3. project analysis tools
TRANSCRIPT
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Project Scheduling
Faculty of Applied Engineering and Urban Planning
Civil Engineering Department
Week ( 6 + 7 )
Lec. ( 11 + 12 + 13 + 14 )
2nd Semester 2008/2009
UP Copyrights 2008
ConstructionProje
ct
M
anagement
Eng: Eyad Haddad
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CH4: Project Scheduling
Construction Project management functions:
Scheduling = Planning + Time
Scheduling is the determination of the timing of the activities comprising
the project to enable managers to execute the project in a timely manner.
1. Planning
2. Organization
3. Supervision
4. Control
1. Time
2. Cost
3. Quality
4. Performance
Scheduling
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CH4: Project Scheduling
The project scheduling is used for:
1. Knowing the activities timing and the project completion time.
2. Having resources available on site in the correct time.
3. Making correction actions if schedule shows that the plan will result in
late completion.
4. Assessing the value of penalties on project late completion.
5. Determining the project cash flow.
6. Evaluating the effect of change orders on the project completion time.
7. Determining the value of project delay and the responsible parties.
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4.2 The Critical Path Method (CPM)
The critical path can be defined as
the longest possible path through the "network" of project activities.
(CPM) is the most widely technique used for scheduling, it calculates the
minimum completion time for a project along with the possible start and
finish times for the project activities.
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4.2 The Critical Path Method (CPM)
The critical path itself represents the set or sequence of activities
which will take the longest time to complete.
The duration of the critical path is the sum of the activities'
durations along the path.
Duration of the critical path represents the minimum time required
to complete a project.
Any delays along the critical path would delay the project.
More than one critical path may be among all the project activities,
so completion of the entire project could be delayed by delaying
activities along any one of the critical paths.
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4.2 The Critical Path Method (CPM)
For example,
a project consisting of two activities performed in parallel that each
requires three days would have each activity critical for a completion in
three days.
Critical path scheduling assumes that a project has been divided into
activities of fixed duration and well defined predecessor relationships.
A predecessor relationship implies that one activity must come
before another in the schedule
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The CPM is a systematic scheduling method for a project network and involves
four main steps:
1. A forward path to determine activities early-start times;
2. A backward path to determine activities late-finish times;
3. Float calculations ( Free & Total ) float; and
4. Identifying critical activities.
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4.3.1 Activity-on-node networks calculations
The objective of arrow network analysis is to compute each event in the
network its early and late timings. These times are defined as
Early event time (ET) is the earliest time at which an event can occur,
considering the duration of preceding activities.
Late event time (LT) Is the latest time at which an event can occur if the
project is to be completed on schedule.
i jx
ETj LTjETi LTi
dx
. Forward Path:1
ETj = ETi + dx
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. Forward Path:1
1 3
5
7
9 11
0
Project
Start=0
A
d=3
C4
E
5
B
3
D
6 d2
d13
Es+d=EF
6
3+3=60+3=3
9
6+0=6
3+4=7
9+0=9
14
9+5=14
9
3+6=9
1A
Project
Start=0
1A
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. Backward Path2LS = LF d
1 3
5
7
9 11
0 0
3-3=0
A3
C4 E5
B
3
D
6 d2
d13 3
9-4=5
6 9
9-0=9
9-6=3
9 9
14-5=9
LF-d=LS
14 14
9 9
9-0=9
9-3=6
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3. Float Calculations:
First, let's tabulate the information we have as shown in next Table
One important aspect is Total-Float (TF) calculations, which determine the
flexibility of an activity to be delayed.
Total Float (TF) = LF EF
= LS ES
:TF.
Free Float (FF) = ETj ETi d
or FF = smallest ES (of succeeding activities) EF (of current activity)
:FF.
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3. Float Calculations:
Total Float (TF) = LF EF
= LS ES
:TF.
Free Float (FF) = ETj ETi d
or FF = smallest ES (of succeeding activities) EF (of current activity)
:FF.
i j
ES EF
A
LS LF
AOA
ES EF
ES EF
A
B
LS LF
LS LF
ES EF
A
LS LF
AON
TF
i j
ES EF
A
LS LF
AOA
i j
ES EF
B
LS LF
AOA
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Total Float (TF) = LF EF = LS ES
Free Float (FF) = ETj ETi d
or FF = smallest ES (of succeeding activities) EF (of current activity)
Critical
Activity
TotalFloat
(TF)
LateFinish
(LF)
EarlyFinish
(EF)
Late Start
(LS)
EarlyStart
(ES)
DurationActivity
Yes033003A
No396633B
No297534C
Yes099336D
Yes01414995E
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4.3.2 Precedence Diagram Method (PDM):
Precedence Diagram Method (PDM) is the CPM scheduling method used for AON
networks and it follows the same four steps of the CPM for AOA method.
Forward PathForward path can proceed from one activity to the other; the process is as
follow .
3 6
B(3)
3 7
C(4)
3 9
D(6)
0 3
A(3)
9 14
E(5)
Earlystart
Name(duration)
Earlyfinish
Latestart
Latefinish
6,7,or 9
Fig. 4.8: Forward Path in PDM Analysis
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Backward Path:
3 6
B(3)
3 7
C(4)
3 9
D(6)
0 3
A(3)
9 14
E(5)
Earlystart
Name(duration)
Earlyfinish
Latestart
Latefinish
6,5, or 3
149
96
95
93
30
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Floats
Activity A7 days Activity B13 days Activity C4 days
Start CompletionProject duration = 24 days
CASE 1: All activities are critical: total float and free floats for all activities = 0
Activity A
7 days
Activity B
13 days
Activity C
4 days
Start CompletionTotal Float = 5Free Float = 5
CASE 2: Activity sequence in which one activity has total and free float
Activity D
8 days
Activity A
7 days
Activity B
13 days
Activity C
4 days
Start Completion
Total Float of D = 5 Total Float of E = 5
Free Float of D = 0 Free Float = 5
CASE 3: Activity sequence illustrating total and free float
Activity D
5 days
Activity E
3 days
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2-Floats
Areas of shared float
Activity duration Total Float
Start Event Finish Event
TLi TEjTEi TLj
Activity duration Free Float
Activity duration Independent Float
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Float Calculations:
Total Float (TF) = LF EF= LS ES
Free Float (FF) = ETj ETi d
Duration
3
3
46
5
ES
0
3
33
9
LF
3
9
99
14
LS
0
6
53
9
EF
3
6
79
14
TF
0
3
20
0
Activity
A
B
CD
E
Critical Act.
Yes
No
NoYes
Yes
MDPPDM C l l ti
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A
3
B
3
C
5
D
7
E
4
F
6
G
4
I
9
H
6
J
8
Fn
12 20
10 166 10
6 12
8 12
10 19
3 6
3 8
3 10
0 3
12 20
14 208 12
6 12
8 12
11 20
3 6
3 8
4 11
0 3
Act
Dur
ES EF
LS LF
TF/FF
ethod)MiagramDrecedenceP(PDM =PDM Calculations
Example
0/ 0
0/ 0
0/ 0
1/ 0
2/ 0
0/ 0
0/ 0
1/1
4/4
0/0
TF/FF
TFi = LFi - EFi
Free Float (FF) = ETj
ETi
dor FF = smallest ES (of succeeding activities) EF (of current activity)
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Precedence Relationships - Lead & LagFFij Lag time for a finish-to-finish relationship. (The succeeding
activity finishes this amount of time after the completion of thepreceding activity.)
SSij Lead time for a start-to-start relationship. (The preceding
activity starts this much earlier than the start of the
succeeding activity.)
FSij Lag time for a finish-to-finish relationship. (The succeeding
activity starts this amount of time after the completion of the
preceding activity.)
SFij Lead time for a start-to-finish relationship. (The preceding
activity starts this much earlier than the completion of the
succeeding activity.)
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PRECEDENCE LOGIC1. Preceding Activities.
Which activities must be finished before this activity may begin ?
What is the time lag? (finish to start.)
Which activities must be started before this activity may begin?
What is the lead time (start to start.)
Which activities must be finished before this activity may be completed?
What is the lag time? (Finish to finish)
Which activities must be started before this activity is completed?What is the lead time ? (start to finish.)
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R. RUSTOM 22
Follow: PRECEDENCE LOGIC
2. Succeeding Activities
Which activities can begin after the finish of this activity?
What is the time lag? (finish to start.)
Which activities can begin after the start of this activity?
What is the lead time? ( Start to start )
Which activities can be completed after the finish of this activity?
What is the lag time? (Finish to finish.)
Which activities can finish after the start of this activity? What is
the lead time? (Start to finish.)3. Concurrent Activities.
Which activities can be carried out at the same time?
(Start to start equals zero, that is, SS = 0 in this case.)
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Lead/Lag Relationships
ES DESC.EF ES DESC. EF
FF ij
FS ij
SS ijSF ij
Forward Pass
Backward Pass
i Di jDj
LS DESC.LF LS DESC. LF
FF jk
FS jk
SS jk
SF jk
j Dj kDk
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PDM Activity Diagramming Methods
Activity No.
Duration RESP.StartSide
Finish
Side
METHOD 1
Activity No.
Duration RESP.StartSide
Finish
Side
METHOD 2
DESCRIPTION DESCRIPTION
ES
LS
EF
LF
Activity No.
LS LF
Sta
rtSide
Finish
Side
METHOD 3
Activity No.
Sta
rtSide
Finish
Side
METHOD 4
DESCRIPTION DESCRIPTION
ES
LS
EF
LF
DUR TF
ES EFDuration RESP.
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Logical Relationships of PDM
12
FINISH - TO - START
Layout & Excavate
2 GO
12Install exterior
Conduit & piping
5 EL
20
FINISH - TO - FINISH
Install fuel tanks
2 GO
12Install exterior
Conduit & piping
5 EL
10Contract
Award
2 GO
10Layout &
Excavate
2 GO
START - TO - FINISH
12
Layout &
Excavate
2 GO
18
Install fuel
tanks
2 ME
START - TO - START
12
Layout & Excavate
2 GO
12Install exterior
Conduit & piping
5 EL
Relationship with Lag
1
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PDM Calculation Procedure(Assumes no splitting of activity is allowed)
FORWARD PATH
Step 1
jiji
jiji
iji
iji
j
DSFES
DFFEF
SSES
FSEF
MaxES
1
Step 2
jjj DESEF
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Follow PDM Calculation Procedure
BACKWARD PATH
Step 1
iijj
iijj
ijj
ijj
i
DSFLF
DSSLS
FFLF
FSLS
alTimeTer
MinLF
min
Step 2
iii DLFLS
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Calculation of Total Float and Free Float
Total Float
iii EFLFTF
Free Float
iijj
iijj
iijj
iijj
ESSFEF
EFFFEF
ESSSES
EFFSES
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A
10
B
7
C
10
D
10
E4
F
3
G
10
H
15
I
7
K
5
L
5
J
3
M
6
N
8
SS5
FS2
FF2
SS5
FF1
FS5
FS3
SF7
SS2
SS10, FF2
FS2
SS3
FF2, SS1
FS1
FF0
1 11
6 13
11 21
11 21
7 11
15 18
21 31
16 31
16 23
23 28
28 33
11 14
31 37
38 46
38 46
ESi + SSij
1 +5 = 6
EFi + FFi - Di
11 + 0 - 4
FS0
FS0
EFi + FSij
13 + 2
ESi + SFij - Dj
15 + 7 -5
EFi + FFij - Dj
28 + 2 - 8
ESi + SSij
23 + 1
EFi + FFij-Dj13 + 2 -10
FS0
ESi +SSij
11 + 5
EFi + FFij - Dj
21 + 1 - 7
EFi + FSij
11 +5
ESi + SSij
21 + 2
ESi + SSij
16 + 10
EFi + FFij - Dj
31 + 2 - 5
EFi+FSij
23 + 2
FS0
EFi + FSij
14 + 3
ESi+SSij
28+3EFij+FSij
37+1
FORWARD PASS
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A
10
B
7
C
10
D
10
E4
F
3
G
10
H
15
I7
K
5
L
5
J
3
M
6
N
8
SS5
FS2
FF2
SS5
FF1
FS5
FS3
SF7
SS2
SS10, FF2
FS2
SS3
FF2, SS1
FS1
FF0
38 46
38 46
31 37
31 37
23 28
37 42
28 33
28 33
11 14
25 28
15 18
35 38
21 31
35 45
16 31
16 31
16 23
19 26
6 13
26 33
11 21
11 21
11 21
15 25
7 11
11 14
1 11
1 11
LFj - FFij
46 - 2
LSj - SSj - Di
38 - 1 + 5
LSj - FSij
38 - 1
LSj - SSij + Di
31 - 3 + 5
LSj - FSij
31 - 3
LFj - Sfij + Di
42 - 7 + 3
LSj - SSij + Di
37 - 2 + 10
LFi - FFij
33 - 2
LSj - SSij + Di
28 - 10 + 15
LSj - FSij
28 - 2LSj - FSij
19 - 5
LFj - FFij
26 - 1
LSj - SSij + Di
16 - 5 + 10
FS0
LSj - FSij
35 - 2
LSj - SSij + Di26 - 5 + 10
SF0
SF0
SF0
LFj - FFij
45 - 2
BACKWARD PASS
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A
10
B
7
C
10
D
10
E
4
F
3
aG
10
H
15
I
7
K
5
L
5
J
3
M
6
N
8
SS5
FS2
FF2
SS5
FF1
FS5
FS3
SF7
SS2
SS10, FF2
FS2
SS3
FF2, SS1
FS1
FF0
38 46
38 46
31 37
31 37
28 33
28 33
11 14
25 28
23 28
37 42
15 18
35 38
21 31
35 45
16 31
16 31
1623
19 26
6 13
26 33
11 21
11 21
11 21
15 25
7 11
11 14
1 11
1 11
ESj - SSij - ESi
6-5-1
ESj - FSij - EFi
15 - 2-13
ESj - Sfij - ESi
28 - 7 - 15 ESj - SSij - ESi
38 - 1 - 23
EFj - FFij - EFi
46 - 2 - 28
ESj - FSij - EFi
38 - 1 - 37
ESj - FSij - EFi31 - 3 - 14
ESj - FSij - EFi
11 - 0 - 11
ESj - FFij -EFi11 - 0 - 11
EFj - FFij - EFi
31 - 2 - 13
ESj - SSij - ESi
16 - 5 - 11
ESj - FSij -EFi
21 - 0 - 21
FS0
ESj - FFij - EFi
23 - 1 - 21
ESj - FSij - EFi
16 - 5 - 11
FS0
ESj - SSij - ESi
23 - 2 - 21
ESj - FSij - EFi
28 - 2 - 23
EFj - FFij - EFi
33 - 2 - 31
ESj - SSij - ESi
28 - 10 - 16
ESj - SSij - ESi
31 - 3 28
0/0
20/0
0/0
4/1
3/0
20/0
14/0
0/0
3/3
14/14
0/0
14/14
0/0
0/0
FS0
FS0
ESj - FSij - ESj
11 - 0 - 1
ESj - FSij - Efi
11 - 0 - 11
TF/FF
TFi = LFi - EFi
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4.4 Time-Scaled Diagrams:
Time-scaled diagrams are used extensively in the construction industry.
Such diagrams enable one
to determine immediately which activities are scheduled to
proceed at any point in time .to monitor field progress.
it can be used to determine resources need.
The time scale used in time-scaled diagrams can be either the calendar datesor the working periods (ordinary dates), or using both at the same time.
Its disadvantage is that it needs a great effort to be modified or updated. Also,it can not be used to
represent overlapping activities.
A
3
C
4
B3
D
6
E
5
3
2
Time-scaleddiagram
1 2 3 4 5 6 7 8 9 10 11 12 13 14
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The TF for activity A equals the smallest of the sum of the floats along all pathsfrom the end of activity A to the end of the project. The float on path ABE = 3,path ACE = 2 and path ADE = 0, then the TF of activity A = 0. The calculationsare shown in Table 4.2.
Table 4.2 Time-scaled diagram calculations
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Schedule Presentation:4.5
After the AOA and AON calculations are made, it is important to present theirresults in a format that is clear and understandable to all the parties involved in
, named afterBar chart or Gantt chartthe project. The simplest form is thethe person who first used it. A bar chart is a time versus activity chart in which
activities are plotted using their early or late times.
a) Earlybar chat
b) Latebar chart
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The bar chart representation:
It shows various details. Float times of activities, critical activities can be shownin a different color, or bold borders, as shown in Figure 4.12. The bar chart canalso be used for accumulating total daily resources and / or costs, as shown atthe bottom part of Figure 6.13. In this figure, the numbers on each activity
represent the number of labors needed.
Figure 4.13: Using bar chart to accumulate resources
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4.6 Criticisms to Network Techniques:
1- Assume all required resources are available:
The CPM calculations do not incorporate resources into their formulation. Also,
as they deal with activity durations only, it can result in large resourcefluctuations. Dealing with limited resources and resource leveling, therefore,has to be done separately after the analysis.
2- Ignore project deadline:
The formulations of CPM and PDM methods do not incorporate a
deadline duration to constrain project duration.
3- Ignore project costs:
Since CPM and PDM methods deal mainly with activities durations, they do notdeal with any aspects related to minimize project cost.
4- Use deterministic durations:
The basic assumption in CPM and PDM formulations is that activity durationsare deterministic. In reality, however, activity durations take certain probabilitydistribution that reflect the effect of project conditions on resource productivityand the level of uncertainty involved in the project.
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Solved Examples4.7
3.1Example
For the project data in Table 4.3, answer the following questions:
a) Draw an AOA network of the project?
b) Perform forward path and backward path calculationsc) What is the effect of delaying activity D by 3 days?
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Solution:
a, b
0
1 A 2
3
5 6
0
2
4
2 2
8 8
14 14 16 16
9 11
B
6
E
6
C
3 F
3
G
21D
8,or10
14,or122,or 8
9,or 5
c) Total float of activity D = LF ES d = 11 8 1 = 2.
3 2l
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3.2Example
Perform PDM calculations for the small project below and determine activitytimes. Durations are shown on the activities.
S l ti 7 9
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Solution:
1 5
B(4)
1 5
5 6
D(1)
5 6
6 7
G(1)
6 7
7 14
J(7)
7 14
14 16
L(2)
14 16
1 2
C(1)
6 7
2 4
E(2)
7 9
4 5
H(1)
9 10
2 4
F(2)
8 10
5 9
K(4)
10 14
0 1
A(1)
0 1
7 9
I(2)
12 14
7or85or4
9or9or14
1or6
12or7
3 3E l
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3.3Example
For the activities listed in the table below, draw the time-scaled diagram andmark the critical path. Determine the completion time for the project. Tabulateactivities times and floats.
S l ti
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Solution:
3 4E l
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3.4Example
Perform PDM calculations for the small AoN network shown here. Pay specialattention to the different relationships and the lag times shown on them.
Solution:
0 3
A(3)
0 3
2 5
B(3)
4 7
3 7
C(4)
3 7
3 9
D(6)
4 10
7 12
E(5)
7 12
SS2
FF2
5 or 7 or
2=9-2-5
12-2=10
4 or 3 or5=4-2+3
4Exercise
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(Cont.)4Exercise
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(Cont.)4Exercise
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(Cont.)4Exercise
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(Cont.)4Exercise
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(Cont.)4Exercise
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(Cont.)4Exercise
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