network planning methods example pert & cpm

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Network Planning Methods Network Planning Methods Example PERT & CPMExample PERT & CPM

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Terms Used in Project Management Activity : A certain amount of work or task required in the

project Activity duration: In CPM the best estimate of time to

complete an activity . In PERT the expected time or average time to complete an activity

Critical activity : An activity that has no room for schedule slippages : if it slips the entire the entire project completion will slip. An activity with zero slack

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Critical path: The chain of critical activities for the project .The longest path through the network

Dummy activity :An activity that consumes no time but shows precedence among activities

Earliest finish (EF): The earliest that an activity can finish from the beginning of the project

Earliest start ( ES): The earliest that an activity can start from the beginning of the project

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Event :A beginning , a completion point ,or a milestone accomplishment within the project . An activity begins and ends with events

Latest finish (LF) : The latest that an activity can finish from the beginning of the project

Latest start (LS) :The latest that an activity can start from the beginning of the project

Most likely time ( t m) : The time for completing the activity that is is the consensus best estimate, used in PERT

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Optimistic Time (to): The time for completing an activity if all goes well : used in PERT

Pessimistic Time (tp): The time for completing an activity if bad luck is encountered : used in PERT

Predecessor activity : An activity that must occur before another activity .

Slack : The amount of time that an activity or group of activities can slip without causing a delay in the completion of the project

Successor activity : An activity that must occur after another activity

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Conventions used in drawing network diagrams (Arrows & Circles )

Activity on Arrow (AOA) : The activities are denoted by Arrows and events are denoted by circles

Activity on Node(AON) : Activities are denoted by circles(or nodes) and the precedence relation ships between activities are indicated by arrows

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AOA Project Network for HouseAOA Project Network for House

32 0

1

31 1

11 2 4 6 7

3

5

Lay foundation

Design house and obtain financing

Order and receive materials

Dummy

Finish work

Select carpet

Select paint

Build house

AON Project Network for House

13

22

43

31 5

1

61

71Start



Select paintSelect carpet

Lay foundations Build house

Finish work

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Situations in network diagramSituations 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 B or D can start

A

C

B

D

Dummy

A must finish before B can start

both A and C must finish before D can start

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Forward PassForward 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 earliest start time plus activity time

EF= ES + t

Latest Start Time (LS)

Latest time an activity can start without delaying critical path time

LS= LF - t

Latest finish time (LF)

latest time an activity can be completed without delaying critical path time

LS = minimum LS of immediate predecessors

Backward Pass

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CPM analysisCPM analysis

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

Compute the activity’s float

float = LS - ES = LF - EF Float is the maximum amount of time that this activity can be delay

in its completion before it becomes a critical activity, i.e., delays completion of the project

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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Relationship between activities Project duration Critical path Slack for non – critical activities Crashing (cost / time trade-offs) Resource usage

PERT / CPMPERT / CPMNetwork planning methods that generate:Network planning methods that generate:

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St. Paul’s HospitalSt. Paul’s Hospital

ImmediateActivity Description Predecessor(s)

A Select administrative and medical staff.B Select site and do site survey.C Select equipment.D Prepare final construction plans and layout.E Bring utilities to the site.F Interview applicants and fill positions in nursing,

support staff, maintenance, and security.G Purchase and take delivery of equipment.H Construct the hospital.I Develop an information system.J Install the equipment.K Train nurses and support staff.

——ABB

ACDAE,G,HF,I,J

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——ABB

ACDAE,G,HF,I,J

AON Network

FinishStart

A

B

C

D

E

F

G

H

I

J

K

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——ABB

ACDAE,G,HF,I,J

Completion Time

FinishStart

K9

I15

F10

C10

D10

E24

G35

H40

J4

A12

B9

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——ABB

ACDAE,G,HF,I,J

Completion Time

FinishStart

K9

I15

F10

C10

D10

E24

G35

H40

J4

A12

B9

Path Expected Time (wks)

A-I-K 36A-F-K 31A-C-G-J-K 70B-D-H-J-K 72B-E-J-K 46

CriticalPath

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Critical PathCritical Path The longest path in the network Defines the shortest time project can be completed Critical path activity delay project delay

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Begin at starting event and work forward ES is earliest start

ES = 0 for starting activities ES = Maximum EF of all

predecessors for non-starting activities

EF is earliest finish EF = ES + Activity time

Earliest Start and Earliest FinishEarliest Start and Earliest Finish

ESES

LS

EFEF

LF

Activity Name

Activity Duration

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A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

I

15

F

10

FinishStart

Earliest Start / Earliest FinishEarliest Start / Earliest Finish

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Earliest Start / Earliest FinishEarliest Start / Earliest Finish

Finish

Earliest start time Earliest finish time

A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 72

22 57

59 6319 59

9 33

0 9 9 19

12 22

Critical path

Start

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Begin at ending event and work backward LF is latest finish

LF = Maximum EF for ending activities

LF = Minimum LS of all successors for non-ending activities

LS is latest start LS = LF – Activity time

Latest Start and Latest FinishLatest Start and Latest Finish

ES

LS

EF

LF

Activity Name

Activity Duration

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Latest Start / Latest FinishLatest Start / Latest Finish

A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 72

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 72

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Latest start time Latest finish time

Critical path

FinishStart

What do you notice about ES/LS & EF/LF?

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What do you notice about ES/LS & EF/LF?

For Activity A ES = 0 LS = 2 Meaning: Due to some reason of if activity A is not started

at 0 weeks but 1, 2 or 3 weeks, even then completion of project is not delayed

For Activity B ES = 0 LS = 0 Meaning Any delay in start would delay project completion.

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Activity Slack AnalysisActivity Slack Analysis

A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 72

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 72

14 24 24 59

0 9 9 19 19 59

35 59

59 63


Critical path

FinishStartSlackK = 63 – 63 = 0

or

SlackK = 72 – 72 = 0

Slack = LS – ES

or

Slack = LF – EF

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Activity Slack AnalysisActivity Slack Analysis

A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 72

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 72

14 24 24 59

0 9 9 19 19 59

35 59

59 63


Critical path

FinishStart

Node Duration ES LS Slack

A 12 0 2 2BB 99 00 00 00C 10 12 14 2DD 1010 99 99 00E 24 9 35 26F 10 12 53 41G 35 22 24 2HH 4040 1919 1919 00I 15 12 48 36JJ 44 5959 5959 00KK 66 6363 6363 00

Activity slack = maximum delay time

Critical path activities have zero slack

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Activity SlackActivity Slack

How much would we like to reduce the time for activity B?

C

15

5 20

10 25

A

5

0 50 5

FinishStart

B

20

5 25

5 25D

10

25 35

25 35

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PERT PERT PERT is based on the assumption that an activity’s duration follows a

probability distribution instead of being a single value Three time estimates are required to compute the parameters of an

activity’s duration distribution: pessimistic time (tp ) - the time the activity would take if things did

not go well most likely time (tm ) - the consensus best estimate of the activity’s

duration optimistic time (to ) - the time the activity would take if things did go

well

Mean (expected time): te =tp + 4 tm + to

6

Variance: Vt =2 =tp - to

6

2

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PERT analysisPERT 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 critical activities (all of the activities that make up the critical path) and taking the square root of that sum

Probability computations can now be made using the normal distribution table.

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Probability computationProbability computation

Determine probability that project is completed within specified time

Z = x -

where = tp = project mean time

= project standard mean time

x = (proposed ) specified time

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Normal Distribution of Project TimeNormal Distribution of Project Time

= tp Timex

Z

Probability

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PERT Example 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 3

D A 4 5 6 E A 0.5 1 1.5 F B,C 3 4 5 G B,C 1 1.5 5 H E,F 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.5 K G,I 3 5 7

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PERT ExamplePERT Example

AA

DD

CC

BB

FF

EE

GG

II

HH

KK

JJ

PERT Network

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Activity Expected Time Variance A 6 4/9

B 4 4/9 C 3 0 D 5 1/9 E 1 1/36 F 4 1/9 G 2 4/9 H 6 1/9 I 5 1 J 3 1/9 K 5 4/9

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Activity ES EF LS LF Slack A 0 6 0 6 0 *critical

B 0 4 5 9 5 C 6 9 6 9 0 * D 6 11 15 20 9 E 6 7 12 13 6 F 9 13 9 13 0 * G 9 11 16 18 7 H 13 19 14 20 1 I 13 18 13 18 0 * J 19 22 20 23 1 K 18 23 18 23 0 *

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Vpath = VA + VC + VF + VI + VK

= 4/9 + 0 + 1/9 + 1 + 4/9

= 2

path = 1.414

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

From the Standard Normal Distribution table:

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

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PROJECT COSTPROJECT COST

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Cost consideration in projectCost consideration in project

Project managers may have the option or requirement to crash the project, or accelerate the completion of the project.

This is accomplished by reducing the length of the critical path(s).

The length of the critical path is reduced by reducing the duration of the activities on the critical path.

If each activity requires the expenditure of an amount of money to reduce its duration by one unit of time, then the project manager selects the least cost critical activity, reduces it by one time unit, and traces that change through the remainder of the network.

When there is more than one critical path, each of the critical paths must be reduced.

If the length of the project needs to be reduced further, the process is repeated.

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Project CrashingProject Crashing Crashing

reducing project time by expending additional resources

Reduction in activity duration by any change in its resources, resource use, method or material is referred to as crashing of the activity

Crash time an amount of time an activity is reduced

Crash cost cost of reducing activity time

Goal reduce project duration at minimum cost

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Activity crashingActivity crashingA

ctiv

ity

cost

Activity time

Crashing activity

Crash time

Crash cost

Normal Activity

Normal time

Normal cost

Slope = crash cost per unit time

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Time-Cost RelationshipTime-Cost Relationship Crashing costs increase as project duration decreases Indirect costs increase as project duration increases Reduce project length as long as crashing costs are less than

indirect costsTime-Cost Tradeoff

cost

time

Direct cost

Indirect cost

Total project costMin total cost = optimal project time

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Project Crashing exampleProject Crashing example

111122

2288

441122

3344 55

44

6644

7744

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Time Cost dataTime Cost data

Activity Normal time

Normal cost Rs

Crash time

Crash cost Rs

Allowable crash time

slope

1

2

3

4

5

6

7

12

8

4

12

4

4

4

3000

2000

4000

50000

500

500

1500

7

5

3

9

1

1

3

2800

3500

6000

71000

1100

1100

21000

5

3

1

3

3

3

1

400

700

2000

8000

1100

1100

7000

75000

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112

28

34 5

4

64

74

12

4Project duration = 36

From…..

To…..17

28

34 5

4

64

74

R400

12

4

Project

duration = 31

Additional cost = R2000

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GANTT CHARTGANTT CHART

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Gantt ChartGantt ChartGantt Chart was developed by…

Henry Laurence Gantt (1861-1919) was a mechanical engineer and management consultant who is most famous for developing the ‘Gantt chart’ in the 1910s. These Gantt charts were employed on major infrastructure projects including the Hoover Dam and Interstate highway system. He refined production control and cost control techniques.

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Example of Gantt ChartExample of Gantt Chart

| | | | |Activity


Lay foundation


Build house

Select paint

Select carpet

Finish work

00 22 44 66 88 1010MonthMonth

MonthMonth11 33 55 77 99

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Gantt ChartGantt ChartActivities in Buy a HouseActivities in Buy a House

` BUY A HOUSE

LOCATION FINANCINGFIND HOUSE

1 - Criteria 3- Determine affordability

6- Type of House

2- Visit Locations

4- Determine mortgage provider

7- Find Real Estate Agent

5- Lockup mortgage commitment

8- Look for House

9- Make Offer, P&S Agreem't

10 - Closing

TASK PREDECESSOR1-criteria 32-visit loc. 13-affordability4-mortgage co 35-mortg lock 46-type of hse 17-real est agent 2, 68-look for hse 79-offer, P&S 5, 810-closing 9

network planning methods example pert & cpm

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