Transcript Document

ME 380
Project Planning
Critical Path Method (CPM)
Elements: Activities & Events
Feature: Precedence relations
Activity
A
Duration
4
Precedence
-
B
C
D
5
3
3
A
A
E
2
B, C
Activities Table
Critical Path Method (CPM)
Graphical representation :
Activities :
(edges)
Events :
(vertices)
C
T
(Time reqd. for activity)
Critical Path Method (CPM)
Precedence:
Activities B & C precede Activity E
B
E
C
This “Event” cannot occur before both
activities B & C have been completed
Critical Path Method
Example
Activity
A
B
C
D
E
Duration
4
5
3
3
2
Precedence
A
A
B, C
Critical Path Method (CPM)
The project sequence graph is constructed:
D
A
Project
Start
C
Now what ???
B
E
Project
End
Critical Path Method (CPM)


Events are consolidated to provide the
specified precedence.
“Dummy” activities are added if necessary.
A
D
Project
Start
B
C
Project
End
E
Dummy Activity Example
To be able to bolt a bracket to a panel, the operations
required are :




Design bracket
Build bracket
Build panel
Drill holes in panel
A
D
C
A
C
A
B
C
D
A
A,C
B
D
A
B
C
D
Critical Path Method (CPM)

Activity times (duration) are added next :
A
4
Project
Start
B
5
3 C
D
3
Project
End
E
2
Critical Path Method (CPM)
The CRITICAL PATH is the path through the project
on which any delay will cause the completion of the
entire project to be delayed:
A
4
Project
Start
B
5
3 C
D
3
E
2
Project
End
Critical Path Method (CPM)

For fairly simple projects, the critical path is
usually the longest path through the project.

For projects with several parallel and interlinked
activities, this may not always be the case.

For more complicated projects, the critical path
can be determined with an ‘earliest time’ forward
sweep through the diagram followed by a ‘latest
time’ reverse sweep.
Critical Path Method (CPM)
The EARLIEST starting time of each activity is
associated with the events. It corresponds to the
longest time of any path from any previous event.
4
0
Project
Start
A
4
B
5
3 C
7
D
3
E
2
Project
End
9
Critical Path Method (CPM)
The LATEST starting time of each activity is also
associated with the events. It corresponds to the
longest time of any path from any subsequent event.
0
0
Project
Start
A
4
B
5
4
4
3 C
7
7
D
3
E
2
Project
End
9
9
Critical Path Method (CPM)
The CRITICAL PATH is the path along which the earliest
time and latest time are the same for all events, and
the early start time plus activity time for any activity
equals the early start time of the next activity.
0
0
Project
Start
A
4
B
5
4
4
3 C
7
7
D
3
E
2
Project
End
9
9
Critical Path Method (CPM)


This project cannot be completed in less than 9
weeks given the expected duration of the activities.
However, activities B & D could be delayed or
extended by up to 2 weeks each without affecting the
minimum project completion time. This is termed
‘float’ or ‘slack’ time.
0
0
Project
Start
A
4
B
5
4
4
3 C
7
7
D
3
Project
End
E
2
9
9
Example
Activity
A
B
C
D
E
F
G
H
I
J
K
Duration
3
3
4
1
3
2
2
4
1
3
5
Precedence
A
C
B, D
A, B, D
C, F
G
C
E, G
F, H, I
Example
B
A
E
J
F
Project
Start
G
D
C
K
I
H
Project
End
Example
Activity
Duration
Earliest
Start
Latest
Start
Float
A
3
0
0
0
B
3
3
3
0
C
4
0
1
1
D
1
4
5
1
E
3
6
13
7
F
2
6
6
0
G
2
8
8
0
H
4
10
10
0
I
1
4
13
9
J
3
10
16
6
K
5
14
14
0
Summary: CPM Steps

List all activities and expected durations.

Construct CPM diagram for activities list.

Determine EARLIEST start time for each event
(working forward from project start).

Determine LATEST start time for each event
(working backwards from project end).

Identify the CRITICAL PATH (and the ‘float’
time for any non-critical activities).
Using Estimates of Activity times




The estimated duration of any activity is just that – an
estimate.
There is usually an optimistic time (shortest time, TS)
associated with any activity – 1 in 100 chance of taking
less time than this.
There is also usually a pessimistic time (longest time,
TL) associated with any activity – 1 in 100 chance of
taking longer than this.
If TM is the most likely time for a specific activity, then a
mean and variance for the activity can be calculated,
assuming that TS, TL and TM are the parameters
describing a Beta distribution.
Using Estimates of Activity times
The estimated time TEST is calculated as:
TEST = (TS + 4.TM + TL)/6
and the variance of this is:
2 = (TL – TS)2/36
from the previous Example
Activity
Duration
TM
TS
TL
TEST
Earliest
Start
Latest
Start
Float
A
3
1
5
3.0
0
0.5
0.5
B
3
2
4
3.0
3
3.5
0.5
C
4
3
10
4.83
0
0
0
D
1
1
5
1.67
4.83
4.83
0
E
3
2
6
3.33
6.50
14.84
8.34
F
2
1
7
2.67
6.50
6.5
0
G
2
1
4
2.17
9.17
9.17
0
H
4
3
6
4.17
11.34
11.34
0
I
1
0
3
1.17
4.83
14.34
9.51
J
3
1
6
3.17
11.34
18.17
6.83
K
5
3
12
5.83
15.51
15.51
0
PERT/CPM
The critical path has now become C-D-F-G-H-K
with a total estimated time of 21.3 days
(i.e. 15.51 + 5.83)
The std. deviation along the critical path is the
square root of the sum of the individual
variances:
CP =  C2 + D2 + F2 + G2 + H2 + K2
which for this data is 2.36 days