The document discusses project scheduling and control techniques, specifically critical path method (CPM). It provides an overview of key CPM concepts like critical path, critical activities, forward and backward pass to determine earliest and latest start/finish times. It includes an example of developing an activity on arrow (AOA) network diagram for a sample project and calculating the earliest start/finish times. It also discusses limitations of CPM and provides steps in CPM project planning and an overview of Gantt charts.

1. Project Scheduling and Control
Techniques
Project Evaluation Planning & Management
Prepared by
S. M. ZUBAER HOSSAIN
1

2. Building the Network: AOA
1 Task Predecessor
1 c 3
a -
S a S a b -
t t c a
a a d b
r r e b
b b d 4
t 2 t f c, d
2
g e
e
5
Dummy Activity
c
1
S a 3 F c
t f S 1 3 F
a i a i
n t
r d a n
b i d
t 4 i
s r b 2
g s
2 4 h t e
e h
5
2

3. Situations in Network Diagram
B
A
C A must finish before either B or C can start
A
C
both A and B must finish before C can start
B
A C
both A and B must finish before either of C or D can start
B
D
A B
A must finish before B can start
Dummy
C D both A and C must finish before D can start
3

4. Critical path Method (CPM)
■ Path
- A connected sequence of activities leading from the starting event to the ending event
■ Critical Path
- The longest path (time); determines the project duration
■ Critical Activities
- All of the activities that make up the critical path
■ Forward Pass
- Earliest Start Time (ES)
• earliest time an activity can start
• ES = maximum EF of immediate predecessors
- Earliest finish time (EF)
• earliest time an activity can finish
• earliest start time plus activity time
EF = ES + t
4

5. ■ Backward Pass
- Least Start Time (LS)
• Least time an activity can start without delaying critical path
time
- LS = LT – t
- Least finish time (LF)
• least time an activity can be completed without delaying
critical path time
• LS = minimum LS of immediate predecessors
5

6. Example : Develop the network (AOA) for a project with
following activities and immediate predecessors
Activity A B C D E F G H I
Immediate Predecessors - - A A A E D,F B,C G,H
Completion Time 5 6 4 3 1 4 14 12 6
EST EFT
EST=Earliest start time
Activity Activity
EFT=Earliest finish time
name duration
LST=Latest start time
LFT=Latest finish time
LST LFT
D[5,8]
2 5
3[7,10]
1 4 7
6
3 6

7. Example : develop the network (AON) for a project with following activities and
immediate predecessors
Activity a b c d e f g h i j
Immediate predecessors - - a a a b, c d d, e f g, h
Duration 5 4 3 4 6 4 5 6 6 4
5 9
d4 9 14
7 11 g5
17 21
0 5 5 11 12 17
Solution: j4 E
s a5 e6 11 17 17 21
EST EFT
N
t 0 5 5 11 D
EST-Earliest start time h6 12 18
EFT-Earliest finish time a 5 8 11 17
LST-Latest start time i6
LFT-Latest finish time r c3 8 12
t 15 21
LST LFT 0 4 8 11 f4
b4 11 15
7 11
7

8. Example 5: draw the network for the following relationship:
Activity C can be performed at the same time as E; but D cannot be started unless
both C and A are completed; A and B can be performed simultaneously , B has also
constraint on activity C and E , both D and E should be completed before the
object is achieved.
C
2
6
1
7
3
8
81

9. Steps in CPM Project Planning
 Specify the individual activities
 Determine the sequence of those activities
 Draw a network diagram.
 Estimate the completion time for each activity.
 Identify the critical path (longest path through the network)
 Update the CPM diagram as the project progresses.
CPM limitations
 CPM was developed for complex but fairly routine projects with
minimal uncertainty in the project completion times. For less routine
projects there is more uncertainty in the completion times, and this
uncertainty limits the usefulness of the deterministic CPM model. An
alternative to CPM is the PERT project planning model, which allows a 9 82

10. Gantt chart
Gantt chart: During the era of scientific management, Henry Gantt
developed a tool for displaying the progression of a project in the
form of a specialized chart. An early application was the tracking of
the process of ship building projects. Today, Gantt’s scheduling tool
takes the form of a horizontal bar graph and is known as a Gantt
chart, a basic sample of which is shown below:
Task Duration Jan F Ma Ap Ma Ju Jul Aug Sep Oct Nov Dec
e r r y n
b
1 2 mo.
2 2 mo.
3 2 mo.
4 2 mo.
5 2 mo.
6 2 mo.
Gantt Chart Format
83
10

11. Thank you
11