Project Management

Chapter 7
Project Management
© 2007 Pearson Education
Project Management
Used to manage large complex projects
Has three phases:
1. Project planning
2. Project scheduling
3. Project controlling
Phase 1: Project Planning
What is the project goal or objective?
What are the activities (or tasks) involved?
How are activities linked?
How much time required for each activity?
What resources are required for each
Phase 2: Project Scheduling
1. When will the entire project be
2. What is the scheduled start and end time
for each activity?
3. Which are the “critical” activities?
4. Which are the noncritical activities?
Phase 2: Project Scheduling (cont.)
5. How late can noncritical activities be w/o
delaying the project?
6. After accounting for uncertainty, what is
the probability of completing the project
by a specific deadline?
Phase 3: Project Controlling
At regular intervals during the project the
following questions should be considered:
Is the project on schedule? Early? Late?
Are costs equal to the budget? Over
budget? Under budget?
Are there adequate resources?
What is the best way to reduce project
duration at minimum cost?
Identifying Activities
• Subdivides a large project into smaller units
• Each activity should have a clearly defined
starting point and ending point
• Each activity is clearly distinguishable from
every other activity
• Each activity can be a project in itself
Work Breakdown Structure (WBS)
Divides the project into its various
subcomponents and defines hierarchical
levels of detail
Major tasks in project
Subtasks in major tasks
Activities to be completed
Example Work Breakdown
Identify for Each Activity:
• Which other activities must be completed
previously (predecessors)
• Time required for completion
• Resources required
This completes the project planning phase.
Project Scheduling Phase
Commonly used techniques:
• Program Evaluation and Review
Technique (PERT)
• Critical Path Method (CPM)
Project Management Example:
General Foundry Inc.
• Have 16 weeks to install a complex air
filter system on its smokestack
• May be forced to close if not completed
w/in 16 weeks due to environmental
• Have identified 8 activities
Drawing the Project Network
• AON – Activity on Node networks show
each activity as a node and arcs show the
immediate predecessor activities
• AOA – Activity on Arc networks show
each activity as an arc, and the nodes
represent the starting and ending points
We will use the AON method
AON Network for General Foundry
Activity Time Estimates
Determining the Project Schedule
• Some activities can be done
simultaneously so project duration should
be less than 25 weeks
• Critical path analysis is used to
determine project duration
• The critical path is the longest path
through the network
Critical Path Analysis
Need to find the following for each activity:
Earliest Start Time (EST)
Earliest Finish Time (EFT)
Latest start time (LST)
Latest Finish Time (LFT)
Forward Pass
• Identifies earliest times (EST and EFT)
• EST Rule: All immediate predecessors
must be done before an activity can begin
– If only 1 immediate predecessor, then
EST = EFT of predecessor
– If >1 immediate predecessors, then
EST = Max {all predecessor EFT’s}
• EFT Rule:
EFT = EST + activity time
Node Notation:
Forward Pass: Earliest Start and Finish
Backward Pass
• Identifies latest times (LST an LFT)
• LFT Rule:
– If activity is the immediate predecessor
to only 1 activity, then
LFT = LST of immediate follower
– If activity is the immediate predeccor to
multiple activities, then
LFT = Min {LST of all imm. followers}
• LST Rule:
LST = LFT – activity time
Backward Pass: Latest Start and Finish Times
Slack Time and Critical Path(s)
• Slack is the length of time an activity can
be delayed without delaying the project
Slack = LST – EST
• Activities with 0 slack are Critical Activities
• The Critical Path is a continuous path
through the network from start to finish that
include only critical activities
Project Schedule and Slack Times
Critical Path and Slack Times
Total Slack Time vs. Free Slack Time
• Total slack time is shared by more than 1
Example: A 1 week delay in activity B will
leave 0 slack for activity D
• Free slack time is associated with only 1
Example: Activity F has 6 week of free
slack time
Variability in Activity Times
Activity times are usually estimates that
are subject to uncertainty
• Approaches to variability:
1. Build “buffers” into activity times
2. PERT – probability based
3. Computer simulation
PERT Analysis
• Uses 3 time estimates for each activity
Optimistic time (a)
Pessimistic time (b)
Most likely time (m)
• These estimates are used to calculate an
expected value and variance for each
activity (based on the Beta distribution)
• Expected activity time (t)
t = (a + 4m + b)
• Variance = [ (b – a) / 6 ]2
• Standard deviation = SQRT(variance)
= (b – a)
Go to file 7-1.xls
Project Variance and Standard Deviation
• Project variance (σp2)
= ∑ (variances of all critical path activities)
σp2 = 0.11 + 0.11 + 1.0 + 1.78 + 0.11
= 3.11
• Project standard deviation (σp)
= SQRT (Project variance)
σp = SQRT ( 3.11) = 1.76
Probability of Project Completion
• What is the probability of finishing the
project within 16 weeks?
• Assumptions:
– Project duration is normally distributed
– Activity times are independent
• Normal distribution parameters:
μp = expected completion time= 15 weeks
σp = proj standard deviation = 1.76 weeks
Normal Probability Calculations
Z = (Target time – expected time)
Z = (16 - 15) = 0.57
This means 16 weeks is 0.57 standard
deviations above the mean of 15 weeks.
Probability Based on
Standard Normal Table
Prob (proj completion < 16 weeks) = 0.7158
Project Duration for
a Given Probability
• What project duration does General
Foundry have a 99% chance of completing
the project within?
i.e. Prob (proj duration < ? ) = 0.99
• From Std. Normal Table, this corresponds
to Z = 2.33
Z = (? - 15) = 2.33
So ? = 15 + 2.33 x 1.76 = 19.1 weeks
Scheduling Project Costs
1. Estimate total cost for each activity
2. Identify when cost will actually be spent
(we will assume costs are spread evenly)
3. Use EST and LST for each activity to
determine how costs are spread over
Monitoring and
Controlling Project Costs
• While the project is underway, costs are tracked
and compared to the budget
• What is the value of work completed?
Value of work completed
= (% of work completed) x (total activity budget)
• Are there any cost overruns?
Cost difference
= (Actual cost) – (Value of work completed)
Project Crashing
• Reducing a project’s duration is called
• Some activities’ times can be shortened
(by adding more resources, working
overtime, etc.)
• The crash time of an activity is the
shortest possible duration, and has an
associated crash cost
Steps in Project Crashing
1. Compute the crash cost per time period
2. Find the current critical path (CP)
3. Find the lowest cost way to crash the CP
by 1 time period
4. Update all activity times. If further
crashing is needed, go to step 2.
Crashing Using
Linear Programming
Decision: How many time periods to crash
each activity?
Objective: Minimize the total crash cost
Decision Variables
Ti = time at which activity i starts
Ci = number of periods to crash activity i
• An activity cannot begin before all
immediate predecessors are complete
• There is a maximum amount that each
activity can be crashed
Go to file 7-2.xls

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