1. PERT & CPM
…are the two most widely use techniques for
planning and coordinating large-scale projects…
…by using PERT or CPM, managers are able to
obtain:
1. A graphical display of projects activities.
2. An estimate of how long the project will
take.
3. An indication of which activities are the most
critical to timely completion of the project.
4. An indication of how long any activity can be
delayed without lengthening the project.
2. PERT & CPM
The network diagram:
• The arrows represent the project
activities
• The nodes represent both
beginnings and endings of
activities
3. CPM Terminology
Activity
A task or a certain amount of work required in the
project
Requires time to complete
Represented by an arrow
Dummy Activity
Indicates only precedence relationships
Does not require any time of effort
4. CPM Terminology
Event
Signals the beginning or ending of an activity
Designates a point in time
Represented by a circle (node)
Network
Shows the sequential relationships among activities
using nodes and arrows
5. CPM Terminology
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
6. CPM Terminology
Earliest Start (ES)
The earliest that an activity can begin; assumes all
preceding activities have been completed
Earliest Finish (EF)
ES + activity time
Latest Finish (LF)
The latest that an activity can finish and not change the
project completion time
Latest Start (LS)
LF - activity time
7. Steps in CPM Analysis
Draw the CPM network
A graphic view of the relationships among the required
activities
Analyze the paths through the network
Determine the length of each path (time required to
complete each path)
Starting at the beginning of the network and working
toward the end (from left to right), determine the ES and EF
for each activity
. . . more
8. Steps in CPM Analysis
Path analysis (continued)
Identify the critical path(s) (the longest path[s]
through the network)
The critical path(s) determines how long the project
will take
. . . more
9. Steps in CPM Analysis
Determine the slack for each activity
Working from the end of the project network (from
right to left), find the LF and the LS for each activity
Compute the activity’s slack
slack = LS - ES = LF - EF
Slack is the maximum amount of time that this activity
can be delay in its completion before it becomes a
critical activity, i.e., delays completion of the project
25. Crash time (summary)
Length after crashing n days
Path n = 0 1 2 3
1 2 5 6 18 18 18* 17
1 3 4 5 6* 20* 19* 18* 17
Activity crashed 1 3 4 5 5 6
Cost (crash) RM300 RM600 RM800 Total :
RM1,700
26. TUTORIAL EXERCISE – Q1 Syarikat Kukuh
Syarikah Kukuh is planning to develop and market a new racing bicycle. The project
comprise of the following activities.
Activity Normal cost (RM) Duration (day) Cost to reduce/day
(RM)
Time can be
shorten until (day)
1 2 4000 5 600 2
1 3 12000 3 1000 2
1 4 10000 10 1600 7
2 5 2000 7 800 6
3 6 8000 8 1800 6
4 6 12000 7 1200 4
4 7 6000 4 1000 3
5 8 14000 6 1400 5
6 8 16000 5 1400 3
7 8 4000 6 1200 4
The contract specifies a RM2000 per day penalty for each day the completion of the
project extends past 15 days:
27. Required to:
a) Draw the network diagram
b) Determine the critical path
c) Determine the normal time (day) and cost
(RM) to finish the project
d) Determine the optimum time (day) and
cost (RM) to finish the project
28. Solution (a) – Tutorial (Q1 – Syarikat Kukuh)
Please draw the network
29. Solution (b) – Tutorial (Q1 – Syarikat Kukuh)
Please determine the critical path
30. Solution (c) – Tutorial (Q1 – Syarikat Kukuh)
Activity Normal cost (RM) Duration (day) Cost to reduce/day
(RM)
Time can be
shorten until (day)
1 2 4000 5 600 2
1 3 12000 3 1000 2
1 4* 10000 10* 1600 7
2 5 2000 7 800 6
3 6 8000 8 1800 6
4 6* 12000 7* 1200 4
4 7 6000 4 1000 3
5 8 14000 6 1400 5
6 8* 16000 5* 1400 3
7 8 4000 6 1200 4
Critical
1468
Total cost:
RM88000
Normal day:
22 days
Normal cost (RM): Total cost + Penalty = RM88000 + (7*RM2000) = RM102000
31. Solution (d) – Tutorial (Q1 – Syarikat Kukuh)
Path 0 1 2 3 4 End/stop
Activity crashed
Cost crashed
Complete and determine the optimum day and cost to finish the project