CPM PERT
description
Transcript of CPM PERT
CPM/PERTCPM/PERT
S. Ajit
ProjectProject
“A project is a series of activities directed to the accomplishment of a desired objective.”
HistoryHistory
PERT was developed by the US Navy for the planning and control of the Polaris missile program and the emphasis was on completing the program in the shortest possible time. In addition PERT had the ability to cope with uncertain activity completion times (e.g. for a particular activity the most likely completion time is 4 weeks but it could be anywhere between 3 weeks and 8 weeks).
CPM was developed by Du Pont and the emphasis was on the trade-off between the cost of the project and its overall completion time (e.g. for certain activities it may be possible to decrease their completion times by spending more money - how does this affect the overall completion time of the project?)
Developed in the 1950s
CPM - Critical Path MethodCPM - Critical Path Method
Definition: In CPM activities are shown as a network of precedence relationships using activity-on-node network construction– Single estimate of activity time– Deterministic activity times
USED IN : Production management - for the jobs of repetitive in nature where the activity time estimates can be predicted with considerable certainty due to the existence of past experience.
PERT - PERT - Project Evaluation & Review Project Evaluation & Review
TechniquesTechniques Definition: In PERT activities are shown as a network of
precedence relationships using activity-on-arrow network construction– Multiple time estimates – Probabilistic activity times
USED IN : Project management - for non-repetitive jobs (research and development work), where the time and cost estimates tend to be quite uncertain. This technique uses probabilistic time estimates.
The Project NetworkThe Project Network
Use of nodes and arrows
Arrows An arrow leads from tail to head directionally– Indicate ACTIVITY, a time consuming effort that is
required to perform a part of the work.
Nodes A node is represented by a circle- Indicate EVENT, a point in time where one or more
activities start and/or finish.
– An activity is a time-consuming effort that is required to complete part of a project. Shown as an arrow on the diagram
– An event is denoted by a circle and defines the end of one activity and beginning of the next. An event may be a decision point.
Activity Event
The Project NetworkThe Project Network
Activity SlackActivity Slack
Each event has two important times associated with it :
- Earliest time , Te , which is a calendar time when an event can occur when all the predecessor events completed at the earliest possible times
- Latest time , TL , which is the latest time the event can occur with out delaying the subsequent events and completion of project.
Difference between the latest time and the earliest time of an event is the slack time for that event
Positive slack : Slack is the amount of time an event can be delayed without delaying the project completion
Critical PathCritical Path
Is that the sequence of activities and events where there is no “slack” i.e.. Zero slack
Longest path through a network
minimum project completion time
Questions Answered by CPM & PERTQuestions Answered by CPM & PERT
Completion date?
On Schedule?
Within Budget?
Critical Activities?
How can the project be finished early at the least cost?
ExampleExample1. Construct the CPM Network using the details below and determine the critical path
Activity Immediate Predecessor
Duration
A - 1
B A 4
C A 2
D A 2
E D 3
F D 3
G E 2
H F,G 1
I C,H 3
J B 2
1 2
CPM NETWORK
A
1 7
4
2
3
CPM NETWORK
A
B
D
C
1 7
6
5
4
2
3
CPM NETWORK
A
B
DF
E
C
1 7
6
5
4
2
3
CPM NETWORK
A
B
DF
GE
C
1 7
6
5
4
2
3
CPM NETWORK
A
B
DF
GE
C
H
1 7
6
5
4
2 8
3
CPM NETWORK
A
B
DF
GE
C
IH
1 7
6
5
4
2 8
3
CPM NETWORK
A
J
B
DF
GE
C
IH
1 7
6
5
4
2 8
3
CPM NETWORK with duration of each activity
A(1)
J(2)
B(4)
D(2)
F(3)G(2)
E(3)
C(2)
I(3)
H(1)
1 7
6
5
4
2 8
3
To find the Critical Path
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
0
LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
0 0 1
LFT EST
To find the Critical Path
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
0 0 1
0 3
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
0
0 6
0 1
0 3
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
0
0 6
0 1
0 3
0 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
00 9
0 6
0 1
0 3
0 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
0 0 9
0 6
0 5
0 1
0 3
0 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
00 9
0 12
0 6
0 5
0 1
0 3
0 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
00 9
12 12
0 6
0 5
0 1
0 3
0 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
09 9
12 12
0 6
0 5
0 1
0 3
0 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
09 9
12 12
0 6
0 5
0 1
0 3
8 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
09 9
12 12
6 6
0 5
0 1
0 3
8 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
09 9
12 12
6 6
0 5
0 1
3 3
8 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
09 9
12 12
6 6
0 5
1 1
3 3
8 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
09 9
12 12
6 6
10 5
1 1
3 3
8 8
To find the Critical Path LFT EST
1 7
6
5
4
2 8
3
A(1)
J(2)
B(4)
D(2)F(3)
G(2)E(3)
C(2)
I(3)H(1) 0
09 9
12 12
6 6
10 5
1 1
3 3
8 8
Critical Path
Critical Path
A – B – E – G – H - I
Critical Path
1 - 2 - 4 – 5 – 6 – 7 - 8
CPM - ExampleCPM - Example
Critical Path
1 - 2 - 4 – 5 – 6 – 7 – 8
Critical Path
A – B – E – G – H - IProject Completion Time = 12 months
PERTPERTProbabilisticThree estimates
– to (a) – optimistic time
– tp (b) – pessimistic time
– tl (m) – most likely time
Mean µ = (to + 4* tl + tp)/6
Variance σ2 = [(tp – to)/6]2
Activity Predecessor
a m b
A - 6 7 8
B - 1 2 9
C - 1 4 7
D A 1 2 3
E A,B 1 2 9
F C 1 5 9
G C 2 2 8
H E,F 4 4 4
I E,F 4 4 10
J D,H 2 5 14
K G,I 2 2 8
PERT – Example: PERT – Example: Construct Project network, find the Construct Project network, find the expected duration and variance for each activity & find the expected duration and variance for each activity & find the
critical path and expected project completion timecritical path and expected project completion time
Activity
Predecessor
a m b µte
A - 6 7 8 7
B - 1 2 9
C - 1 4 7
D A 1 2 3
E A,B 1 2 9
F C 1 5 9
G C 2 2 8
H E,F 4 4 4
I E,F 4 4 10
J D,H 2 5 14
K G,I 2 2 8
PERT – Example: PERT – Example: Mean µ = (tMean µ = (too + 4* t + 4* tll + t + tpp)/6)/6 Variance Variance σσ22 = [(t = [(tpp – t – too)/6])/6]22
Activity
Predecessor
a m b µte
A - 6 7 8 7
B - 1 2 9 3
C - 1 4 7
D A 1 2 3
E A,B 1 2 9
F C 1 5 9
G C 2 2 8
H E,F 4 4 4
I E,F 4 4 10
J D,H 2 5 14
K G,I 2 2 8
PERT – Example: PERT – Example: Mean µ = (tMean µ = (too + 4* t + 4* tll + t + tpp)/6)/6 Variance Variance σσ22 = [(t = [(tpp – t – too)/6])/6]22
Activity
Predecessor
a m b µte
σ2
A - 6 7 8 7
B - 1 2 9 3
C - 1 4 7 4
D A 1 2 3 2
E A,B 1 2 9 3
F C 1 5 9 5
G C 2 2 8 3
H E,F 4 4 4 4
I E,F 4 4 10 5
J D,H 2 5 14 6
K G,I 2 2 8 3
PERT – Example: PERT – Example: Mean µ = (tMean µ = (too + 4* t + 4* tll + t + tpp)/6)/6 Variance Variance σσ22 = [(t = [(tpp – t – too)/6])/6]22
Activity
Predecessor
a m b µte
σ2
A - 6 7 8 7 0.11
B - 1 2 9 3
C - 1 4 7 4
D A 1 2 3 2
E A,B 1 2 9 3
F C 1 5 9 5
G C 2 2 8 3
H E,F 4 4 4 4
I E,F 4 4 10 5
J D,H 2 5 14 6
K G,I 2 2 8 3
PERT – Example: PERT – Example: Mean µ = (tMean µ = (too + 4* t + 4* tll + t + tpp)/6)/6 Variance Variance σσ22 = [(t = [(tpp – t – too)/6])/6]22
Activity
Predecessor
a m b µte
σ2
A - 6 7 8 7 0.11
B - 1 2 9 3 1.78
C - 1 4 7 4
D A 1 2 3 2
E A,B 1 2 9 3
F C 1 5 9 5
G C 2 2 8 3
H E,F 4 4 4 4
I E,F 4 4 10 5
J D,H 2 5 14 6
K G,I 2 2 8 3
PERT – Example: PERT – Example: Mean µ = (tMean µ = (too + 4* t + 4* tll + t + tpp)/6)/6 Variance Variance σσ22 = [(t = [(tpp – t – too)/6])/6]22
Activity
Predecessor
a m b µte
σ2
A - 6 7 8 7 0.11
B - 1 2 9 3 1.78
C - 1 4 7 4 1.00
D A 1 2 3 2 0.11
E A,B 1 2 9 3 1.78
F C 1 5 9 5 1.78
G C 2 2 8 3 1.00
H E,F 4 4 4 4 0
I E,F 4 4 10 5 1.00
J D,H 2 5 14 6 4.00
K G,I 2 2 8 3 1.00
PERT – Example: PERT – Example: Mean µ = (tMean µ = (too + 4* t + 4* tll + t + tpp)/6)/6 Variance Variance σσ22 = [(t = [(tpp – t – too)/6])/6]22
1
4
2
3
A(7)
J(6)
B(3)
D(2)
F(5)
G(3)
E(3)
C(4) I(5)
H(4)
6 6
To find the Critical Path LFT EST
K(3)
1
4
26
3
A(7)
J(6)
B(3)
D(2)
F(5)
G(3)
E(3)
C(4) I(5)
H(4)
6 6
To find the Critical Path LFT EST
K(3)
1
6
5
4
2
3
A(7)
J(6)
B(3)
D(2)
F(5)
G(3)E(3)
C(4) I(5)
H(4)
6 6
To find the Critical Path LFT EST
K(3)
1
6
5
4
2
3
A(7)
J(6)
B(3)
D(2)
F(5)
G(3)E(3)
C(4) I(5)
H(4)
6 6
To find the Critical Path LFT EST
K(3)
1
7
6
5
4
2
3
A(7)
J(6)
B(3)
D(2)
F(5)
G(3)
E(3)
C(4) I(5)
H(4)
6 6
To find the Critical Path LFT EST
K(3)
1
7
6
5
4
2
3
A(7)
J(6)
B(3)
D(2)
F(5)
G(3)
E(3)
C(4) I(5)
H(4)
6 6
To find the Critical Path LFT EST
K(3)
1
7
6
5
4
2
3
A(7)
J(6)
B(3)
D(2)
F(5)
G(3)
E(3)
C(4) I(5)
H(4)
6 6
To find the Critical Path LFT EST
K(3)
1
7
6
5
4
2
83
A(7) J(6)
B(3)
D(2)
F(5)
G(3)
E(3)
C(4) I(5)
H(4)
6 6
To find the Critical Path LFT EST
K(3)
1
7
6
5
4
2
83
A(7)J(6)
B(3)
D(2)
F(5)
G(3)
E(3)
C(4) I(5)
H(4)
6 6
To find the Critical Path LFT EST
K(3)
1
7
6
5
4
2
83
A(7) J(6)
B(3)
D(2)
F(5)
G(3)
E(3)
C(4) I(5)
H(4) 0 0
To find the Critical Path LFT EST
K(3)
1414
4 5
7 7
77
10 10
15 17
20 20
1
7
6
5
4
2
83
A(7) J(6)
B(3)
D(2)
F(5)
G(3)
E(3)
C(4) I(5)
H(4) 0 0
K(3)
1414
4 5
7 7
77
10 10
15 17
20 20
Critical path 1 – 2 – 3 – 5 – 6 – 8
Critical path A – Dummy – E – H – J
PERT - ExamplePERT - Example What is the probability of completing the project within
25 weeks?
Σσ2 = 5.89 σ = √(Σσ2) = 2.43 Ts (Scheduled time) = 25 weeks Z = (Ts – Te) / σ = (25 – 20) / 2.43 = 2.06 From z table (normal table) z(2.06) = 97.68 %
Activities
Variance
A 0.11
Dummy 0
E 1.78
H 0
J 4
PERT - ExamplePERT - Example What is the probability of completing the project within
15 weeks?
Σσ2 = 5.89 σ = √(Σσ2) = 2.43 Ts (Scheduled time) = 15 weeks Z = (Ts – Te) / σ = (15 – 20) / 2.43 = -2.06 From z table (normal table) z(-2.06) = 100 - 97.68 %
• = 2.02 %
Activities
Variance
A 0.11
Dummy 0
E 1.78
H 0
J 4
Limitations of CPM/PERTLimitations of CPM/PERT
Clearly defined, independent and stable activities
Specified precedence relationships Over emphasis on critical paths