Spring 2008, King Saud University Activity on Node Dr. Khalid Al-Gahtani 1 CPM Network Computation

Spring 2008, King Saud University

Activity on NodeDr. Khalid Al-Gahtani

1

CPM Network Computation

Activity AOA AON

Depends on t

1-2 A ─ 3 2-3 B A 4



2

AOA

B 4

A 3

1

2

3

Activity Name

Activity Duration

AON

3

A

4

B



3

Drawing CPM Networks

• Prerequisites: Before drawing a CPM network, we must have:

– List of all activities comprising the project– Order of precedence of each activity– Duration estimate of each activity



4

Example:

Activity Depends on

(Immediate Predecessor(s)) Duration (Day)

(Time to perform) a ─ 14 b ─ 3 c ─ 7 d a, b 4 e b, c 10



5

Activity on arrow Solution

a

b

c

d

e

Dummy



6

Activity-on-node Solution

START

a

b

c

d

e

FINISH



7

Class work#1: Draw AON Network for the fowling project:

Activity Depends upon Activity Depends upon A G F B A I F F A J H H A K I, J, F C B, A L G, D, E D B M K E C N L, M



8

“Activity on Node”

• Nodes = Activities• Links = Precedence Relationships• Dummy activities are not required

ES t ES Activity Name

LS TF LF



9

Example

Activity Depends on Duration (Days) A 5 B A 15 C A 10 D B 15 E B, C 10 F D, E 5



10

AON

START

A

B

C

D

E

F

FINISH

ES t EF

LS TF LF

Name



11

AON

0 0 0

0 0

START

0 5 5

0 5

A

5 15 20

5 20

B

5 10 15

15 25

C

20 15 35

20 35

D

20 10 30

25 35

E

35 5 40

35 40

F

40 0 40

40 40

FINISH

ES t EF

LS TF LF

Name



12

Constraints with Lead/lag time



13

Finish-to-Start (FSij):

• FSij is equal to the minimum number of time units that must transpire from the completion of the predecessor (i) prior to the start of the successor (j).

• The time between the finish of one activity and the start of its successor is called “Lag”.



14

Finish-to-Start (FSij):

• If the relationship is not listed on the dependency arrow, FS is assumed with Lag= 0.

• Example: a planner may wish to have an activity of removing formwork from a new building component follow the concrete pour by some pre-defined lag period to allow setting.



15

Start-to-Start (SSij):

• SSij is equal to the minimum number of time units that must be complete on the preceding activity (i) prior to the start of the successor (j).



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Start-to-Start (SSij):

• “Lag” is always applied to SS relation.• Example: parallel in starting of Installing

and Finishing the walls activity of 100 rooms on a project must be 10 days difference (SS=10 days).– You don’t have to wait installing 100 wall’s

room to start doing the finishing work.



17

Finish-to-Finish (FFij):

• FFij is equal to the minimum number of time units that must remain to be completed on the successor (j) after the completion of the predecessor (i).

• It is applied as productivity control.



18

Finish-to-Finish (FFij):

• The finish date of Installing and Finishing walls’ activity of 100 rooms on a project must have 10 days difference in order to control productivity (FF=10 days).– In this example, the productivity of installing

the walls’ activity might be less than finishing the rooms’ activity.

• “Lag” is always applied to FF relation as buffer between the two activities.



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Start-to-Finish (SFij):

• SFij is equal to the minimum number of time units that must transpire from the start of the predecessor (i) to the completion of the successor (j).

• It is applied also for controlling productivity



20

Start-to-Finish (SFij):

Example: The start date of Installing 100 rooms’ wall’s activity and the finish date of Finishing same walls’ activity of a project must maintain 30 days difference to control productivity (SF=30 days).

“Lag” is always applied to SF relation as buffer between the two activities.

• It is not recommended to use by planner.



21

Start-to-Start and Finish-to-Finish (ZZij):

• ZZij is a combination of two constraints. i.e., a start-to-start and finish-to-finish relationship. It is written with the SSij time units first, followed by the FFij time units.

• These two relations are used combined to maintain buffer between the start and finish of two activities.



22

Forward Pass Computations

EFj = ESj + Dj

ESj = Max all i

jiji

jiji

iji

iji

DSFES

DFFEF

SSES

FSEF

Time Initial



23

Backward Pass Computation

LFi = Min all j

iijj

iiji

ijj

ijj

DSFLF

DSSLS

FFLF

FSLS

Time Terminal

LSi = LFi Dj



24

Example

4

A

ES D EF

LS F LF Activity

2

B

1

F

6

E

5

K

2

C

3

L

1

G

6

D

2

H

FS 4 SS 3

SF 4

SF 5

FF 1 SF 5

FS 4



25

Example Solution

0 4 4

0 0 4 A

ES D EF

LS F LF Activity

4 2 6

5 1 7 B

4 1 5

10 6 11 F

16 6 22

16 0 22 E

4 5 9

4 0 9 K

10 2 12

11 1 13 C

9 3 12

11 2 14 L

9 1 10

9 0 10 G

9 6 15

10 1 16 D

14 2 16

14 0 16 H

FS 4 SS 3

SF 4

SF 5

FF 1 SF 5

FS 4

Documents

Spring 2008, King Saud University Activity on Node Dr. Khalid Al-Gahtani 1 CPM Network Computation