Download - Pert Cpm Example
-
PERT / CPM
-
PERT / CPM or Network Analysis
CPM Critical Path Method Developed in 1957 by Du Pont First used in the construction of a new chemical
plant PERT Program Evaluation Review
Technique Developed in 1958 by Navy Used in the POLARIS missile program
-
Planning, Scheduling & Control Useful for project management
How long will it take to complete? What are the critical task that can delay the
completion? How long can certain task be prolonged before
becoming critical?
-
Network Implementation Define project and all significant activities or
tasks with single start and stop times. Develop the relationships between tasks. Draw the network with single start and end. Assign time or cost for each task. Compute the longest path through the
network. This is the critical path. Use network to plan, schedule and manage
project.
-
Useful Questions Building the Network
Is this a start activity? Is it a finish activity? Which activity precedes this one? Which activity follows it? Which activity is concurrent?
-
Drawing the Network Network begins with a single event and ends
with a single event. Each activity is represented by an arrow. Events are represented by circles and
precede and follow each activity. Consecutive activities must be separated by
events. No pair of events can be directly connected
by more than one activity without intervening events.
-
Parallel Paths Require Event
-
Rules for Network Construction (continued)
If an activity R precedes several otherwise unrelated activities S & T, then they must be separate by event.
If several otherwise unrelated activities R & S both precede activity T, then they must be separate by event.
-
Example
RS
TR
S
T
-
Dummy Activities Some precedence relations will require one
or more dummy activities. Dummy activities have 0 duration and are
represented by dashed arrows. Contribute to number of alternate paths but
not duration. Example:
A precedes D A and B precede E B and C precede F
-
Dummy Activity Example
A
B
C
D
E
F
-
Example Network Table
Activity Duration Preceded ByA 3B 3 AC 4D 1 CE 3 B, DF 2 A, B, DG 2 C, FH 4 GI 1 CJ 3 E, GK 5 F, H, I
-
CPM Example Network
A
B E
J
C
D
I
F
G
H K
3
3
4
1
3
2
1
24
3
5
-
Example: Alternate Paths
Path LengthA-B-E-J 12
A-B-F-G-dummy-J 13A-B-F-G-H-K 19
C-D-E-J 11C-D-F-G-dummy-J 12
C-D-F-G-H-K 18C-I-K 10
-
Path LengthA-B-E-J 12
A-B-F-G-dummy-J 13A-B-F-G-H-K 19
C-D-E-J 11C-D-F-G-dummy-J 12
C-D-F-G-H-K 18C-I-K 10
-
CPM Example NetworkCritical Path
A
B E
J
C
D
I
F
G
H K
3
3
4
1
3
2
1
24
3
5
-
Alternate Paths Evaluation alternative paths relative to critical
path Earlist Start (ES) for each activity trace forward
from start to beginning of the activity. When several paths exist use longest.
Latest Start (LS) for each activity trace backwards from project end to tail of each activity. When several paths exist use longest. Subtract from critical path time.
Total Float (TL): TL = LS ES
-
CPM Example Network
A
B E
J
C
D
I
F
G
H K
3
3
4
1
3
2
1
24
3
5
F: ES=3+3=6; LS=19-(5+4+2+2)=6; TF=0
-
CPM Example Network Table
Activity Duration ES LS TFA 3 0 0 0B 3 3 3 0C 4 0 1 1D 1 4 5 1E 3 6 13 7F 2 6 6 0G 2 8 8 0H 4 10 10 0I 1 4 13 9J 3 10 16 6K 5 14 14 0
Project Duration =19
-
PERT Program Evaluation and Review Technique
Allows uncertainity to be included in activity times
Assume a Beta probability distribution Defined with three parameters:
ts shortest time to accomplish activity
tl longest time to complete activity
tm most likely time
Expected duration; te = ( ts + 4tm + tl ) / 6 Standard deviation; = (tl ts) / 6
-
PERT Example Network
A
B E
J
C
D
I
F
G
H K
1-3-5
2-3-4
3-4-101-1-5
2-3-6
1-2-7
0-1-3
1-2-43-4-6
1-3-6
3-5-12
-
PERT Example Network TableActivity Expected Time Variance ES LS TF
A 3.00 0.44 0.00 0.50 0.50B 3.00 0.11 3.00 3.50 0.50C 4.83 1.36 0.00 1.00 0.00D 1.67 0.44 4.83 4.83 0.00E 3.33 0.44 6.50 14.84 8.34F 2.67 1.00 6.50 6.50 0.00G 2.17 0.25 9.17 9.17 0.00H 4.17 0.25 11.34 11.34 0.00I 1.17 0.25 4.83 14.34 9.51J 3.17 0.69 11.34 18.17 6.83K 5.83 2.25 15.51 15.51 0.00
Project Duration = 21.34