Project Management and Statistical Process Control Homework Assignment
Project Management
PERT Network Diagram 1 illustrates the ten interrelated activities that comprise a certain project.
PERT Network Diagram 1
The information presented in Table 1 represents the optimistic activity time (a), most probable activity time (m), and pessimistic activity time (b) in weeks for each activity associated with the project.
|
Activity
|
Optimistic (a)
|
Most Probable (m)
|
Pessimistic (b)
|
|
A
|
2
|
3
|
4
|
|
B
|
1
|
3
|
5
|
|
C
|
2
|
5
|
8
|
|
D
|
1
|
2
|
3
|
|
E
|
2
|
4
|
6
|
|
F
|
1
|
3
|
5
|
|
G
|
2
|
4
|
6
|
|
H
|
1
|
3
|
5
|
|
I
|
2
|
4
|
6
|
|
J
|
1
|
4
|
7
|
1. Using the information provided in Table 1, calculate the expected activity time (t) in weeks for each activity and then enter this information in the appropriate data field provided for each activity in PERT Network Diagram 2 in order to complete this diagram. What is the expected activity time in weeks for each of the ten activities? (Arrange your answers in alphabetical order by activity beginning with activity A and ending with activity J).
2. Using the information provided in Table 1, calculate the variance for the estimated activity time for each activity. (Arrange your answers in alphabetical order by activity beginning with activity A and ending with activity J).
3. Using the information in completed PERT Network Diagram 2, calculate the overall estimated activity time in weeks for each path through the network; identify which path constitutes the critical path.
4. Using the information provided in Table 1, calculate the standard deviation for the project.
5. Using the information provided in Table 1 and completed Project Network Diagram 2, calculate the probability of the project critical path activities being completed in less than or equal to 24 weeks.
The information presented in Table 2 represents the calculated Earliest Start, Earliest Finish, Latest Start and Latest Finish times for each activity.
Table 2
|
Activity
|
Earliest Start
|
Earliest Finish
|
Latest Start
|
Latest Finish
|
|
A
|
0
|
3
|
0
|
3
|
|
B
|
3
|
6
|
3
|
6
|
|
C
|
6
|
11
|
6
|
11
|
|
D
|
11
|
13
|
16
|
18
|
|
E
|
6
|
10
|
7
|
11
|
|
F
|
11
|
14
|
11
|
14
|
|
G
|
18
|
22
|
18
|
22
|
|
H
|
0
|
3
|
7
|
10
|
|
I
|
3
|
7
|
10
|
14
|
|
J
|
14
|
18
|
14
|
18
|
1. Using the information provided in Table 2, calculate the slack time in weeks for each activity. (Arrange your answers in alphabetical order by activity beginning with activity A and ending with activity J).
The information presented in Table 3 represents the total budgeted cost for each activity associated with the project.
|
Activity
|
Total Budgeted Cost
|
|
A
|
$22,000
|
|
B
|
$30,000
|
|
C
|
$24,000
|
|
D
|
$8,000
|
|
E
|
$7,000
|
|
F
|
$9,000
|
|
G
|
$10,000
|
|
H
|
$12,000
|
|
I
|
$23,000
|
|
J
|
$11,000
|
2. Using the information provided in Table 2 and Table 3, calculate the budgeted costs for week seven of the project based upon using the Earliest Start Date for each activity and calculate the budgeted costs for week seven of the project based upon using the Latest Start Date for each activity in order to then calculate the difference in the cashflow for week seven between these two scenarios.
3. Using the information provided in Table 2 and Table 3, calculate the budgeted costs for week eighteen of the project based upon using the Earliest Start Date for each activity and calculate the budgeted costs for week eighteen of the project based upon using the Latest Start Date for each activity in order to then calculate the difference in the cashflow for week eighteen between these two scenarios.
Table 4 represents the percentage of completion and actual cost of work performed data for each activity associated with the project at a certain point in time during the project.
|
Activity
|
Total Budgeted Cost
|
Percent of Completion
|
Actual Cost of Work Completed
|
|
A
|
$22,000
|
100%
|
$23,000
|
|
B
|
$30,000
|
100%
|
$28,000
|
|
C
|
$24,000
|
100%
|
$27,500
|
|
D
|
$8,000
|
85%
|
$7,300
|
|
E
|
$7,000
|
65%
|
$9,800
|
|
F
|
$9,000
|
0%
|
$0
|
|
G
|
$10,000
|
0%
|
$0
|
|
H
|
$12,000
|
45%
|
$5,100
|
|
I
|
$23,000
|
0%
|
$0
|
|
J
|
$11,000
|
0%
|
$0
|
4. Using the information provided in Table 4, calculate the value of work completed and activity difference for each activity. Which activity evidences the single largest activity difference (regardless of whether it is a cost overrun or cost underrun) at this particular point in the project?
5. Using the information provided in Table 4, calculate the overall cost overrun or cost underrun for the project at this particular point in the project.
Table 5 represents the estimated crash time in weeks and associated total crash cost for each activity.
|
Activity
|
Crash Time
(Weeks)
|
Total Crash Cost
|
|
A
|
2
|
$25,000
|
|
B
|
2
|
$40,000
|
|
C
|
4
|
$27,000
|
|
D
|
1
|
$9,000
|
|
E
|
3
|
$8,500
|
|
F
|
2
|
$12,000
|
|
G
|
3
|
$11,000
|
|
H
|
2
|
$15,000
|
|
I
|
3
|
$26,000
|
|
J
|
3
|
$13,000
|
6. Using the information in completed PERT Network Diagram 2 and Table 5, crash the network in order to reduce the estimated project duration to 20 weeks while minimizing the overall crash cost. Which critical path activity would be the most logical choice for the first activity to crash?
7. Which critical path activity would be the most logical choice for the second activity to crash?
8. What is the total estimated cost associated with crashing the network to reduce the estimated project duration to 20 weeks at the lowest possible overall crash cost?
9. After successfully crashing the network to reduce the estimated project duration to 20 weeks, which path through the crashed network constitutes the critical path?