Critical Path Method (CPM)

CPM is a network diagramming technique used to predict total project duration.

CPM is an analysis technique with three main purposes:

To calculate the project’s finish dateTo indentify to what extent each activity in the

schedule can slip(float) without delaying the projectTo identify the activities with highest risk that cannot

slip without changing the project finish date

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CPMHow does the Critical Path Method calculate the

project’s finish date?o Forward pass calculation calculates Early Start and Early Finish dateso Backward pass calculation calculates Late Start and Late Finish dates

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Early Start (ES) is the earliest date a task can start

Early Finish (EF) is the earliest date a task can be completed

Late Start (LS) is the latest date a task can start without delaying the project and date

Late Finish (LF) is the latest date a task can finish without delaying the project end date

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5

Start

D5

F2

C6

Finish

E4

B1

A2

Forward Pass

0 0

0 1511652

550

1515

1111 13

• Early Start (ES) = Latest related early date of all immediate predecessors

ES= immediate Predecessors’ ES maxEarly finish (EF) = Early Start + Duration EF= ES + D

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Activity A

ES EF

ES=3

ES=9

ES=10D

7

Start

D5

F2

C6

Finish

E4

A2

0

0

0

0

0

108

50

15

15

11

1165

1110

2

550

115

1515

1515

1111 13

B1

1513

Backward Pass

Late Finish (LF) = Earliest related late date of all immediate successors

LF= immediate Successors’ LF minLate Start (LS) = Late Finish – Duration LS= LF-D

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Activity A

LS LF

LF=3

LF=9

LF=10D

The purpose of backward pass is to find the float.Float is the amount of time an activity can be

delayed or lengthened. Also called slack.Total float: the amount of time an activity can be

delayed or extended without extending the overall project’s completion time

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What is the total Float for activity A?

10

Start

D5

F2

C6

Finish

E4

A2

0

0

0

0

0

108

50

15

15

11

1165

1110

2

550

115

1515

1515

1111 13

B1

1513

11

Total float = LF-ES-D

A2

0

108

65

1110

2B1

LFLSEFES

10820A

A

Float

Float

Total Float: TF= LF - ES – D TF= LF – (ES+D) = LF-EF TF= LF-D-ES= LS-ES

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Activity A

LS LF

ES EF

Free Float: the amount of time an activity can be delayed without delaying the early start date of its subsequent tasks

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Activity A

LS LF

ES EF

What is the FF for activity A?

What would happen if A uses its max float? (A)EF=LF=10 (B) ES=LS=10IF the early finish date of activity A =5 the early start date of activity B=5 FF=5-2=3

14

A2

0

108

65

1110

2B1

Free Float: the amount of time an activity can be delayed without delaying the early start date of its subsequent tasks

EF= ES(B) – EF(A) EF= ES(earliest successor)- EF

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Activity A

LS LF

ES EF

Why floats are important in the critical path method?

If an activity has a TF=0, what does this mean?Floats determine thee criticality of an activityCritical activities have the least amount of FloatFloats determine the critical path

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The critical path is made of activities that cannot be delayed without delaying the final date of the project

If an item is on critical path, it has a zero floatThe critical path is the path with longest durationIt is possible to have more than one critical path

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What is the critical path?What is the length of the critical path?

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Start

D5

F2

C6

Finish

E4

A2

0

0

0

0

0

108

50

15

15

11

1165

1110

2

550

115

1515

1515

1111 13

B1

1513

Critical Path Method (CPM)CPM is a network diagramming technique used

to predict total project durationA critical path for a project is the series of

activities that determines the earliest time by which the project can be completed

The critical path is the longest path through the network diagram and has the least amount of slack or float

Slack or float is the amount of time an activity may be delayed without delaying a succeeding activity or the project finish date

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Calculating the Critical PathFirst develop a good network diagramAdd the duration estimates for all activities on

each path through the network diagramThe longest path is the critical pathIf one or more of the activities on the critical path

takes longer than planned, the whole project schedule will slip unless the project manager takes corrective action

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