The document discusses the Critical Path Method (CPM) for project management. CPM determines the total calendar time required for a project by adding the times for activities in each sequence. The critical path is made up of activities where any delay will delay the whole project. Non-critical activities can be delayed within their slack time without impacting the project duration. Dummy activities with zero duration are sometimes added to networks to maintain clear precedence relationships between tasks that share start and end nodes.

1. CPM – Critical Path Method

2. CPM – Critical Path Method
Software Project Management 2 Maria Petridou
• It is determined by adding the times for the activities in each
sequence.
• CPM determines the total calendar time required for the project.
• If activities outside the critical path speed up or slow down (within
limits), the total project time does not change.
• The amount of time that a non-critical activity can be delayed
without delaying the project is called slack-time.

3. CPM – Critical Path Method
Software Project Management 3 Maria Petridou
 ET – Earliest node time for given activity duration and precedence
relationships
 LT – Latest node time assuming no delays
 ES – Activity earliest start time
 LS – Activity latest start time
 EF – Activity earliest finishing time
 LF – Activity latest finishing time
 Slack Time – Maximum activity delay time

4. Dummy Activities
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• Sometimes it is necessary to insert dummy activities (duration
zero) in order to maintain the clarity of the diagram and the
precedence relationships between activities.
• In activity-on-arrow PERT diagrams, each activity must be uniquely
identifiable by its start and end nodes.
• However, sometimes multiple tasks have the same predecessors
and successors.

5. Dummy Activities
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Case One
• A task should be uniquely identifiable from its start node and finish
node
 This means that two or more tasks cannot share the same start
and finish nodes
1 2 3 4A D
C
Tasks B and C
have the same
start and finish
nodes
Task D has
immediate
predecessors of
B and C
B

6. Network Planning Techniques
• Program Evaluation & Review Technique (PERT):
– Developed to manage the Polaris missile project
– Many tasks pushed the boundaries of science &
engineering (tasks’ duration = probabilistic)
• Critical Path Method (CPM):
– Developed to coordinate maintenance projects in the
chemical industry
– A complex undertaking, but individual tasks are routine
(tasks’ duration = deterministic)

7. PERT and CPM
• Graphically display the precedence
relationships & sequence of activities
• Estimate the project’s duration
• Identify critical activities that cannot be
delayed without delaying the project
• Estimate the amount of slack associated with
non-critical activities

8. 8
Project Activities
in Constructing a House

9. 9
PERT Network for
Constructing a House