A project refers to the process of creating a complex, one-of-a-kind product or
service for some specific objectives. Examples of projects include new product design,
facility construction, software system design, capital equipment purchase.
Project management is the planning, scheduling, organizing, directing, and
controlling of resources for a project.
Defining a Project (Statement of Work)
A project is typically defined through a series of activities (tasks), subtasks, work
packages, and milestones.
Organization for Project Management
1. Line-staff organization.
2. Pure project organization.
3. Matrix organization.
Key Considerations in Project Management
1. Time - schedule.
2. Cost - resource requirements.
Project Life Cycle
1. Definition phase.
2. Planning phase.
3. Execution phase.
5. Delivery phase.
Network Representation of a Project
Networks are commonly used in project management to describe the logical
constraints among the activities and to analyze the effects of scheduling decisions on
cost and performance.
Types of Networks
Activity-On-Node (AON) Networks
Activity-On-Arc (AOA) Networks
A path is a set of nodes connected by arrows, which begins at the initial node of a
network and ends at the terminal node.
A critical path is the longest path in a network, i.e., the path with the longest
Activities on a critical path are called critical activities.
Temporal Analysis of Networks
* When will the project be complete?
* Which activities will contribute directly to the duration of the project?
Early Start Time (ES) = The earliest time at which an activity could possibly be
started = the maximum EF time of all its immediate
Early Finish Time (EF) = ES + activity duration.
Late Finish Time (LF) = The latest time at which an activity could be completed
without delaying the project beyond its due date = the
minimum LS time of all its successors
Late Start Time (LS) = LF - activity duration.
Total Slack or Float (S) = The amount of time that an activity may delay in start time
without delaying the project, given that all other activities on
the same path are not delayed.
= LF - EF = LS – ES
Activity Duration ES EF LF LS S
1-2 8 _
2-4 6 1-2
1-3 4 -
3-5 9 1-3
2-5 11 1-2
4-5 3 2-4
5-6 1 2-5, 3-5, 4-5,
Program Evaluation and Review Technique (PERT)
PERT is very useful in planning and scheduling a large project consisting of
numerous activities with uncertain durations, such as research and development
EXPECTED DURATIONS OF ACTIVITIES
PERT calculates the "expected" duration of an activity as a weighted average of
t e = ( t 0 + 4t m + t p ) / 6
t o = Optimistic Estimate
t m = Most Likely Estimate
t p = Pessimistic Estimate
VARIABILITY OF ACTIVITY DURATIONS
PERT defines the variance of an activity duration as:
V = [(tp - to)/6]2
DURATION OF A PATH IN PERT
Given the expected duration of each activity, the expected duration of a path is
equal to the sum of the expected durations of all the activities on that path.
Similarly, the variance of a path duration is defined as the sum of the variances of
all activities on that path.
The path having the longest expected duration is defined as the critical path.
PROBABILITY OF COMPLETING A PROJECT
PERT assumes that the duration of a path has a normal distribution. Probability
statements about the possible duration of a project can then be made accordingly.
Variance of Probability of
Path Expected Duration
Path Duration Completion
a-b-c 10.0 0.944
d-e-f 16.0 1.00
g-h-i 13.5 1.139
What is the probability that the project can be completed within 15 weeks of its start?