Project_Network Analysis(PERT and CPM) L1

7/30/2019 Project_Network Analysis(PERT and CPM) L1

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Network Analysis

Project Management - CPM/PERT

OR


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What exactly is a project?PM 1 Im in charge of the construction of a retail development in thecentre of a large town. There are 26 retail units and a super market inthe complex. My main responsibilities are to co-ordinate the work of the various contractors to ensure that the project is completed tospecification, within budget and on time.

PM 2 I am directing a team of research scientists. We are runningtrials on a new analgesic drug on behalf of a pharmaceutical company.It is my responsibility to design the experiments and make sure that

proper scientific and legal procedures are followed, so that our resultscan be subjected to independent statistical analysis.


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PM 2 I am directing a team of research scientists. We are runningtrials on a new analgesic drug on behalf of a pharmaceutical company.

It is my responsibility to design the experiments and make sure thatproper scientific and legal procedures are followed, so that our resultscan be subjected to independent statistical analysis.

PM 1 Im in charge of the construction of a retail development in thecentre of a large town. There are 26 retail units and a super market in

the complex. My main responsibilities are to co-ordinate the work of the various contractors to ensure that the project is completed tospecification, within budget and on time.


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Characteristic of a project

A project is a temporary endeavour involving a connected sequence of activities and a range of resources, which is designed to achieve a

specific and unique outcome and which operates within time, costand quality constraints and which is often used to introduce change.

A unique, one-time operational activity or effortRequires the completion of a large number of interrelated activitiesEstablished to achieve specific objectiveResources, such as time and/or money, are limited

Project


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Examples constructing houses, factories, shopping malls,

athletic stadiums or arenas developing military weapons systems, aircrafts,

new ships launching satellite systems constructing oil pipelines developing and implementing new computer

systems

planning concert, football games, or basketballtournaments introducing new products into market


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Project Scheduling and Control Techniques

Gantt Chart

Critical Path Method (CPM)

Program Evaluation and Review Technique (PERT)


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History of CPM/PERT

Critical Path Method (CPM) E I Du Pont de Nemours & Co. (1957) for construction of new

chemical plant and maintenance shut-down Deterministic task times Activity-on-node network construction Repetitive nature of jobs

Project Evaluation and Review Technique (PERT) U S Navy (1958) for the POLARIS missile program

Multiple task time estimates (probabilistic nature) Activity-on-arrow network construction Non-repetitive jobs (R & D work)


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Project Network Network analysis is the general name given to certain specifictechniques which can be used for the planning, management andcontrol of projects 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.where j > i

Nodes : A node is represented by a circle- Indicate EVENT, a point in time where one or more activities start and/or

finish.

Activity - A task or a certain amount of work required in the project Requires time to complete Represented by an arrow

Dummy Activity It indicates only precedence relationships

Does not require any time of effort

i j


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Event Signals the beginning or ending of an activity Designates a point in time Represented by a circle (node)

Network Shows the sequential relationships among activities using nodes

and arrows

Activity-on-node (AON)

nodes represent activities, and arrows show precedencerelationships

Activity-on-arrow (AOA)

arrows represent activities and nodes are events for points intime

Project Network


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AOA Project Network for House

32 0

13

1 11

1 2 4 6 7

3

5

Layfoundation

Design houseand obtainfinancing

Order andreceivematerials

Dummy

Finishwork

Selectcarpet

Selectpaint

Buildhouse

AON Project Network for House

13

2

2

43

31 5

1

61

71Start

Design house andobtain financing

Order and receivematerials

Select paintSelect carpet

Lay foundations Build house

Finish work


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Situations in network diagram

AB

C

A must finish before either B or C can start

A

B

C both A and B must finish before C can start

D

C

B

Aboth A and C must finish before either of Bor D can start

A

C

B

D

DummyA must finish before B can start

both A and C must finish before D can start


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Concurrent Activities

2 3

Lay foundation

Order material

(a) Incorrect precedencerelationship

(b) Correct precedencerelationship

3

42

DummyLayfoundation

Order material

1

2 0


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Network exampleImmediate

Activity Predecessor Time (Hr.)A -- 6B -- 8C -- 5D B 13E C 9F A 15G A 17H F 9I G 6J D, E 12


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CPM Example: CPM Network

1 8

3

7

4

2

5

A (6)

F(15)

B (8)

C (5)E(9)

D(13)

G(17) H(9)

I(6)

J(12)

6


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CPM calculation

Path A connected sequence of activities leading from

the starting event to the ending event

Critical Path The longest path (time); determines the project

duration

Critical Activities

All of the activities that make up the critical path

d


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Forward Pass Earliest Start Time (ES) - Earliest time an activity can start

ES = maximum EF of immediate predecessors Earliest finish time (EF) - Earliest time an activity can finish

It is computed by earliest start time plus activity timeEF= ES + t

Earliest Occurrence time of event i is denoted by E i.Therefore, E j = E i + t

Latest Start Time (LS) - Latest time an activity can start withoutdelaying critical path time

LS = LF t

Latest finish time (LF) - Latest time an activity can be completedwithout delaying critical path time

LF = minimum LS of immediate predecessorsLatest Occurrence time of event i is denoted by L j.Therefore, L i = L j t.

Backward Pass


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CPM analysis

Draw the CPM network

Analyze the paths through the network Determine the float for each activity

Compute the activitys float float = LS - ES = LF - EF

Float is the maximum amount of time that this activity can bedelay in its completion before it delays completion of theproject.

Find the critical path is that the sequence of activities and events

where there is no slack i.e.. Zero slack Longest path through a network

Find the project duration is minimum project completion time


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CPM Example: CPM Network

1 8

3

7

4

2

5

A (6)

F(15)

B (8)

C (5)E(9)

D(13)

G(17) H(9)

I(6)

J(12)

6


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CPM Example: Forward Pass

1 8

3

7

4

2

5

A (6)

F(15)

B (8)

C (5)E(9)

D(13)

G(17) H(9)

I(6)

J(12)

6

E8=33

E6=21

E7=23

E5=21

E3=6

E2=8

E4=5

E1=0


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CPM Example: Backward Pass

1 8

3

7

4

2

5

A (6)

F(15)

B (8)

C (5)E(9)

D(13)

G(17) H(9)

I(6)

J(12)

6

E8=33

E6=21

E7=23

E5=21

E3=6

E2=8

E4=5

E1=0L8=33

L7=27

L6=24

L5=21

L4=12

L3=9

L2=8

L1=0


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After Forward and Backward Pass

1 8

3

7

4

2

5

A (6)

F(15)

B (8)

C (5)E(9)

D(13)

G(17) H(9)

I(6)

J(12)

6

E8=33

E6=21

E7=23

E5=21

E3=6

E2=8

E4=5

E1=0L8=33

L7=27

L6=24

L5=21

L4=12

L3=9

L2=8

L1=0

Critical Path1-2-5-8 or B-D-J

Total ProjectCompletiontime = 33 Hrs


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CPM Example

ES and EF Times

1 8

3

7

4

2

5

A(6)

F(15)

B(8)

C(5)E(9)

D(13)

G(17) H(9)

I(6)

J(12)

6

0 6

0 8

0 5


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CPM Example

ES and EF Times

1 8

3

7

4

2

5

A(6)

F(15)

B(8)

C(5)E(9)

D(13)

G(17) H(9)

I(6)

J(12)

6

0 6

0 8

0 55 14

8 21

6 23

6 21


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CPM Example

ES and EF Times

1 8

3

7

4

2

5

A(6)

F(15)

B(8)

C(5)E(9)

D(13)

G(17) H(9)

I(6)

J(12)

6

0 6

0 8

0 55 14

8 21

6 23

6 21

21 33

21 30

23 29

Projects EF = 33


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CPM Example

1 8

3

7

4

2

5

A(6)

F(15)

B(8)

C(5)E(9)

D(13)

G(17)

H(9)

I(6)

J(12)

6

0 6

0 8

0 55 14

8 2121 33

6 23

21 30

23 29

6 21

21 33

27 33

24 33

LS and LF Times


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CPM Example

1 8

3

7

4

2

5

A(6)

F(15)

B(8)

C(5)E(9)

D(13)

G(17)

H(9)

I(6)

J(12)

6

21 33

21 30

23 29

21 33

27 33

24 33

LS and LF Times

0 6

0 8

0 55 14

8 21

6 23

6 21

4 10

0 8

7 12

12 21

8 21

10 27

18 24


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CPM Example Float = LS - ES = LF - EF

1 8

3

7

4

2

5

A(6)

F(15)

B(8)

C(5)E(9)

D(13)

G(17)

H(9)

I(6)

J(12)

6

0 6

0 8

0 55 14

8 21 21 33

6 23

21 30

23 29

6 21

3 9

0 8

7 1212 21

21 33

27 33

8 21

10 27

24 33

9 24

3 4

3

3

4

0

0

77

0


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CPM Example Critical Path

1 8

3

7

4

2

5

A (6)

F(15)

B (8)

C (5)E(9)

D(13)

G(17) H(9)

I(6)

J(12)

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Critical Path1-2-5-8 or B-D-J

Total ProjectCompletiontime = 33 Hrs


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Draw Network Compute Project Completion time and Find Critical path

Immediate

Activity Predecessor Time (days)A -- 8B A 12C A 4D B 2E B 8F D 2G E, F 3H C, G 2I E, F 2J I, H 2


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PERT PERT is based on the assumption that an activitys duration

follows a probability distribution instead of being a single value

Three time estimates are required to compute the parameters of an activitys duration distribution: pessimistic time (t p ) - the time the activity would take if

things did not go well

most likely time (t m ) - the consensus best estimate of theactivitys duration optimistic time (t o ) - the time the activity would take if things

did go well

Mean (expected time): t e = tp + 4 tm + to 6

Variance: Vt= 2 =

tp - to

6

2


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PERT analysis Draw the network.

Analyze the paths through the network and find the critical path. The length of the critical path is the mean of the project duration

probability distribution which is assumed to be normal The standard deviation of the project duration probability

distribution is computed by adding the variances of the criticalactivities (all of the activities that make up the critical path) andtaking the square root of that sum

Probability computations can now be made using the normal

distribution table.


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Probability computation

Determine probability that project is completed within specified time

Z =x -

where = t p = project mean time or mean of the project duration

= project standard mean time

x = (proposed ) specified time


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Normal Distribution of Project Time

Time x

Z

Probability


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PERT Example

Immed. Optimistic Most Likely Pessimistic

Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.)A -- 4 6 8B -- 1 4.5 5C A 3 3 3D A 4 5 6E A 0.5 1 1.5F B,C 3 4 5

G B,C 1 1.5 5H E,F 5 6 7I E,F 2 5 8J D,H 2.5 2.75 4.5

K G,I 3 5 7


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PERT ExampleActivity Expected Time Variance

A 6 4/9B 4 4/9C 3 0D 5 1/9

E 1 1/36F 4 1/9G 2 4/9H 6 1/9

I 5 1J 3 1/9K 5 4/9


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PERT Example

7

2 5

3

A (6)

D (5)

C (3)

B (4)F (4)

E (1)

G (2)

I (5)

H (6)

K (5)

J (3)

1

6

4

PERT Network


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PERT Example

Activity ES EF LS LF Slack A 0 6 0 6 0 *criticalB 0 4 5 9 5C 6 9 6 9 0 *D 6 11 15 20 9E 6 7 12 13 6F 9 13 9 13 0 *G 9 11 16 18 7H 13 19 14 20 1I 13 18 13 18 0 *J 19 22 20 23 1K 18 23 18 23 0 *


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PERT Example

Vcritical path = V A + V C + V F + V I + V K = 4/9 + 0 + 1/9 + 1 + 4/9

= 2critical path = 1.414

z = (24 - 23)/ (24-23)/1.414 = .71

From the Standard Normal Distribution table:P(z < .71) = .5 + .2612 = .7612

What is the probability that the project will complete in 24 days ?


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Probability the project will be completed within 24 hrs

23x

f (x)

24

P (z < .71) = .5 + .2612 = .7612

P (T< 24) = .7612

. 5 0 0 0

. 2 6 1 2

Project_Network Analysis(PERT and CPM) L1

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