CPM/ PERT in Industrial Engineering

7/30/2019 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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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


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






5) Mail brochures to tentative participants A4

6) Estimate number of participants. A5



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






5) Mail brochures to tentative participants A46) Estimate number of participants. A5



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


= 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



= 3- (7 -7) = 3


= 3 - (18 - 18) = 3

d f i7 / 15

10 / 18

18 / 21

3 / 7

FLOAT COMPUTATIONS FOR ACTIVITY


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= 2- (12 - 12) = 2


= 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.

CPM/ PERT in Industrial Engineering

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