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Feb 20, 2024
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Project Management tools, CPM, PERT
Alex Kachura
South university
MBA6012-Operation and Supply management
Cady, Lyle
January 23, 2024
2
Project Management tools, CPM, PERT
Project management is a complex process that requires various techniques to ensure successful project completion. One popular approach is the Critical Path Method (CPM), which identifies the most critical sequence of tasks that must be completed on schedule to meet the project's deadline. The critical path is the sequence of activities that must be completed on time to ensure timely completion of the entire project.
To calculate the critical path, we analyze the network diagram that represents the project's
activities and their dependencies. This process involves identifying the longest sequence of interconnected activities that cannot be delayed without affecting the project's deadline. For example, if an engineering firm is working on a construction project, the critical path includes a series of activities that are essential to complete on time to ensure that the entire project is delivered as planned.
Activity
Immediate Predecessors
Times in Days a
m
b
A
None
1
3
5
B
None
1
2
3
C
A 1
2
3
D
A 2
3
4
E
B 3
4
11
F
C, D 3
4
5
G
D, E
1
4
7
H
F, G
2
4
6
3
A(1,3,5)
/ \
/ \
C(1,2,3) D(2,3,4)
\ /
\ /
F(3,4,5)
| \
G(1,4,7)
| /
H(2,4,6)
The Critical Path Method (CPM) is a project management technique that identifies the most critical activities that must be completed on time to ensure the timely completion of the entire project. The critical path is the longest sequence of tasks that determine the minimum time
required to complete the project.
To identify the critical path, we first construct a network diagram that represents the project's activities and their dependencies. Then, we calculate the duration of each activity and determine which activities are critical. These are the activities with zero slack or float, meaning that any delay in completing them will delay the entire project.
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Once we have identified the critical path, we can estimate the project's completion time using CPM. We do this by adding up the durations of activities along the critical path. The estimated completion time is the minimum time required to complete the project, and it helps in setting realistic deadlines.
The Program Evaluation and Review Technique (PERT) is a statistical tool used to estimate the expected time required to complete each activity. PERT uses three time estimates for each activity: the optimistic time (a), the most likely time (m), and the pessimistic time (b). It calculates the expected time (TE) for each activity using the formula: TE = (a + 4m + b) / 6.
Once we have calculated the expected time for each activity, we can determine the expected time for the critical path by adding up the expected times of all the activities on the critical path. This process helps in accurately estimating the project's completion time, taking into account the uncertainties and risks associated with each activity.
By comparing the estimated completion time using CPM and PERT, we can assess the difference between the two methods(Cohen, E. (n.d.)). In general, PERT estimates are more accurate because they take into account the uncertainties and risks associated with each activity (LaMarco, N. (2019)). However, CPM provides a simpler and more straightforward method for identifying the critical path and estimating the project's completion time.
The difference in estimated completion times arises because CPM assumes a deterministic approach using a single time estimate, while PERT incorporates a probabilistic
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approach, considering the variability in activity duration (LaMarco, N. (2019)). s. PERT's use of weighted average times and a beta distribution for time estimates introduces a level of uncertainty, which can be beneficial in planning for potential delays.
When managing a project, it is essential to choose the right approach to ensure its successful completion. The choice of method depends on the nature of the project, the level of uncertainty associated with each activity, and the available resources. The CPM approach is ideal
for projects with well-defined and stable activity times. This approach is suitable for projects where time is a crucial factor, and there is little uncertainty in activity durations. CPM helps you to identify the critical path, which is the sequence of activities that must be completed on time to ensure the project's timely completion. This method helps in identifying potential delays and taking appropriate measures to mitigate them. On the other hand, PERT is more suitable for complex projects with high levels of uncertainty in activity durations. This approach helps in estimating the project's completion time, taking into account the uncertainties and risks associated with each activity.
Since we have the net work drawn out we now need to do the following to come up with our data/
We will start the Calculate with the Earliest Start (ES) and Earliest Finish (EF): ES of an activity is the maximum of the EFs of its immediate predecessors. EF of an activity is ES + Duration. Calculate Latest Start (LS) and Latest Finish (LF): LF of an activity is the minimum of
the LSs of its immediate successors.
LS of an activity is LF - Duration. Then we will Calculate Total Float (TF): TF = LS - ES
or LF - EF
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Activity A:
ES(A) = 0 (Start)
EF(A) = ES(A) + Duration = 0 + 1 = 1
Activity B:
ES(B) = 0 (Start)
EF(B) = ES(B) + Duration = 0 + 1 = 1
Activity C:
ES(C) = EF(A) = 1
EF(C) = ES(C) + Duration = 1 + 1 = 2
Activity D:
ES(D) = EF(A) = 1
EF(D) = ES(D) + Duration = 1 + 2 = 3
Activity E:
ES(E) = EF(B) = 1
EF(E) = ES(E) + Duration = 1 + 3 = 4
Activity F:
ES(F) = max(EF(C), EF(D)) = max(2, 3) = 3
EF(F) = ES(F) + Duration = 3 + 4 = 7
Activity G:
ES(G) = max(EF(D), EF(E)) = max(3, 4) = 4
EF(G) = ES(G) + Duration = 4 + 1 = 5
Activity H:
ES(H) = max(EF(F), EF(G)) = max(7, 5) = 7
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EF(H) = ES(H) + Duration = 7 + 2 = 9
5. Calculate LS, LF, and TF:
Activity H:
LF(H) = EF(H) = 9
LS(H) = LF(H) - Duration = 9 - 2 = 7
TF(H) = LS(H) - ES(H) = 7 - 7 = 0
Activity G:
LF(G) = min(LF(H)) = 9
LS(G) = LF(G) - Duration = 9 - 6 = 3
TF(G) = LS(G) - ES(G) = 3 - 4 = -1 (critical path)
Activity F:
LF(F) = min(LF(H)) = 9
LS(F) = LF(F) - Duration = 9 - 5 = 4
TF(F) = LS(F) - ES(F) = 4 - 3 = 1
Activity E:
LF(E) = min(LF(G)) = 9
LS(E) = LF(E) - Duration = 9 - 11 = -2 (critical path)
TF(E) = LS(E) - ES(E) = -2 - 1 = -3 (critical path)
Activity D:
LF(D) = min(LF(F), LF(G)) = min(9, 9) = 9
LS(D) = LF(D) - Duration = 9 - 4 = 5
TF(D) = LS(D) - ES(D) = 5 - 1 = 4
Activity C:
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LF(C) = min(LF(F)) = 9
LS(C) = LF(C) - Duration = 9 - 3 = 6
TF(C) = LS(C) - ES(C) = 6 - 2 = 4
Activity B:
LF(B) = min(LF(E)) = 9
LS(B) = LF(B) - Duration = 9 - 3 = 6
TF(B) = LS(B) - ES(B) = 6 - 1 = 5
Activity A:
LF(A) = min(LF(C), LF(D)) = min(9, 9) = 9
LS(A) = LF(A) - Duration = 9 - 1 = 8
TF(A) = LS(A) - ES(A) = 8 - 0 = 8
Critical Path:
The critical path is A -> D -> G -> H with a duration of 9 days. Activities E and F are also part of the critical path.
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Cohen, E. (n.d.). How/to/Use the/Critical/Path/Method/for/Complete/Beginners. Retrieved from https://www.workamajig.com/critical-path-method LaMarco, N. (2019, February 19). How/Does/PERT/&/CPM Work? /Retrieved/from https://smallbusiness.chron.com/pert-cpm-work-69516.html.
Midgie, Rajeshwari, & Yolande. (n.d.). Critical/Path/Analysis/and/PERT/Charts: /Planning/and Scheduling/Projects/That are More/Complex. /Retrieved/December 16, 2019, from
https://www.mindtools.com/article/critical-path-analysis.htm.
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