1

PRECEDENCE DIAGRAMMING METHOD

Professor John W. Fondahl of Stanford University presented the fundamental concepts for

the precedence diagramming technique in 1961. Fondahl placed the activity on the node rather than

on the arrow, as in the i-j method. The arrows connecting the nodes of the network define the

relationships between the activities. Fondahl called the new technique “circle and connecting line”

later the term “activity on node” (AoN) was applied.

The term “precedence diagramming” first appeared around 1964 in the User’s Manual for

an IBM 1440 computer program. One of the principal authors of the manual was J. David Craig of

the IBM Corporation. Craig was also apparently responsible for naming the technique as

“precedence diagramming method” (PDM).

Precedence diagramming allows more flexibility in modelling relationships than i-j

diagramming. I-j method allows only one kind of logical relationship between activities: i.e., a

preceding activity must be complete before any succeeding activity can begin. PDM in contrast,

employs four logical relationships between activities. The PDM method can also use the concept

of lag (days between) activities to further create a flexible scheduling tool. The four logical

relationships used by PDM are:

1) Finish-to-Start (FS) (Similar to AoA)

2) Start-to-Start (SS)

3) Finish-to-Finish (FF)

4) Start-to-Finish (SF) (very rarely found in construction schedules)

Note that PDM’s finish-to-start relationship is the same as the one logical relationship that

AoA use. If only finish-to-start relationships are used in a precedence diagram PDM is similar to

AoA diagram.

The three forms that each of the four relationships may take the concern the use of “lag”.

An activity with a lag relationship must wait until the period of lag has expired before beginning.

Thus, lag is the condition of waiting for a prescribed period before action can start.

2

Comparison between A-O-A and A-O-N

In A-o-A networks, activities are shown by arrows and events are shown by nodes. However, in

precedence diagrams, also known as A-o-N networks, activities are shown on the nodes and

arrows denote the relationships.

Implies: B depends on A, i.e., B cannot start until A has completed.

Implies: B and D depends on A and C.

Implies: D depends on C; B depends on A and C.

A B

C

B

D

A

C

B

D A

A B

A B

C D

dummy

A B

C

D

ADM Representation PDM Representation

1)

2)

3)

4)

Activity

Description

Duration

Activity

Description &

Duration

B

C D

A A B

C D

5)

B

C

D

E

A A

B

C

D

E

3

A

B C

D

E

F

G A B C

D

E

F

G

6)

7)

A

B

C

D

E

F

G A

B

C

D

E

F

G

4

EXAMPLE (A-o-A & A-o-N Comparison):

a) Draw the (Activity on Arrow)

network.

b) Draw the (Activity on Node)

network.

a) A-O-A

b) A-O-N

Activity

A

B

C

D

E

F

G

H

I

J

Predecessor

-

-

-

A

A

B, C

B, C

D

E, F

E, H

A

B

C

D

E

H J

I

G

F

J

Start

B

C

A D H

End

E

F

G

I

5

EXAMPLE 2 (A-o-A & A-o-N Comparison):

a) Draw the (Activity on Arrow)

network.

b) Draw the (Activity on Node)

network.

a) A-O-A

b) A-O-N

Activity

A

B

C

D

E

F

G

H

Predecessor

-

-

A, B

A, B

C, D

B

D

F, G

End Start

B

A

C E

H D

F

G

A

B

C

D

E

H G

F

6

RELATIONSHIPS

1) Finish-to-Start Relationships:

Finish to start relationships with zero lag and with positive lag.

A lag of 14 days is shown between completion of the concrete pouring and removal of formwork.

The relationship indicates that one must wait 14 days after the concrete has been poured before the

removal of formwork can started.

Finish to start relationship with negative lag.

Negative lag, sometimes called “lead” is used in situations, which permit succeeding activities to

begin before preceding activities have been completed.

2) Start-to-Start Relationships:

Start-to-start relationship with positive lag.

Start to start relationships with zero lag are used to show the relationship between two activities

which should be started simultaneously. Above figure, on the other hand, indicates that pipelaying

can start 5 days after excavating has started.

Excavation Pipelaying

SS + 5d

IF PC RF W

14

Install

forms Pour

concrete

Remove

forms

FS + 14d

Excavation Install Fuel

Tanks

FS – 1d

E1 IT

1

E2

t – 1

E1 Pipelaying

(t-5)

E2

5d

7

3) Finish-to-Finish Relationships:

Finish-to-finish relationship with positive lag.

Finish to finish relationships with zero lag are used to show the relationship between two activities

which should be finished simultaneously. Above figure, on the other hand, indicates that backfilling

can finish 2 days after pipelaying has finished.

4) Start-to-Finish Relationships:

This start to finish relationship indicates install carpeting should already be finished when install

wood paneling and base starts.

The BS 4335-1987 recommended symbol for an activity on node is shown below:

Earliest Start Duration Earliest Finish

Label, Description, Resources, etc.

Latest Start Total Float Latest Finish

Pipelaying Backfilling

t

FF + 2d

Backfilling

(t-2)

Pipelaying

Backfilling 2

2d

Install wood

paneling and

base

Install

Carpeting

SF

8

EXAMPLE (Forward and Backward Passes):

A-O-A Diagram

A

16

B

20

C

30

D

15

E

10

H

16

J

15

K

12

G

3 1

2

3 4 5 6

9

16

15

10

020

15

312

0

16

30

GK

Fin

ish

H

C

Sta

rtB

DEJA

ES

DU

RE

F

LS

TF

LF

Leg

end

Act

ivity

Nam

e

A-o

-N D

iag

ram

10

016

16

16

15

31

20

10

30

00

00

20

20

20

15

35

35

338

38

12

50

51

051

35

16

51

030

30

GK

Fin

ish

H

CAJ E

Sta

rtB

D

FO

RW

AR

D P

AS

S:

In o

rder

to

fin

d E

S,

tak

e th

e m

axim

um

of

the

val

ues

th

en;

EF

= E

S +

DU

RA

TIO

N

11

016

16

16

15

31

824

24

39

20

10

30

29

39

00

00

20

20

20

15

35

35

338

38

12

50

51

051

00

20

20

20

35

36

39

39

51

51

51

0

35

16

51

35

51

030

30

21

51

Fin

ish

H

C

E

Sta

rtB

DG

K

AJ

39-1

5=

24

51-1

2=

39

51-1

2=

39

35-1

5=

039-1

0=

29

51-0

=51

39-3

=36

X

51-1

6=

35

51-0

=51

51-1

2=

39

24-1

6=

820-2

0=

051-3

0=

21

LS

LF

LS

LF

BA

CK

WA

RD

PA

SS

: L

F i

s fo

un

d b

y t

akin

g t

he

min

imu

m o

f th

e v

alu

es;

then

LS

= L

F –

D

UR

AT

ION

2

0

12

016

16

16

15

31

88

24

24

839

20

10

30

29

939

00

00

20

20

20

15

35

35

338

38

12

50

51

051

00

00

020

20

035

36

139

39

151

51

051

35

16

51

35

051

030

30

21

21

51

AJ E

Sta

rtB

DG

KF

inis

h

H

C

CA

LC

UL

AT

ION

OF

TO

TA

L F

LO

AT

T

F =

LF

–

EF

= L

S –

E

S

CR

ITIC

AL

PA

TH

B –

D –

H

13

FORWARD PASS:

Earliest start times and earliest finish times are calculated.

(Take the maximum value) = EST

EFT = EST + Duration

BACKWARD PASS:

Latest start time (LST) and latest finish times are determined.

(TAKE THE MINIMUM VALUE) = LFT (Latest Finish Time)

LST = LFT – Duration

After forward & backward pass completed

Description Duration EST LST EFT LFT TF

(weeks)

A 16 0 8 16 24 8

B 20 0 0 20 20 0

C 30 0 21 30 51 21

D 15 20 20 35 35 0

E 10 20 29 30 39 9

G 3 35 36 38 39 1

H 16 35 35 51 51 0

J 15 16 24 31 39 8

K 12 38 39 50 51 1

+16 (Dur) -16 (Dur)

14

TOTAL FLOAT:

The total amount by which an activity can be extended or delayed without affecting total

project time (TPT).

TOTAL FLOAT = LST – EST, or TOTAL FLOAT = LFT – EFT

Note: The backward pass in precedence diagraming method differs from the backward pass

calculation in activity-on-arrow where the latest finish time (LFT) for each activity is calculated.

The difference arises from the fact that in AoN the dependency arrow sets the difference between

the start of an activity and the start of immediately dependent activities.

15

EXAMPLE (Network Calculations):

Activity Predecessor Relationship Duration

A - - 5

B A FS + 1d 5

C A SS + 2d 6

D B FS

2 C FS + 1d

E D FF + 2d 3

F D FS 1

G E SS + 3d

4 F FS + 2d

Start date of the project is 1st of June, 2017. Assume there are no holidays and all days are working

days. Each activity starts in the morning and ends at the end of the day. Calculate the finish date of

the project.

SS+3d

5

B

4

G

3

E

2

D

5

A

6

C

1

F

SS+2d

FF+2d

FS+2d

FS+1d

FS

FS+1d

FS

16

FORWARD PASS:

BACKWARD PASS:

SS+3d

7 5 11

B

17 4 20

G

13 3 15

E

12 2 13

D

1 5 5

A

3 6 8

C

14 1 14

F

SS+2d

FF+2d

FS+2d

FS+1d

FS

FS+1d

FS

12

10 17

16

SS+3d

7 5 11

B

7 0 11

17 4 20

G

17 0 20

13 3 15

E

14 1 16

12 2 13

D

12 0 13

1 5 5

A

1 0 5

3 6 8

C

5 2 10 14 1 14

F

14 0 14

SS+2d

FF+2d

FS+2d

FS+1d

FS

FS+1d

FS

1

3

5

7

13

14

17

EXAMPLE (Network Calculations with Calendar-Hypothetical):

NOTE: In this example, early start and late finish values are based on assumed dates.

SUN MON TUE WED THU FRI SAT

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31

May 2011

2 nd

4 5 th

6 th

5 11 th

10 th

13 th

14 th

20 th

2 nd 4 5

th 9

th 5 13 th

7 th

11 th

14 th

20 th

2 nd 4 5

th 3

th 5 7 th

12 th

16 th

13 th

18 th

1) Finish to Start

A B

FS-3

A B

A B

FS

FS+2

18

2 nd 4 5

th 2

nd 5 6 th

3 th

6 th

3 th

7 th

2 nd 4 5

th 4

th 5 9 th

9 th

12 th

11 th

16 th

3 rd 4 6

th 2

th 5 6 th

11 th

14 th

10 th

14 th

2) Start to Start

A B

SS-1

A B

SS

A B

SS+2

19

16 th 4 20

th 14

th 5 20 th

20 th

24 th

18 th

24 th

10 th 4 13

th 12

th 5 17 th

12 th

16 th

14 th

20 th

11 th 4 14

th 7

th 5 12 th

20 th

24 th

16 th

21 st

FF

A B

FF+3

3) Finish to Finish

B

A

A B

FF-2

20

10 th 4 13

th 4

th 5 9 th

18 th

23 rd

12 th

17 th

12 th 4 16

th 9

th 5 13 th

18 th

23 rd

14 th

20 th

14 th 4 18

th 6

th 5 11 th

25 th

28 th

16 th

21 st

A B

SF-2

SF

4) Start to Finish

A B

SF+2

A B

21

EXAMPLE (Network Calculations with Calendar):

Below given is a network of a construction project, which shows the precedence relationships and

the duration of each activity.

The project will start on 02 May 2017 by referring 6 days working-day calendar (Sundays are non-

working days). May 19, 23, and 24 are also declared as holidays. Assuming that all lag times and

durations are working days, determine the completion date, duration, and critical path (s) of the

project.

MAY 2017

SUN MON TUE WED THU FRI SAT

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31

FS

4

B

10

D

5

G

5

C

6

E

5

A

FS-1d

SS+4d

FS+2d

3

F

FF-1d

FS-1d

FF+3d

SS-1d

22

FORWARD PASS:

FS

8 4 11

B

12 10 26

D

25 5 30

G

6 5 11

C

15 6 22

E

2 5 6

A

FS-1d

SS+4d

FS+2

8 3 10

F

FF-1d

FS-1d

FF+3d

SS-1d

6

22

25

11

29

30

23

BACKWARD PASS:

Completion date: 30th May, 2017

Duration: 22 working days

Critical path: A-B-D-G

FS

8 4 11

B

8 0 11

12 10 26

D

12 0 26

25 5 30

G

25 0 30

6 5 11

C

25 13 30

15 6 22

E

16 1 25

2 5 6

A

2 0 6

FS-1d

SS+4d

FS+2d

8 3 10

F

26 13 29

FF-1d

FS-1d

FF+3d

SS-1d

8

9

11

12

6

25