Network analysisCPM/PERT

BLESSY V.A.

Project A project is a series of activities directed to

accomplishment of a desired objective.

Network analysis Network analysis is the general name given to

certain specific techniques which can be used for the planning, management and control of projects.

NETWORK TECHNIQUES

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PERT CPM

-Project Evaluation and Review Technique Critical Path Method

Gantt Chart also used in schedulingMain difference is probabilistic and deterministic in time estimationBoth use same calculations, almost similar

Activity : An arrow leads from tail to head directionally–Indicate ACTIVITY, a time consuming effort that is required to perform a part of the work.

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

Network :Combination of all project activities and the events

DEFINITION OF TERMS IN A NETWORK ANALYSIS

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ACTIVITY

PRECEEDING

SUCCESSOR

EVENT

Three types of information are needed to describe a project

1.Activity information: Break down the project into its individual activities (at the desired level of detail).

2. Precedence relationships: Identify the immediate predecessor(s) for each activity.

3. Time information: Estimate the duration of each activity.

Types of projectnetworks

activity on arc (AOA) project network where each activity is represented by an arc. A node is used to separate an activity (an outgoing arc) from each of its immediate predecessors (an incoming arc).

activity on node (AON) project network where each activity is represented by a node. The arcs then are used just to show the precedence relationships between the activities.

Network of Four Activities

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1 3 4

2

A

B C

D

Arrows indicate project activities

Nodes correspond to the beginning and ending of activities

CPM - Critical Path MethodDefinition: In CPM activities are shown as a network of

precedence relationships using activity-on-node network construction.

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.

Activity SlackEach event has two important times associated with it :- Earliest time , Te , which is a calendar time when a 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

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Activity, duration, ES, EF, LS, LF

2

3C [5,9]

4 [8,12]

Activity

ES = earliest start time

EF = earliest finish time

LF = latest finish time

LS = latest start time

Critical 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

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• If can spend resources to speed up some activity, do so only for critical activities.

• Don’t waste resources on non-critical activity, it will not shorten the project time.

• If resources can be saved by lengthening some activities, do so for non-critical activities, up to limit of float.

Importance of Float (Slack) and Critical Path

Information's related to paddy field

activity duration1-2 Mat preparation 41-3 Land preparation 33-4 transplanting 34-5 Herbicide application 14-7 Weeding 44-6 Fertilizer application 17-8 harvesting 3

15

13

4

2

5

7

6

8ES= 4LF = 4

ES= 0LF = 0

40

3 ES= 4LF = 4

3 ES= 11LF = 11

1

ES= 8LF = 11

ES=8 LF = 11

ES= 7LF = 7

ES= 14LF = 14

0

01

4

Critical path length is 14 weeks in case of paddy

3

In formations related to cowpea

activity duration1-2 ploughing 21-3 Weeding 23-4 sowing 14-5 Irrigation 14-7 Plant protection 34-6 harvesting 4

17

12

3

5

7

6

4

ES= 0LF = 0

2 ES= 2LF = 2

2 ES= 7LF = 7

1

ES= 5LF = 7

ES=7 LF = 7

ES= 4LF = 4

ES= 10LF = 10

0

03

1

3

Critical path length is 10 weeks in case of cowpea.

activity duration1-2 Plant material preparation 21-3 Land preparation 23-4 planting 24-5 Irrigation 104-7 Fertilizer application 24-8 Pest management 154-6 weeding 168 -9 harvesting 4

Information's related to banana

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13

4

2

5

8

6

9ES= 2LF =2

ES= 0LF = 0

20

2 ES= 2LF = 2

2 ES= 20LF = 20

10

ES= 14LF = 20

ES=20 LF = 20

ES= 4LF = 4

ES= 24LF = 24

016

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Critical path length is 24 weeks in case of BANANA

7

ES=6LF=20

002 4

Information – tapioca

activity Duration1-2 Land preparation 42-3 Planting 43-4 Weeding 153-6 Irrigation 83-5 Fertilizer 126-7 Irrigation 28-9 Inter cropping 69-10 Harvesting 36-8 Shoot removal 4

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1

2

3

4

6

5

8

ES= 0LF = 0

4

ES= 2LF = 2

ES= 23LF = 23

0

ES= 23LF = 23

ES=20 LF = 23

ES= 8LF = 8

ES= 25LF = 27

Critical path length is 36 weeks in case of tapioca.

7

9

104

158

12

2ES= 27LF = 27

4

0ES= 33LF = 33

ES= 36LF = 36

3

6

“From the four networks we can conclude that the minimum possible time to complete the field operations is 36 weeks.”

PERT - Project Evaluation & Review Techniques

Definition: In PERT activities are shown as a network of precedence relationships using activity-on-arrow network construction

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.

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PERT For Dealing With Uncertainty• Use 3 time estimates

m= most likely time estimate, mode.a = optimistic time estimate,b = pessimistic time estimate, and

Expected Value (TE) = (a + 4m + b) /6Variance (V) = ( ( b – a) / 6 ) 2

Std Deviation (δ) = SQRT (V)

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Precedences And Project Activity Times

Immediate Optimistic Most Likely Pessimistic EXP Var S.Dev

Activity Predecessor Time Time Time TE

V

a - 10 22 22 20 4 2

b - 20 20 20 20 0 0

c - 4 10 16 10 4 2

d a 2 14 32 15 25 5

e b,c 8 8 20 10 4 2

f b,c 8 14 20 14 4 2

g b,c 4 4 4 4 0 0

h c 2 12 16 11 5.4 2.32

I g,h 6 16 38 18 28.4 5.33

j d,e 2 8 14 8 4 2

 

Benefits of CPM/PERT

• Useful at many stages of project management

• Mathematically simple• Give critical path and slack time• Provide project documentation• Useful in monitoring costs

1. Construction of a new plant2. Research and development of a new product3. NASA space exploration projects4. Movie productions5. Building a ship6. Government-sponsored projects for developing a new weapons system7. Relocation of a major facility8. Maintenance of a nuclear reactor9. Installation of a management information system10. Conducting an advertising campaign

Applications in the fields

Results of CPM & PERT

• Completion date

• About Schedule

• Within Budget

• Critical Activities

• How can the project be finished early at the least cost

Limitations to CPM/PERT

• Clearly defined, independent and stable activities

• Specified precedence relationships

• Over emphasis on critical paths

Thank you