spring 2008, king saud university activity on node dr. khalid al-gahtani 1 cpm network computation
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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
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
2
AOA
B 4
A 3
1
2
3
Activity Name
Activity Duration
AON
3
A
4
B
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
5
Activity on arrow Solution
a
b
c
d
e
Dummy
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
6
Activity-on-node Solution
START
a
b
c
d
e
FINISH
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
8
“Activity on Node”
• Nodes = Activities• Links = Precedence Relationships• Dummy activities are not required
ES t ES Activity Name
LS TF LF
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
10
AON
START
A
B
C
D
E
F
FINISH
ES t EF
LS TF LF
Name
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
12
Constraints with Lead/lag time
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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”.
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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.
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
16
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.
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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.
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
19
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
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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.
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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.
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
22
Forward Pass Computations
EFj = ESj + Dj
ESj = Max all i
jiji
jiji
iji
iji
DSFES
DFFEF
SSES
FSEF
Time Initial
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
23
Backward Pass Computation
LFi = Min all j
iijj
iiji
ijj
ijj
DSFLF
DSSLS
FFLF
FSLS
Time Terminal
LSi = LFi Dj
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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
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Spring 2008, King Saud University
Activity on NodeDr. Khalid Al-Gahtani
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