Download - CPM/ PERT in Industrial Engineering
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CPM/PERT
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Bigger Perspective
Mechanical Engineering: The role of a mechanical engineeris to
take a product from an idea to the marketplace. In order toaccomplish this, a broad range of skills are needed.
Design
Thermal
Production
Industrial
Industrial Engineering: Industrial engineering is a branch of
engineering dealing with the optimization of complex processes or
systems.
Production and operations management
Supply chain management
Quality Management
Project management
Value engineering,
etc.
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3
WHAT IS A PROJECT?
PURPOSE
An undertaking or venture to accomplish someobjective or goal
STRUCTURE A set of interrelated jobs whose accomplishment
leads to the completion of the project
COMPONENTS
Jobs or activities consume time and resources andare governed by precedence relations
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VARIETY OF PROJECTS
Projects at personal level
Projects in local neighbourhood
Organisational projects National projects
Global projects
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PERSONAL PROJECTS
Preparing for an examination
Writing a book
Getting dressed A birthday function
A family vacation
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PROJECTS IN LOCAL NEIGHBOURHOOD
A school function
Cleanliness drive
Construction of clubs Tree plantation exercise
Establishment of a park
Welcoming a dignitary to the colony
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ORGANISATIONAL PROJECTS
Construction of building, highway
Planning & launching a new product A turnaround in a refinery
A training for managers in the organization
Conducting a marketing survey Completing a financial audit
Disposal of dead stock
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NATIONAL PROJECTS
Launching a new satellite
Literacy campaign
Poverty removal drive
Organizing general elections
Preparation of annual budget
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GLOBAL PROJECTS
Organising peace missions (UN)
Space exploration
Conducting World Trade
Environment protection
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FEATURES OF PROJECTS
Well defined collection of jobs
Generally non-repetitive, one time effort
Jobs interrelated through precedence
Jobs otherwise independent
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PROJECT FEATURES
(Continued)
Jobs consume time and resources
Coordination needed between
individuals, groups & organisations
Constant pressure of conformance to
time/cost /performance goals
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Screening
Project Appraisal
Project Selection
IDEA GENERATION
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LIFE CYCLE OF A PROJECT
Selection of the project
Project Planning
Scope of work & network development
Basic Scheduling
Time Cost tradeoffs
Resource Considerations in projects
Project Implementation Project Completion and Audit
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FORMATION OF PROJECT TEAM
Appointment of Project Manager
Selection of Project team members
Briefing meetings amongst team members Broad consensus about scope of work and
time frame
Development of work breakdown structureand allocation of responsibilities
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WORK BREAKDOWN STRUCTURE
A breakdown of the total project task intocomponents to establish
How work will be done?
How people will be organized?
How resources would be allocated?
How progress would be monitored?
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MEANS OF PROJECT REPESENTATION
Project name and description.
List of jobs that constitute the project.
Gantt or bar chart showing when activitiestake place.
Project network showing activities, their
dependencies and their relation to the whole.
(A-O-A and A-O-N representations)
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WHY USE PROJECT NETWORKS ?
A convenient way to show activities and
precedence in relation to the whole project.
Basis of project planning:
Responsibility allocation
Definition of subcontracting units
Role of different players
Basic scheduling and establishment of work
time tables
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WHY USE PROJECT NETWORKS -II ?
Critical path determination and selective
management control
Deterministic vs probabilistic activity times
Resource planning for projects
Project crashing with time cost tradeoffs
Resource aggregation
Resource levelling
Limited resource allocation
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WHY USE PROJECT NETWORKS - III ?
Project implementation:
Time table for implementation
Monitoring and reporting progress
Updation of schedules and resources Coordination of work with different agencies
The project network is thus a common vehicle
for planning, communicating andimplementing the project right frominception.
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EXAMPLE 1
Organizing a one day Seminar
Generate the list of jobs to be done:
1) Decide date ,budget, venue for seminar.
2) Identify speakers, participants.3) Contact and finalize speakers.
4) Print seminar brochure.
5) Mail brochures to tentative participants6) Estimate number of participants.
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Organizing a one day seminar
7) Decide menu for lunch, tea & coffee
8) Arrange for catering
9) Arrange projection facilities at venue.10) Receive guests at registration.
11) Conduct seminar as per brochure
12) See off guests.
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EXAMPLE 1
Organizing a one day Seminar
Activity Predecessors
1) Decide date ,budget, venue for seminar. --
2) Identify speakers, participants. --
3) Contact and finalize speakers. A2
4) Print seminar brochure. A1, A3
5) Mail brochures to tentative participants A4
6) Estimate number of participants. A5
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Organizing a one day seminar
Activity Predecessors
7) Decide menu for lunch, tea & coffee A6
8) Arrange for catering A1,A79) Arrange projection facilities at venue. A6
10) Receive guests at registration. A5
11) Conduct seminar as per brochure A8, A9, A1012) See off guests. A11
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DRAWING THE PROJECT NETWORK
(A-O-A)
1 2 3 4 5 6 7 8 9 10
A2 A3 A4 A5 A6 A7 A8 A11 A12
A1
A10
A9
Activity Predecessors
1) Decide date ,budget, venue for seminar. --
2) Identify speakers, participants. --
3) Contact and finalize speakers. A2
4) Print seminar brochure. A1, A3
5) Mail brochures to tentative participants A4
6) Estimate number of participants. A5
Activity Predecessors
7) Decide menu for lunch, tea & coffee A6
8) Arrange for catering A1,A7
9) Arrange projection facilities at venue. A6
10) Receive guests at registration. A511) Conduct seminar as per brochure A8, A9, A10
12) See off guests. A11
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DEVELOPING THE PROJECT NETWORK
(A-O-N)
A1 A4 A5 A6 A7 A8
A2 A3 A10
A9 A11 A12
Activity Predecessors
1) Decide date ,budget, venue for seminar. --
2) Identify speakers, participants. --
3) Contact and finalize speakers. A2
4) Print seminar brochure. A1, A3
5) Mail brochures to tentative participants A46) Estimate number of participants. A5
Activity Predecessors
7) Decide menu for lunch, tea & coffee A6
8) Arrange for catering A1,A7
9) Arrange projection facilities at venue. A6
10) Receive guests at registration. A5
11) Conduct seminar as per brochure A8, A9, A10
12) See off guests. A11
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Role of Dummies in Project Network
Logical dummy
Dummy for uniqueness of activity representation
Dummies for creation of a single source and sink
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EXAMPLE 2
Logical dummy
Job Predecessors
a --
b --c --
d a,b
e b,c
1 2 5
3
4
a
b
c
d
e
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EXAMPLE 3
Logical dummy
Job Predecessors
a --
b --c --
d a,b
e a,c
f a,b,c
1 2 5 6
3
4
a
b
ce
f
d
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EXAMPLE 4
Dummy for uniqueness of activity
representationJob Predecessors
a --
b a
c ad a
e b, c, d 1 2 5 6
3
4
a
b
d
c e
EXAMPLE 5
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EXAMPLE 5
DUMMIES FOR CREATION OF
A SINGLE SOURCE AND SINK
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THE ROLE OF DUMMIES IN PROJECT
NETWORKS
Role of Dummy I II III
Network type
A-O-A yes yes yes
A-O-N no no yes
I Correct representation of precedence logic
II Uniqueness of activity representation
III Creation of single source/ sink
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EXAMPLE 6
Inconsistent Network
2 3 4
5 6 7
1 8
A closed loop in a project network
is a logical inconsistency.
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PREREQUISITES FOR A VALID PROJECT
NETWORK
NECESSARY REQUIREMENT
The project network must not have any cycles or
loops, since these represent logical inconsistencies
in representation.
DESIRABLE FEATURES
The project network should have the minimum
number of dummies and no redundancies sincethese unnecessarily clutter the network.
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SUMMARY - I
Project representation on A-O-A and A-O-Nnetwork.
Use of Dummies in project networkrepresentation
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Basic Scheduling with Network
Deterministic (as in CPM) when previous experience yields fairly accurate estimates of activity
duration, eg construction activity, market surveys.
A single time estimate is used for each activity. This is taken from
experts who have prior knowledge and experience of the activity.
Probabilistic (as in PERT)
when there is uncertainty in times, as for instance in R&D
activities, new activities being carried out for the first time.
Three time estimates (optimistic, most likely and
pessimistic) are commonly used for each activity based on
the consensus of the group.
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Basic Scheduling with A-O-A Networks
For Deterministic activity duration(CPM)
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EXAMPLE 7
Job Predecessors Duration (days)
a -- 2
b -- 3
c a 1d a, b 4
e d 5
f d 8
g c, e 6h c, e 4
i f, g, h 3
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PROJECT NETWORK FOR EXAMPLE 7 (A-O-A)
1
2 5 6
3 4 7
8a
b
c
d
e
f
g
h
i
2
3
1
4
5
8
6
4
3
Job Predecessors Duration (days)
a -- 2
b -- 3c a 1
d a, b 4
e d 5
f d 8
g c, e 6h c, e 4
i f, g, h 3
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FORWARD PASS
Initialization:
E1 = 0 (or the project start time S)
(This applies to all source nodes)
Ej= Max (Ei+ tij) for all i before node j
j
iB(j) tijEi
Ej( Set B(j))
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FORWARD PASS
1
2 5 6
3 4 7
8
a
b
c
d
e
f
g
h
i
2
3
1
4
5
8
6
4
3
0
2
3
12
7
16
18
21
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BACKWARD PASS
Initialization:Lj (or the latest occurrence of all ending nodes)
= Project duration, T as determined in the
forward pass Li = Min (Lj-tij) over all successor nodes j of
the node ibeing investigated, (set A(i))
ij
LjLi
tijA(i)
CRITICAL PATH
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CRITICAL PATH
EXAMPLE 7 (A-O-A)
1
2 5 6
3 4 7
8
a
b
c
d
e
f
g
h
i
2
3
1
4
5
8
6
4
3
0
2
3
12
7
16
18
21
0
3
3 7 18
21
1812
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ACTIVITY SCHEDULE
FROM EVENT TIMES
i jtij
Ei
Li
Ej
Lj
Early start of activity ij = ES(ij) = Ei
Early finish of activity ij= EFij = ES(ij)+ tij
Late finish of activity ij = LF(ij) = Lj
Late start of activity ij = LS(ij) = LF(ij) -tij
FORWARD
PASS
BACKWARD
PASS
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EARLY & LATE SCHEDULE
Job duration ES EF LS LF
a 2 0 2 1 3
b 3 0 3 0 3
c 1 2 3 11 12d 4 3 7 3 7
e 5 7 12 7 12
f 8 7 15 10 18
g 6 12 18 12 18h 4 12 16 14 18
i 3 18 21 18 21
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ACTIVITY FLOATS
i j
Ei
Li
Ej
Lj
Ei Li Ej Lj
tij
Total float = F1(ij) = Lj-Ei -tij
Safety float = F2(ij) = Lj- Li-tijFree float = F3(ij) = Ej -Ei -tij
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FLOATS FOR EXAMPLE 7
Job Total Safety Freea 1 1 0b 0 0 0
c 9 8 9d 0 0 0e 0 0 0f 3 3 3
g 0 0 0h 2 2 0i 0 0 0
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INTERPRETATION OF FLOATS
An activity , in general, has both predecessors
and successors. Each of the four kinds of float
depends on how these accommodate the
activity.
activity
Predecessors Successors
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SUMMARY - II
Basic scheduling of projects (A-O-A mode)
Deterministic activity durations
Notion of critical path
Lower bound on project duration
Selective monitoring and control
Critical path determination
Event based algorithms Float calculation and its importance
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Basic Scheduling withA-O-N Networks
For Deterministic activity duration (CPM)
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EXAMPLE
Job Predecessors Duration (days)a -- 2b -- 3c a 1
d a, b 4e d 5f d 8g c, e 6
h c, e 4i f, g, h 3
FORWARD PASS
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FORWARD PASS
FOR EXAMPLE
a cg
b
de
h i
f
2 1 6
3
4
8
345
FORWARD PASS
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FORWARD PASS
(A-O-N Networks)
Initialization:
Early start(ES) for all beginning activities
= 0 (or the start date, S for the project)
Early finish (EF) for activity = ES+ duration
ES(j)= Max (EF all predecessors)
i1
i2j
ip
ES/ EFES/EFES/EF
ES/EF
BACKWARD PASS
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BACKWARD PASS
FOR EXAMPLE
a cg
b
de
h i
f
2 16
3
4
8
345
0 / 2
0 / 3
2 / 3
3 / 77 / 12
12 / 18
12 / 16
7 / 15
18 / 21
BACKWARD PASS
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BACKWARD PASS
(A-O-N Networks)
Initialization
Project duration,T = Max (EF of ending jobs).
LF(all ending jobs) =T
LS = LF- Duration
LF = Min (LS of successors)
LS/LF
LS/LF
LS/LF
LS/LF
CRITICAL PATH
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CRITICAL PATH
FOR EXAMPLE
a cg
b
de
h i
f
2 16
3
4
8
345
0 / 2
0 / 3
2 / 3
3 / 77 / 12
12 / 18
12 / 16
7 / 15
18 / 21
18 /21
10 / 18
14 / 18
12 /1811 / 12
7 / 123 / 7
1 / 3
0 / 3
EARLY & LATE SCHEDULE FOR
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EARLY & LATE SCHEDULE FOR
EXAMPLE
Job duration ES EF LS LF
a 2 0 2 1 3
b 3 0 3 0 3
c 1 2 3 11 12
d 4 3 7 3 7
e 5 7 12 7 12
f 8 7 15 10 18
g 6 12 18 12 18h 4 12 16 14 18
i 3 18 21 18 21
CRITICAL PATH
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CRITICAL PATH
FOR EXAMPLE
a cg
b
de
h i
f
2 16
3
4
8
345
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INTERPRETATION OF FLOATS
An activity , in general, has both predecessors
and successors. Each of the four kinds of float
depends on how these accommodate the
activity.
activity
Predecessors Successors
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FLOATS FOR EXAMPLE
Job Total Safety Freea 1 1 0b 0 0 0
c 9 8 9d 0 0 0e 0 0 0f 3 3 3
g 0 0 0h 2 2 0i 0 0 0
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FLOAT COMPUTATIONS FOR ACTIVITY a
Total Float = LS - ES = LF - EF =1Safety float = Total Float - [Max (LF of predecessors)-ES]
= 1- (0 - 0) = 1
Free float = Total Float -[LF -Min(ES of successors)]
= 1 - (3-2) = 0
a c
d
0 / 2
1 / 3
2 / 3
3 / 7
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FLOAT COMPUTATIONS FOR ACTIVITY c
Total Float = LS - ES = LF - EF =9
Safety float = Total Float - [Max (LF of predecessors)-ES]
= 9- (3 -2) = 8
Free float = Total Float -[LF -Min(ES of successors)]
= 9 - (12-12) = 9
a c g
h
2 / 3
11 / 12
12 / 18
12 / 161 / 3
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FLOAT COMPUTATIONS FOR ACTIVITY f
Total Float = LS - ES = LF - EF =3
Safety float = Total Float - [Max (LF of predecessors)-ES]
= 3- (7 -7) = 3
Free float = Total Float -[LF -Min(ES of successors)]
= 3 - (18 - 18) = 3
d f i7 / 15
10 / 18
18 / 21
3 / 7
FLOAT COMPUTATIONS FOR ACTIVITY
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Total Float = LS - ES = LF - EF =2
Safety float = Total Float - [Max (LF of predecessors)-ES]
= 2- (12 - 12) = 2
Free float = Total Float -[LF -Min(ES of successors)]
= 2 - (18 - 18) = 2
FLOAT COMPUTATIONS FOR ACTIVITY
h
c
e h i
12 / 16
14 / 18
18 / 2111 / 12
7 / 12
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SUMMARY - III
Basic scheduling of projects (A-O-N mode)
Deterministic activity durations
Notion of critical path
Lower bound on project duration
Selective monitoring and control
Critical path determination
- Event based algorithms Float calculation and importance
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Project Scheduling withProbabilistic Activity Times
(PERT)
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UNCERTAIN ACTIVITY DURATIONS
For each activity in the project three
time estimates are obtained
Optimistic time, a
Most likely time, m
Pessimistic time, b
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PERT TIME ESTIMATES
Mean of activity duration =
(a + 4m + b) / 6
Variance of activity duration =
{ (b - a) / 6}2
Standard deviation of activity duration =
Sq. root of variance =(b - a ) / 6
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BASIC PERT PROCEDURE - I
Compute mean and variance of all jobs.
Conduct forward and backward pass on the
project network with expected times of all
activities.
Identify the Critical Path.
Obtain variance of critical path by adding
variance of activities.
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BASIC PERT PROCEDURE - II
Obtain the distribution of the Project
Duration.
Make probability statements about the
project
Chances of meeting the target date.
Probability of exceeding a given ceiling date.
Probability that the project duration is confined toan interval of time.
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AN EXAMPLE
Job Predecessors Time estimates Mean Variancea m b
------------------------------------------------------------------------------------------
A -- 2 4 8 4.33 1
B -- 4 6 10 6.33 1
C A 6 6 6 6.00 0
D A 2 8 14 8.00 4
E A 6 8 12 8.33 1
F B,C 3 6 9 6.00 1
G D,F 8 16 20 15.33 4H D,F 4 4 4 4.00 0
I E,H 4 8 10 7.66 1
SAMPLE NETWORK
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SAMPLE NETWORK
(A-O-A)
1
2 5
6
43
A
BC
D
E
F
H
I
G
4.33
6.33
6
6
8
8.33
4
7.66
15.33
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FORWARD & BACKWARD PASS
1
2 5
6
43
A
BC
D
E
F
H
I
G
4.33
6.33
6
6
8
8.33
4
7.66
15.33
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1
2 5
6
43
A
BC
D
E
F
H
I
G
4.33
6.33
6
6
8
8.33
4
7.66
15.33
CRITICAL PATH
0
4.33 20.33
31.66
16.3310.33
10.33 16.33
31.66
244.33
0
DISTRIBUTION OF THE PROJECT
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DISTRIBUTION OF THE PROJECT
DURATION
Project duration follows a Normal
Distribution with
Mean = 31.66 Variance = 6 = (2.45)2
-3 -2 -1 0 1 2 3
24.31 31.66 39.01
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CONFIDENCE INTERVALS
Chances that the project is completed within
mean +/- 1 sigma 68% (29.21 --34.11)
mean +/- 2 sigma 95% (26.76 -- 36.56)
mean +/_ 3 sigma 99% (24.31 -- 39.01)
PROBABILITY
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PROBABILITY
STATEMENTS - I
Probability of meeting a Target Date,
say 36 days
Z (Standard normal deviate) =
(36 - 31.66)/2.45 = 4.34/2.45 = 1.77
Area from normal tables = 0.9616
PROBABILITY
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PROBABILITY
STATEMENTS - II
Probability of exceeding a ceiling, say
28 days
Z (Standard normal deviate) =
(28 - 31.66)/2.45 = -3.66/2.45 = - 1.49
Area from normal tables = 0.0681
PROBABILITY
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PROBABILITY
STATEMENTS - III
Probability of duration lying in an interval,
say 28 to 36 days
Area from normal tables =0.9616 - 0.0681
= 0.8935
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STANDARD PERT ASSUMPTIONS
1. The activities are independent
2 The critical path contains a large no. of activities
so that we can invoke the Central Limit Theorem.
3 .All activities not on the critical path are ignored.
4. Activity times follow a Beta distribution.
5. The mean and variance of the activities are given
by (a+4m+b)/6 and [(b-a)/6]2.
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SUMMARY - IV
Basic PERT analysis
Three time estimates for activities
Mean and variance computation
Forward and backward pass on the network
Critical path identification
Distribution of project completion time
Probability statements about project completion.