help line service to customers. Due to the exploratory nature of the project, the team has decided to use PERT to arrive at a planned completion date estimate for WordPro's top management. The project network is shown below, along with the three estimate's of each activities' duration in days.
|
Activity
|
Optimistic (a)
|
Most Likely (m)
|
Pessimistic (b)
|
|
A
|
1
|
4
|
7
|
|
B
|
2
|
3
|
10
|
|
C
|
2
|
5
|
6
|
|
D
|
3
|
5
|
7
|
|
E
|
3
|
6
|
9
|
|
F
|
2
|
3
|
16
|
|
G
|
2
|
3
|
4
|
A. Given these estimates of activity times, compute the expected activity duration and variance for each activity.
B. Find the early and late start schedules for each activity in the project. What is the length of the critical path?
C. What is the probability that the project will be completed on or before the end of the 20th day? What is the probability that the project will be completed in 23 days or less?
D. Are there any non-critical activities that could also delay the project beyond the critical path length? Discuss your answer.
Q6. A quality circle team at Superchip, a semiconductor manufacturer, must implement a new means of placing serial numbers on the companies' semiconductor chips that may be more easily read by the user. The project is being implemented due to a rash of recent thefts of the companies most popular processor chip, which is used in personal computers. The team has developed the following project network for the project, along with the estimates of activity duration listed on the network. All durations are in weeks.
A. Find the early and late start and finish times for each activity.
B. What is the Critical Path and what is its duration?
C. If activity B's duration were extended to 6 days, how would the project duration be affected?
D. Which activities have slack, and how much slack do they have?
Q7. The following network diagram represents a small product development project with uncertain activity durations. The PERT estimates are also given for each activity. Please assist the project manager in answering the following questions regarding this project.
A. Calculate the activity durations and variances. Which of the two paths connecting A and G is Critical?
|
Activity
|
Optimistic (a)
|
Most Likely (m)
|
Pessimistic (b)
|
|
A
|
2
|
6
|
7
|
|
B
|
4
|
9
|
10
|
|
C
|
1
|
3
|
8
|
|
D
|
3
|
5
|
6
|
|
E
|
2
|
5
|
10
|
|
F
|
1
|
3
|
9
|
|
G
|
3
|
6
|
9
|
B. What is the expected completion time for G? What is the probability that the project will be completed in 25 weeks? 26, 27 and 28 weeks?
Q8. General Contractors, Inc., a metal works plant in Arizona, has long been trying to avoid the expense of installing air pollution control equipment. The local environmental protection group has recently given the company 12 weeks to install a complex air filter system on its main smokestack. General Contractors was warned that it will be forced to close unless the device is installed in the allotted period. Homer Simpson, the managing partner, wants to make sure the installation of the filtering system progresses smoothly and on time.
The activities involved in the project, the precedence relations between them, and the activity durations in weeks are shown in the following table:
TABLE 1: Activities and Immediate Predecessors
|
Activity
|
Description
|
Duration
|
Predecessor
|
|
A
|
Build internal components
|
2
|
None
|
|
B
|
Modify roof and floor
|
3
|
None
|
|
C
|
Construct collection stack
|
2
|
A
|
|
D
|
Pour concrete and install frame
|
4
|
B
|
|
E
|
Build high-temperature burner
|
4
|
C
|
|
F
|
Install control system
|
3
|
C
|
|
G
|
Install air pollution device
|
5
|
D, E
|
|
H
|
Inspection and testing
|
2
|
F, G
|
A. Draw the project network diagram.
B. What are the path lists and the critical path?
C. Crash the project as much as possible and draw a time-cost trail-off curve.
D. Develop a solution concluding with 12 week duration.
An analysis of early times shows that the duration of the project given the normal activity times is longer than has been allotted for the project. Mr. Simpson realizes that the project time must be reduced, but would like to accomplish the time reduction at least cost. Therefore, a tabulation of the normal and crash times and costs for each activity is compiled from time and cost estimates from the construction company involved, with the following result:
TABLE 2: Normal and Crash Data for General Contractors, Inc.
|
Activity
|
Normal
Time
|
Crash
Time
|
Normal
Cost $
|
Crash
Cost $
|
|
A
|
2
|
1
|
22,000
|
22,900
|
|
B
|
3
|
1
|
30,000
|
34,000
|
|
C
|
2
|
1
|
26,000
|
25,800
|
|
D
|
4
|
3
|
48,000
|
49,000
|
|
E
|
4
|
2
|
56,000
|
57,400
|
|
F
|
3
|
2
|
30,000
|
30,500
|
|
G
|
5
|
2
|
80,000
|
86,000
|
|
H
|
2
|
1
|
16,000
|
19,000
|