1. Construction Project Management
UP Copyrights 2008
Faculty of Applied Engineering and Urban Planning
Civil Engineering Department
Construction Project Management
2nd Semester 2008/2009
Project Scheduling
Week ( )
Lec. ( )
Eng: Eyad Haddad

2. CH4: Project Scheduling Scheduling = Planning + Time
Construction Project management functions:
1. Planning
تخطيط
2. Organization
تنظيم
3. Supervision
مراقبه
4. Control
تحكم
1. Time
الوقت
2. Cost
التكلفة
3. Quality
الجودة
4. Performance
الانجاز
Scheduling
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.

3. CH4: Project Scheduling
The project scheduling is used for:
Knowing the activities timing and the project completion time.
Having resources available on site in the correct time.
Making correction actions if schedule shows that the plan will result in
late completion.
Assessing the value of penalties on project late completion.
Determining the project cash flow.
Evaluating the effect of change orders on the project completion time.
Determining the value of project delay and the responsible parties.

4. 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.

5. 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.

6. 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

7. The CPM is a systematic scheduling method for a project network and involves four main steps:
A forward path to determine activities early-start times;
A backward path to determine activities late-finish times;
Float calculations ( Free & Total ) float; and
Identifying critical activities.

8. i j x dx 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.
1. Forward Path:
ETj = ETi + dx
ETi
LTi
ETj
LTj i j x dx

9. 1. Forward Path: 5 d1 B 3 A A A C4 E 1 1 1 3 9 11 d=3 5 D 6 d2 7 6
3+3=6
Es+d=EF
Project
Start=0
Project
Start=0
9+5=14
0+3=3 d1 B 3 14 3 A A A C4 E 1 1 1 3 9 11
d=3 5 D 9 6 d2
6+0=6
3+4=7 7 9
9+0=9
3+6=9

10. 2. Backward Path LS = LF – d 9 5 d1 B 3 14 3 A C4 E 1 3 9 11 3 5 D 9 6
9-3=6 5
9-0=9
9-4=5
3-3=0
9-6=3 d1 B 3 3 14 14 3 A C4 E 1 3 9 11 3 5 D 9 9 6 d2
14-5=9
LF-d=LS 7 9 9
9-0=9

11. 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
ملاحظة : TF دوما يستخدم للنشاط الواحد.
Free Float (FF) = ETj – ETi – d
or FF = smallest ES (of succeeding activities) – EF (of current activity)
ملاحظة : FF دوما يستخدم للنشاطين السابق واللاحق.

12. 3. Float Calculations: Total Float (TF) = LF – EF = LS – ESj A LS LF LS LF
AON
AOA
Free Float (FF) = ETj – ETi – d
or FF = smallest ES (of succeeding activities) – EF (of current activity)
ملاحظة : FF دوما يستخدم للنشاطين السابق واللاحق. ES EF ES EF ES EF ES EF A i j B i j A B LS LF LS LF LS LF LS LF
AOA
AOA

13. 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
Total Float
(TF)
Late Finish
(LF)
Early Finish
(EF)
Late Start
(LS)
Early Start
(ES)
Duration
Yes 3 A No 9 6 B 2 7 5 4 C D 14 E

14. 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 Path
Forward path can proceed from one activity to the other; the process is as follow . 3 6
B(3)
6,7,or 9
Early start
Early finish 3 3 7 9 14
A(3)
C(4)
E(5)
Name (duration)
Late start
Late finish 3 9
D(6)
Fig. 4.8: Forward Path in PDM Analysis

15. Backward Path: 3 6 B(3) 6 9 3 3 7 9 14 A(3) C(4) E(5) 3 5 9 9 14
Early start
Early finish 3 3 7 9 14
A(3)
C(4)
E(5) 3 5 9 9 14
Name (duration)
6,5, or 3
Late start
Late finish 3 9
D(6) 3 9

16. Floats Start Completion Start Completion Start Completion
Project duration = 24 days
Activity A
7 days
Activity B
13 days
Activity C
4 days
CASE 1: All activities are critical: total float and free floats for all activities = 0
Total Float = 5
Free Float = 5
Start
Completion
Activity D
8 days
Activity A
7 days
Activity B
13 days
Activity C
4 days
CASE 2: Activity sequence in which one activity has total and free float
Total Float of D = Total Float of E = 5
Free Float of D = Free Float = 5
Start
Completion
Activity D
5 days
Activity E
3 days
Activity A
7 days
Activity B
13 days
Activity C
4 days
CASE 3: Activity sequence illustrating total and free float

17. Floats - 2 TEi TLi TLj TEj Finish Event Start Event Activity duration
Total Float
Activity duration
Free Float
Activity duration
Independent Float
Areas of shared float

18. Total Float (TF) = LF – EF
Float Calculations:
Total Float (TF) = LF – EF
= LS – ES
Free Float (FF) = ETj – ETi – d
Activity
Duration ES LF LS EF TF
Critical Act. A 3 3
Yes 3 B 3 3 9 6 No 6 3 C 4 3 9 5 No 7 2 9 3
Yes D 6 3 9 E 5 9 14 9
Yes 14

19. PDM Calculations (PDM = Precedence Diagram Method) Example2/ 4/ 4 0/ 12 20 10 16 6 3 6 E 4 B 3 H 6 12 20 14 8 6 11 3 4 0/ 0/ 0/ 0/ 3 3 8 A 3 C 5 F 6 J 8 Fn 0/
TF/FF 8 12 1/ ES EF 3 10 G 4
Act
Dur D 7 1/ 1 10 19 LS LF I 9
TF/FF
TFi = LFi - EFi
Free Float (FF) = ETj – ETi – d
or FF = smallest ES (of succeeding activities) – EF (of current activity)

20. Precedence Relationships - Lead & Lag
FFij Lag time for a finish-to-finish relationship. (The succeeding activity finishes this amount of time after the completion of the preceding 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.)

21. PRECEDENCE LOGIC 1. Preceding Activities.الفعاليات السابقة
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.)

22. Follow: PRECEDENCE LOGIC
2. Succeeding Activities الفعاليات اللاحقة
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.)
R. RUSTOM

23. Lead/Lag Relationships
FF ij
Forward Pass j i Dj
ES DESC. EF
ES DESC. EF Di
FS ij
SS ij
SF ij
FF jk
Backward Pass k j Dk
LS DESC. LF Dj
FS jk
LS DESC. LF
SS jk
SF jk

24. PDM Activity Diagramming Methods
Activity No. ES
Activity No. EF
DESCRIPTION
DESCRIPTION
Start Side
Finish Side
Start Side
Finish Side LS LF
Duration
RESP.
Duration
RESP.
METHOD 1
METHOD 2
Activity No.
DUR TF ES
Activity No. EF
DESCRIPTION
DESCRIPTION
Start Side
Finish Side
Start Side
Finish Side LS LF ES EF
Duration
RESP. LS LF
METHOD 3
METHOD 4

25. Logical Relationships of PDM12 20 12
Layout & Excavate
Install fuel tanks
Layout & Excavate GO GO GO 12 12 12 1
Install exterior
Conduit & piping
Install exterior
Conduit & piping
Install exterior
Conduit & piping EL EL EL
START - TO - START
FINISH - TO - FINISH
Relationship with Lag 10 10 12 18
Contract
Award
Layout &
Excavate
Layout &
Excavate
Install fuel
tanks GO GO GO ME
FINISH - TO - START
START - TO - FINISH

26. PDM Calculation Procedure (Assumes no splitting of activity is allowed)

27. Follow PDM Calculation Procedure

28. Calculation of Total Float and Free Float

29. FORWARD PASS ESi + SFij - Dj 15 + 7 -5 EFi + FSij 13 + 2 ESi + SSij
23 + 1 13 15 18 23 28 6
SF7
FS2 F 3 K 5
EFi + FFij - Dj B 7
ESi + SSij
21 + 2
EFi + FFij-Dj
FF2, SS1
ESi + SSij
1 +5 = 6 21
FF2
SS2 11 21 31 38 46
SS5 C 10
FS0 G 10
ESi + SSij N 8
FS0 28 1 11
ESi +SSij
11 + 5 33
ESi+SSij
28+3
EFi + FFij - Dj
EFij+FSij
37+1 L 5 38 46 A 10
SS5
SS3
SS10, FF2
FS1
FS0 11 21 16 31 31 37
EFi + FFij - Dj D 10 H 15
EFi+FSij
23 + 2 M 6
EFi + FFi - Di
FS2
FF1
EFi + FSij
14 + 3
FS3 16 23
FF0
EFi + FSij
11 +5 7 11 I 7
FS5 11 14 E 4 J 3
FS0
FORWARD PASS

30. BACKWARD PASS LFj - Sfij + Di 42 - 7 + 3 LSj - FSij 35 - 2
LSj - SSj - Di 15 18 23 28 6 13
SF7
FS2 F 3 K 5
LFj - FFij
46 - 2 B 7
LSj - SSij + Di
LFj - FFij
45 - 2
LSj - SSij + Di
FF2, SS1 33 35 38 37 42 26
FF2 11 21
SS2 21 31 38 46
SS5 C 10
FS0 G 10
LSj - SSij + Di N 8 28 33 1 11
LSj - SSij + Di
LSj - SSij + Di 11 21
LFi - FFij
33 - 2 L 5 A 10
SF0 35 45 38 46
SS5
SS3
SS10, FF2
FS1
SF0 11 21 31 37 16 31 1 D 10
LFj - FFij
26 - 1 28 33 M 6 11 H 15
LSj - FSij
38 - 1
FS2 15 25
FF1
LSj - FSij
28 - 2 31 37 16 31
FF0 7 11
LSj - FSij 16 23
FS3 E 4 I 7
FS5
LSj - FSij
31 - 3 11 14 11 14 J 3 19 26
SF0
BACKWARD PASS 25 28

31. TFi = LFi - EFi 20/0 ESj - Sfij - ESi 28 - 7 - 15 ESj - FSij - EFi 15 18
ESj - SSij - ESi
14/14
20/0 F 3 23 28 6 13
SF7
FS2 K 5
EFj - FFij - EFi
ESj - SSij - ESi
6-5-1 B 7 35 38
EFj - FFij - EFi
14/0
FF2, SS1 37 42
FF2 21 31
0/0 26 33
SS2
ESj - SSij - ESi
0/0
ESj - FSij -EFi 38 46
SS5 aG 10
ESj - FSij - ESj
0/0 11 21
0/0 N 8
FS0
EFj - FFij - EFi 28 33
ESj - SSij - ESi 1 11 C 10
ESj - SSij - ESi 35 45
FS0 L 5 A 10 38 46
ESj - SSij - ESi
SS3
0/0
0/0 11 21
SS5 31 37
FS1 16 31
ESj - FSij - Efi 28 33
ESj - FSij - EFi 11 M 6 1
4/1 H 15
SS10, FF2
FS0 11 21
ESj - FFij - EFi
FS2 D 10 31 37 16 31
FF1
ESj - FSij - EFi
FF0
3/3
FS3 15 25
ESj - FSij - EFi 16 23
ESj - FFij -EFi
ESj - FSij - EFi
3/0
14/14 I 7 7
FS5 14 11 11 E 4 J 3 19 26
FS0 11 14 25 28
TF/FF
TFi = LFi - EFi
ESj - FSij - EFi

32. 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 dates or 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. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 B
Time-scaled diagram 3 3 A C E 3 4 2 5 D 6

33. The TF for activity A equals the smallest of the sum of the floats along all paths from 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 calculations are shown in Table 4.2.
Table 4.2 Time-scaled diagram calculations

34. 4.5 Schedule Presentation:
After the AOA and AON calculations are made, it is important to present their results in a format that is clear and understandable to all the parties involved in the project. The simplest form is the Bar chart or Gantt chart, named after the 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) Early bar chat
b) Late bar chart

35. The bar chart representation:
It shows various details. Float times of activities, critical activities can be shown in a different color, or bold borders, as shown in Figure The bar chart can also be used for accumulating total daily resources and / or costs, as shown at the bottom part of Figure In this figure, the numbers on each activity represent the number of labors needed.
Figure 4.13: Using bar chart to accumulate resources

36. 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 resource fluctuations. 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 incorporateغير مندمجة a deadline duration to constrain project duration.
3- Ignore project costs:
Since CPM and PDM methods deal mainly with activities durations, they do not deal with any aspects related to minimize project cost.
4- Use deterministic durations:
The basic assumption in CPM and PDM formulations is that activity durations are deterministic. In reality, however, activity durations take certain probability distribution that reflect the effect of project conditions on resource productivity and the level of uncertainty involved in the project.

37. 4.7 Solved Examples
Example 3.1
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 calculations
c) What is the effect of delaying activity D by 3 days?

38. c) Total float of activity D = LF – ES – d = 11 – 8 – 1 = 2.
Solution:
a, b 8 8
8,or10 3
2,or 8 E
14,or12 B 6 2 2 14 14 16 16 6 G 1 A 2 5 6 2 2 D 1 C F 3 3 4
9,or 5 9 11
c) Total float of activity D = LF – ES – d = 11 – 8 – 1 = 2.

39. Example 3.2
Perform PDM calculations for the small project below and determine activity times. Durations are shown on the activities.

40. Solution: 7 9 I(2) 1 5 5 6 6 7 B(4) D(1) G(1) 1 5 5 6 6 7 12or7 L(2) 714
B(4)
D(1)
G(1)
9or9or14 1 5 5 6 6 7 14 16
12or7
L(2) 7 14 1 14 16
J(7)
A(1) 7 14 1
1or6 1 2 2 4 4 5
C(1)
E(2)
H(1) 6 7 7 9 9 10
7or8
5or4 5 9 2 4
K(4)
F(2) 10 14 8 10

41. Example 3.3
For the activities listed in the table below, draw the time-scaled diagram and mark the critical path. Determine the completion time for the project. Tabulate activities times and floats.

42. Solution:

43. Example 3.4
Perform PDM calculations for the small AoN network shown here. Pay special attention to the different relationships and the lag times shown on them.
SS2 2 5
B(3) 4 7
5 or 7 or 2=9-2-5 3 3 7 7 12
A(3)
Solution:
C(4)
E(5) 3 3 7 7 12
4 or 3 or 5=4-2+3 3 9
FF2
D(6) 4 10
12-2=10 8

44. Exercise 4

45. Exercise 4 (Cont.)

46. Exercise 4 (Cont.)

47. Exercise 4 (Cont.)

48. Exercise 4 (Cont.)

49. Exercise 4 (Cont.)

50. Exercise 4 (Cont.)