The critical path method

floats

Computation Algorithm Activity-On-Node.

The calculation procedure for a node network is identical for an arrow network.

One of the main issues in the node diagram is the style in which the calculations and related activity information are shown.

Activity- Duration

ES EF

LS LF

3-3

Latest Start and Finish Steps

Latest Finish

ES

LS

EF

LF

Earliest Finish

Latest Start

Earliest Start

Activity N

ame

Activity Duration

Computation Algorithm Activity-On-Node.

A - 8

0 8

0 8

start

C- 6

0 4

6 10

B - 4

D -11

F- 3

E- -9

G - 1

19

19 20

178

20

161610

14

8

19

14

1910

134

198

19

FloatsTotal Float: The total float for an activity is the maximum amount of time that

the activity can be delayed without extending the completion time of the overall project. However, such a delay might postpone the early start of one or more of its following activities

The total float for each activity is the difference between the activity’s late start and early start, or the difference between its late finish and early finish.

TF(x) = total float for activity x = LS(x) - ES(x) = LF(x) - EF(x)

FloatsFree Float: The free float for an activity is the maximum amount of time that

the activity can be delayed without delaying the early start of any of its followers.

The free float for each activity may be determined as the minimum of the early starts of all the activity’s immediate followers minus the activity’s early finish.

FF(x) = free float for activity x =Min {ES (all immediate followers of x)}- EF(x)

The critical activities have zero float- total or free.

Computation Algorithm Activity-On-Node.

A - 8

0 8

0 8

start

C- 6

0 4

6 10

B - 4

D -11

F- 3

E- -9

G - 1

19

19 20

178

20

161610

14

8

19

14

1910

134

198

19

Floats.

Activity Duration(weeks)

ES LS TF FF

A 8 0 0 0 0B 4 0 6 6 4-4=0C 6 8 10 2 14-14=0D 11 8 8 0 0E 9 4 10 6 19-13=6F 3 14 16 2 19-17=2G 1 19 19 0 0

Gantt chart showing floats

9

• Activities 1-3 and 2-4 have total float of 1 week each, represented by the solid timeline which begins at the latest start and ends at the latest finish. The difference is the float, which gives us the flexibility to schedule the activity.

10

3-11

• Provides activity information– Earliest (ES) & latest (LS) start– Earliest (EF) & latest (LF) finish– Slack (S): Allowable delay

• Identifies critical path– Longest path in network– Shortest time project can be completed– Any delay on critical path activities delays project– Critical path activities have 0 slack

Critical Path Analysis

Effect of the imposed finish date on the schedule

• In many cases, the calculated finish date is different from that set by the owner.

• The contractor must adjust the schedule.• The concept is simple: 1-Do the CPM forward pass as usual. 2-Start with the imposed finish date for your backward-pass.

The imposed finish date may be earlier or later than the calculated finish date.

• If the imposed finish date is earlier than the calculated one, the activities on the critical path will have negative float.

the contractor should accelerate the project by an amount equal to the negative float of the critical path.

• If the imposed date is later than the calculated one, the contractor is in a good situation.

3-13

AON Network for Milwaukee General Hospital Includes Critical Path

Slack=0

Start

A

B

C

D

F

F

G

H

H13

132

15

15

H

G8

85

13

13

H

F4

103

7

13H

C2

22

4

4

H

E4

44

8

8

H

D3

44

7

8H

B0

13

3

4

H

A0

02

2

2

H0

00

0

0

Slack=0 Slack=0

Slack=0

Slack=0

Slack=6

Slack=1Slack=1

Start

3-14

Gantt ChartEarliest Start and Finish

Milwaukee General Hospital

A Build internal componentB Modify roof and floorC Construct collection stackD Pour concrete and install frameE Build high-temperature burnerF Install pollution control systemG Install air pollution devicH Inspect and test

1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16

3-15

Gantt ChartLatest Start and Finish

Milwaukee General Hospital

A Build internal componentB Modify roof and floorC Construct collection stackD Pour concrete and install frameE Build high-temperature burnerF Install pollution control systemG Install air pollution devicH Inspect and test

1 2 3 4 5 6 7 8 9 10 1112 13 1415 16

Problem1

For the following project: construct the arrow and

node diagram, perform the CPM

calculations, mark the critical path, determine the free

floats and the total floats for each activity

Activity Duration ( weeks)

Immediate predecessors

 

ABCDEFGHIJ

62947510832

------------A, BBDD, EC, F, GC, GH, I