Project management teaching

Project Management
Concepts
Sudip R Chandra
Computer Science & Engg.
24th
September 2013
1

Project, Defined
 A project is an endeavor to accomplish a specific objective through a
unique set of interrelated tasks and the effective utilization of resources.
 It has a well-defined objective stated in terms of scope, schedule, and
costs.
 Project s are “born” when a need is identified by the customer – the people
or organization willing to provide funds to have the need satisfied.
 It is the people (project manager and project team), not the procedures and
techniques, that are critical to accomplishing the project objective.
 Procedures and techniques are merely tools to help the people do their
jobs.

Examples of Projects
 Planning a wedding
 Designing and implementing a computer system
 Hosting a holiday party
 Designing and producing a brochure
 Executing an environmental clean-up of a contaminated site
 Holding a high school reunion
 Performing a series of surgeries on an accident victim

Phases of the Project Life
Cycle 1
 The first phase involves the identification of a
need, problem, or opportunity.
The need and requirements are usually written by
the customer into a document called a request for
proposal (RFP).

Cycle 2
 The second phase is the development of a
proposed solution to the need or problem.
This phase results in the submission of a
proposal.
The customer and the winning contractor
negotiate and sign a contract (agreement).

Cycle 3
 The third phase is performing the project.
Different types of resources are utilized
Results in the accomplishment of the project
objective

Cycle 4
 The final phase is terminating the project.
Perform close-out activities
Evaluate performance
Invite customer feedback

The Project Management
Process The project management process means planning the work and then working the plan.
 7 steps of planning
1. Clearly define the project objective.
2. Divide and subdivide the project scope into major “pieces”
3. Define the specific activities for each piece (work package)
4. Graphically portray the activities that need to be performed fro each work
package in order to accomplish the project objective – in the form of network
diagram.
5. Make a time estimate for how long it will take to complete each activity –
resources needed.
6. Make a cost estimate for each activity.
7. Calculate a project schedule and budget to determine whether the project can
be completed within the required time, with the allotted founds, and with the
available resources.

Work Breakdown Structure
(WBS)
 The second step is to determine what activities
need to be performed.
 A list of all the activities must be developed.
 The WBS is a hierarchical tree of end items to
be accomplished.
 A work item is one small piece of the project.
 A work package is the lowest-level item.

1. Start new project
 Turn on the Project Guide
On the Tools menu, click Options, and then
click the Interface tab.
In the Project Guide settings section, select
the Display Project Guide check box.
 Manually set up a new project

Project – Project Information…
or View – Turn on project guide…
http://office.microsoft.com/en-us/project/HA102639631033.aspx

2. Tasks
 There are four major types of tasks:
1. Summary tasks - contain subtasks and their related
properties
2. Subtasks - are smaller tasks that are a part of a
summary task
3. Recurring tasks - are tasks that occur at regular
intervals
4. Milestones - are tasks that are set to zero duration and
are like interim goals in the project

Tools – Options… - check “Show project
summary task”

Tasks can be linked in four
ways
 Finish-Start FS Predecessor finishes and the other
starts
 Start-Finish S-F Task begins at the same time as its
predecessor
 Finish-Finish F-F Both tasks finish at the same time
 Start-Start S-S Start of the predecessor determines
when the other starts

Constraints
 Certain tasks need to be completed within a
certain date.
 Intermediate deadlines may need to be
specified.
 By assigning constraints to a task you can
account for scheduling problems.
 There are about 8 types of constraints and
they come under the flexible or inflexible
category.

Defining a Timeline
 Find an optimistic value, D(o),
 a pessimistic value, D(p) and
 a realistic value, D(r) .
 Then: Duration = ( D(o) + D(p) + 4 x
D(r) ) / 6

The importance of tracking
progress
 Techniques to manage projects effectively:
 Critical Path Management (CPM) and
 Program Evaluation and Review Techniques (PERT).
 They are similar and you will now often find the technique referred to as:
CPM/PERT.
 The technique involves using network models to trace the links between tasks
and to identify the tasks which are critical to meeting the deadlines.
Once you've identified the critical path, any delay on any part of the critical path
will cause a delay in the whole project.
It is where managers must concentrate their efforts.
 In MS Project, you use the Tracking Gantt diagram to show the critical path in
red and you can see the PERT diagram by looking at the Network view.

Gantt Chart View – critical
path
 A Gantt chart is a type of bar chart that
illustrates a project schedule.
 Critical path: View – More views… -
Detail Gant

Views
 Views allow you to examine your project from different
angles based on what information you want displayed at
any given time.
 You can use a combination of views in the same window
at the same time.
 Project Views are categorized into two types:
• Task Views (5 types)
• Resource Views (3 types)

Saving a baseline
 Baseline plan: The original project plans used to track
progress on a project.
 The baseline plan is a snapshot of your schedule at the
time that you save the baseline and includes information
about tasks, resources, and assignments.
 You can set a baseline for your project, enabling you to
compare your progress with the original plan and any
additional baselines you set at milestones throughout
your project.

Saving a Baseline
 Tools – Tracking – Save Baseline…
http://office.microsoft.com/home/video.aspx?assetid=ES102776241033&width=1024&height=768&startindex=0&CTT=11&O

Manage the project
resources:
 Resources are of three types:
 work resources, material resources and cost resources.
 Work resources complete tasks by expending time on them. They are usually people and
equipment that have been assigned to work on the project (you track their participation by the
amount of time they spend).
 Material resources are supplies and stocks that are needed to complete a project. You assign
material resources by the quantity that you need: two tons of gravel or 300 gallons of diesel
fuel, for instance. Because materials aren't measured by time, quantities usually affect only the
cost of your project. Materials affect dates or duration only when you have to wait for those
materials to become available.
 Cost. Cost resources are the new kid on the Project 2007 block, and they're strictly cost; no
time, no quantities—just dollars. Expenses, such as travel or fees, increase the project price
tag, but they aren't associated with work or material resources.
 You must start by identifying the resources available along with their
costs.
 Resource costs will be multiplied by duration to calculate project costs.
 You have to open the Resource sheet to specify the project resources
and costs.
• people
• equipme
nt
• supplies

Fields in the Resource Sheet may be blank or contain different types of information
depending on the type of resource. For example, a work resource doesn't have a Material
label, and costs are calculated initially as dollars per hour. Material resources have a cost
per unit—per pound, gallon, or piece—and the Material label field defines the units. Cost
resources receive a value only when you assign them to tasks.

Use the Detail Gantt view to
find slack (float)
 On the View menu, click More Views.
 In the Views list, click Detail Gantt, and then
click Apply.
 On the View menu, point to Table, and then
click Schedule. In the chart portion of the view,
slack appears as thin bars to the right of tasks,
with slack values adjoining the regular Gantt
bars.

To shorten a project
schedule
 Reduce duration of activities on critical
path
More resources
Change their scope

Technically Constrained Activity Sequence

Painting Project Showing Needed Resources

Create a budget for your
project
 Step 1:
Create budget resources for your project
 Step 2: Assign the budget resources to the projec
 Step 3: Enter values for the budget resources
 Step 4: Categorize resource costs according to th
 Step 5: Group resources to view how they compa

Step 1: Create budget resources
for your project
 Create Budget-Travel and Budget-Labor
on your resource sheet
View – Resource Sheet

Check
the check
box for
Budget

Step 2: Assign the budget resources
to the project summary task
 Gent chart view – Tools – Options –
View Tab – Show project summary
task (check box)
 Task is added to the top of the project list.
Select this task.
 Click on Button “Assign Resources”
 Select the two budget resources you
created earlier and click “Assign”

Step 3: Enter values for the
budget resources
 View – Resource Usage view
 Add Budget Cost and Budget Work fields
(columns):
Insert – Column – Budget Cost and Budget
Work
Add values for travel and Labor cost

Add: 15,000 for Budget-Travel and 30,000
for Budget-Labor (Budget Work column)

Step 4: Categorize resource costs
according to their budget type
Create custom filed (column)
 Open Resource Sheet view
 Tools – Customize – Fields
 Choose Resource text filed and rename:
Budget Type

Select Option Button: Roll down unless
manually entered
Add field to the resource sheet view: Insert – column – choose
Budget Type column ( you can now identify your resources as labor
or travel

Step 5: Group resources to view
how they compare against the
budget
 Resource Usage view
 Project – Group by: No Group –
Customize Group By… - Select the
Budget Type field

Viewing Project Cost
Information
 Right click the Select All button and click
Cost
 Or
 View – Table: Entry – Cost

Reports
 Cost Report: Reports - Reports – Costs
– Cash Flow:
Edit – Column list
 Project Summary report: Reports –
Overview – Project Summary

Scheduling
 One of the most
important things you
can do is schedule.
 Also one of the first things you should do!
 Tools help
Microsoft Project
OpenProj.org
OpenWorkbench.org
Coming up: Planning

Planning
 The bad news: time flies
 The good news: you’re the pilot!
 You must begin planning
immediately
Given limited information
Plan anyway and then
revise
Coming up: Creating a plan:
Things to know

Creating a plan: Things to know
 Scope
 Context. How does the software to be built fit into a larger system,
product, or business context and what constraints are imposed as a
result of the context?
 Information objectives. What customer-visible data objects
(Chapter 8) are produced as output from the software? What data
objects are required for input?
 Function and performance. What function does the software
perform to transform input data into output? Are any special
performance characteristics to be addressed?
 Software project scope must be unambiguous and
understandable at the management and technical
levels. Coming up: Creating a plan:
Things to do

Creating a plan: Things to do
 Problem Decomposition: Sometimes called
partitioning or problem elaboration
 Once scope is defined …
 It is decomposed into constituent functions
 It is decomposed into user-visible data objects
or
 It is decomposed into a set of problem classes
 Decomposition process continues until all
functions or problem classes have been defined
(this won’t be far at the beginning of your
project) Coming up: Create a
schedule

Schedule
 List of tasks
With dates
With assigned resources (people)
With durations
With predecessors and successors
 How do you get buy-in from the team for a
schedule?
History
Increments Coming up: Schedule Terms

Schedule Terms
 Critical path
 Sequence of tasks that form the longest path to
completion of the project. Any delay on any of these
will make the overall completion date move.
 Slack
 Amount of time a task can be delayed without
affecting the overall completion date.
 Start slack - amount before task needs to start
 Finish slack - amount before task needs to finish
 Milestone - An import date in the schedule
 Dependencies - relationship between tasks
Coming up: Schedule
Dependencies

Schedule Dependencies
 FS - Finish to start (most common)
 A FS B. B doesn’t start until A is finished
 Build wall FS Paint wall
 FF - Finish to finish
 A FF B. B doesn’t finish before A is finished
 Write final chapter FF Complete Index
 SS - Start to start
 A SS B. B doesn’t start until A has started
 Project funded SS project management activities begin
 SF - Start to finish
 A SF B. B doesn’t finish before A has started
 Once A starts, B is allowed to finish
 B=Baby sit a child, A=parent comes home Coming up: Resource
Leveling

Resource Leveling
 A process to examine a project for an unbalanced
use of people and to resolve over-allocations or
conflicts
 Happens when multiple tasks are scheduled at the
same time for the same person
 Solution:
 Make tasks sequential by introducing “fake”
dependencies
 Split resource usage among tasks (50% on task 1, 50%
on task 2)
Coming up: Auto Resource
Leveling

Auto Resource Leveling
 Some tools (not Open Project) provide auto
resource leveling
 Tool automatically ensures no person works
over 100% of the time (automatically makes
tasks sequential)
 Advantageous because this does not
introduce “fake” dependencies
Coming up: Gantt Chart

Gantt Chart
Coming up: Finding
Critical Path

Finding Critical Path
 Draw a network diagram of the activities
 Determine the Early Start (ES) of each
node. Work from beginning node (ES=0)
to final node
 ES - earliest time the activity can start
 ES = Max(ESprevNode + DurationPrevNode)
Coming up: Finding Critical
Path
A
C
B
ES: 4
ES: 2
10
7 ES: ??

Finding Critical Path
 Determine the Late Start (LS) of each
node. Work from the final node to the
beginning node.
The latest time the activity can start without
changing the end date of the project
LS = MIN(LSnext - DurationNode)
For the last node LS = ES
Coming up: Example
A
C
B
LS: ?
LS: ?
10
7 LS: 12
A
C
B
LS: ?
LS: 13
10
7
LS: 12

Example
Here's the example:
Activity Description Predecessor Duration
A Product design (None) 5 months
B Market research (None) 1
C Production analysis A 2
D Product model A 3
E Sales brochure A 2
F Cost analysis C 3
G Product testing D 4
H Sales training B, E 2
I Pricing H 1
J Project report F, G, I 1Coming up: Example Node
Network

Example Node Network
A
E
D
C
I
G
F
J
B
H
Here's the example:
B Market research(None) 1
C Production A 2
D Product model A 3
F Cost analysis C 3
I Pricing H 1
J Project report F, G, I 1
ES:0
LS:
ES:5
LS:
ES:0
LS:
ES:5
LS:
ES:5
LS:
ES:7
LS:
ES:9
LS:
ES:8
LS:
ES:7
LS:
ES:12
LS:
Coming up: Example Node
Network
ES(H)
ES(E)+dur(E) = 5 + 2 = 7
ES(B)+dur(B) = 0 + 1 = 1
Maximum = 7 = ES(H)
ES(J)
ES(F)+dur(F) = ?
ES(G)+dur(G) = ?
ES(I) + dur(I) = ?
Maximum = ? = ES(J)

A
E
D
C
I
G
F
J
B
H
Here's the example:
C Production A 2
D Product model A 3
F Cost analysis C 3
I Pricing H 1
ES:0
LS:0
ES:5
LS:5
ES:0
LS:8
ES:5
LS:7
ES:5
LS:7
ES:7
LS:9
ES:9
LS:11
ES:8
LS:8
ES:7
LS:9
ES:12
LS:12
Coming up: Example Node
Network
LS(F)
LS(J)-dur(F) = 12 – 3
= 9
LS(A) =
LS(C) – dur(A) = 7 – 5 = 2
LS(D) – dur(A) = 5 – 5 = 0
LS(E) – dur (A) = 7 – 5 = 2
Minimum = 0 = LS(A)

A
E
D
C
I
G
F
J
B
H
Here's the example:
C Production A 2
D Product model A 3
F Cost analysis C 3
I Pricing H 1
ES:0
LS:0
ES:5
LS:5
ES:0
LS:8
ES:5
LS:7
ES:5
LS:7
ES:7
LS:9
ES:9
LS:11
ES:8
LS:8
ES:7
LS:9
ES:12
LS:12
Coming up: Game Development In-Class
Exercise

Game Development In-Class Exercise
TASK DURATION (days) PREDECESSORs
A Graphics Engine 14
B Sound Engine 5 I
C Music Engine 5 J
D Input Engine 10 A
E Gameplay/general
programming
31 B, C, D
F Physics 7 E
G 2D Artwork 14
H 3D Artwork 21 G
I Sound Effects 14
J Music 9
K Level Design 21 F, H
Find the critical path
Coming up: Review
Questions

Schedule Example
 Lets try to schedule this work among our
three developers “John, Mary, Carl”
Coming up: Scheduling
Steps
TASK DURATION (days) PREDECESSORs
A Graphics Engine 14
B Sound Engine 5 I
C Music Engine 5 J
D Input Engine 10 A
E Gameplay/general
programming
31 B, C, D
F Physics 7 E
G 2D Artwork 14
H 3D Artwork 21 G
I Sound Effects 14
J Music 9
K Level Design 21 F, H

Scheduling Steps
 Add in all the tasks (preferably in a hierarchy)
 Add in all the dependencies
 Break down large tasks into smaller tasks.
Optimally (in Dan Fleck’s opinion) you want
to schedule so the duration of each smallest
task is at most 3-5 days
 Assign people (resources) to tasks
 Level your resources
Coming up: Classic Mistakes

Classic Mistakes
 Overly optimistic schedule
 Failing to monitor schedule
 Failing to update schedule
 Adding people to a late project
 Failure to manage expectations of others
 Leaving out a task
Coming up: Scope Creep

Earned Value Management
 How much work you planned to have accomplished by
now (in dollars or hours) called the Planned Value
 How much you have actually spent by now (in dollars or
hours), called Actual Cost
 The value, in terms of your baseline budget, of the work
accomplished by now (in dollars or hours), called the
Earned Value!
Coming up: Earned Value
Management
Idea is to link schedule and cost together to monitor
both in the same “units” of value

 Planned value (PV) - the value of all resources
needed to meet the project’s objectives
 Each objective of a project has an associated
planned value
 Budgeted (cost) at completion (BAC) - The sum
of all the PVs
 Earned value (EV) - the amount of value
completed at any point during the project
 Actual Cost (AC) - actual amount of money you
have spent so far. In a perfect project AC and
EV are the same. Coming up: Earned Value
Management Example

Example
 We’ve budgeted $200 to buy, setup, network
and test a new system
 Our planned values (PVs) of each task are:
 Buy - $50, Setup - $75, network - $50, test - $25
 Our BAC is therefore $200
 We’ve now completed phase one, and thus our
earned value (EV) is now $50.
 To do this we spent $60 (our actual cost (AC))
Coming up: Earned Value
Management Example

Example
 Schedule performance index (SPI)
 EV / PV --> 50/50 = 1 (perfect).
 Our group is on schedule
 Cost performance index (CPI)
 EV / AC --> 50/60 = 0.83
 For every dollar spent, I get 83 cents worth of work.
 Estimated cost at completion (EAC)
 BAC / CPI = 200 / 0.83 = $240.96
 Schedule Variance (SV) : EV - PV
 Cost Variance (CV) : EV - AC Coming up: EVM Example 2 from:
http://www.hyperthot.com/pm_cscs.htm
Memorization Hint:
Most equations
begin with earned
value

EVM Example 2 from:
http://www.hyperthot.com/pm_cscs.htm
 PLANNED VALUE (Budgeted cost of the work scheduled)
= 18 + 10 + 16 + 6 = $50
 EARNED VALUE (Budgeted cost of the work performed)
= 18 + 8 + 14 + 0 = $40
 ACTUAL COST (of the work performed) = $45 (Data from Acct.
System)
 Therefore:
 Schedule Variance = 40 - 50 = -$10
 Schedule Performance Index = 40 / 50 = 0.8 Coming up: What is
earned value?
What is planned value at time X?
What is earned value at time X?
Line is at 16, blue
bar ends at 14
Line is at 6
Earned – Planned. Perfect is?

What is earned value?
 A. The amount of money you get upon
completion of a task
 B. The value of an activity
 C. The value of the work completed by
now in the schedule
 D. The value of all activities planned to be
completed by now in the schedule
Coming up: Why do you use
earned value management?

Why do you use earned value
management?
 A.It is required by my contract
 B. Measuring value give you more
information than measuring cost or time
alone
 C. I don’t use it
 D. It guarantees my project will be done
on time
Coming up: Scheduling
Rules of Thumb

Scope Creep
 The scope of your project is all the work you
initially planned to do.
 Scope creep is when your project gets new
tasks throughout it’s lifetime without adding
more resources to handle new tasks. The
scope is “creeping” up…
 Scope changes are OK, and really
unavoidable… that’s fine. However you must
update the resources (time, features or
people accordingly)
Coming up: Why would
scope changes occur?
Scope
BOO!

Why would scope changes
occur?
 A. You get more money to do more things
 B. The customer asks you to do
something extra because “it is critical for
success”
 C. A competing product has a feature that
you must have to be competitive
 D. All of these
Coming up: Which are
causes of scope creep?

Scope Change versus Creep
Your company has a $1million dollar
contract with a defined scope.
Scope change:
Customer: please add all these requirements,
and I’ll increase the contract to $2million dollars
Manager: Certainly! 
Scope creep:
Customer: please add all these requirements, and I’ll be
really happy.
Manager: Certainly! 
Change is good!

Which are causes of scope creep?
 A. poor change control
 B. lack of proper initial identification of
what is required to satisfy project
objectives
 C. a weak project manager
 D. all of these
Source: Wikipedia: Scope Creep
Coming up: Managing Scope

Managing Scope
 How to deal with the inevitable “Scope
creep”?
 Joint Application Development and
prototyping
 Formal change approval
 Defer additional requirements as future
system enhancements
Scope
Coming up: Managing Risk

Managing Risk
 Document your risks in a risk management plan
1 Description of risk
2 Likelihood of occurrence (0-100%)
3 Impact - 1(low)  5 (high), or cost $20,000
4 Exposure = Impact * Likelihood
5 Mitigation strategy
 How to lessen the impact of the risk
 How to lessen the likelihood
 An action plan if risk occurs
 Update and track your risks
 Communicate your risks to upper managementComing up: Projects get into
trouble when…

Coming up: Common-Sense
Approach to Projects
Projects get into trouble when…
 Software people don’t understand their customer’s needs.
 The product scope is poorly defined.
 Changes are managed poorly.
 The chosen technology changes.
 Business needs change [or are ill-defined].
 Deadlines are unrealistic.
 Users are resistant.
 Sponsorship is lost [or was never properly obtained].
 The project team lacks people with appropriate skills.
 Managers [and practitioners] avoid best practices and lessons
learned.

Coming up: References
Common-Sense Approach to Projects
 Start on the right foot. This is accomplished by working hard (very hard) to
understand the problem that is to be solved and then setting realistic
objectives and expectations.
 Maintain momentum. The project manager must provide incentives to
keep turnover of personnel to an absolute minimum, the team should
emphasize quality in every task it performs, and senior management
should do everything possible to stay out of the team’s way.
 Track progress. For a software project, progress is tracked as work
products (e.g., models, source code, sets of test cases) are produced and
approved (using formal technical reviews) as part of a quality assurance
activity.
 Make smart decisions. In essence, the decisions of the project manager
and the software team should be to “keep it simple.”
 Conduct a postmortem analysis. Establish a consistent mechanism for
extracting lessons learned for each project.

References
 www.projity.com
 Wikipedia: Project Management
 Pressman R., Software Engineering A Practical Approach, Ch 21
 Pressman R., Software Engineering A Practical Approach, Slides for Ch 21
 Kazman R., The CIO, People Issues, Project & Change Management,
kazman.shidler.hawaii.edu/619ch12.ppt
 Pratt M, Earned Value Management,
http://www.computerworld.com/action/article.do?
command=viewArticleBasic&articleId=110065&intsrc=article_pots_bot
End of presentation

Next week
 Review student essays (due in a week)
 Homework 6 due
Please submit sceenshots (in a word
document or pdf) to blackboard
 Testing

Analyzing Cost-Time Trade-
Offs
 There are always cost-time trade-offs in
project management.
 You can completing a project early by hiring more
workers or running extra shifts.
 There are often penalties if projects extend
beyond some specific date, and a bonus may be
provided for early completion.
 Crashing a project means expediting some
activities to reduce overall project completion
time and total project costs.

Cost to Crash
 To assess the benefit of crashing certain activities,
either from a cost or a schedule perspective, the
project manager needs to know the following times
and costs.
 Normal time (NT) is the time necessary to complete
and activity under normal conditions.
 Normal cost (NC) is the activity cost associated
with the normal time.
 Crash time (CT) is the shortest possible time to
complete an activity.
 Crash cost (CC) is the activity cost associated with
the crash time.

Cost to Crash per Period
The Cost to Crash per Time Period =
CC − NC
NT − CT
Crash Cost − Normal Cost
Normal Time − Crash Time

Linear cost assumption
8000 —
7000 —
6000 —
5000 —
4000 —
3000 —
0 —
Directcost(dollars)
| | | | | |
5 6 7 8 9 10 11
Time (weeks)
Crash cost (CC)
Normal cost (NC)
(Crash time) (Normal time)
Estimated costs
for a 2-week
reduction, from
10 weeks to
8 weeks
5200
Cost-Time Relationships in Cost Analysis

 The objective of cost analysis is to
determine the project schedule that
minimizes total project costs.
 A minimum-cost schedule is
determined by starting with the normal
time schedule and crashing activities
along the critical path in such a way that
the costs of crashing do not exceed the
savings in indirect and penalty costs.
Minimizing CostsMinimizing Costs

 Use these steps to determine the minimum cost
schedule:
1. Determine the project’s critical path(s).
2. Find the activity or activities on the critical path(s)
with the lowest cost of crashing per time unit.
3. Reduce the time for this activity until…
a. It cannot be further reduced or
b. Until another path becomes critical, or
c. The increase in direct costs exceeds the savings that result
from shortening the project (which lowers indirect costs &
penalties).
4. Repeat this procedure until the increase in direct
costs is larger than the savings generated by
shortening the project.
Minimum Cost ScheduleMinimum Cost Schedule

Regular & Crash Times & Cost to Crash
Activity Regular Time Crash Time
Total Cost
to Crash
Cost Per Unit
of Crash Time
$ A* 2 1 $1,000
$ B* 4 2 $ 500
$ C* 2 2 C
$ D* 1 1 C
$ E 3 1 $ 200
$ F* 2 2 C
$ G* 1 1 C
$ H* 12 8 $ 800
$ I* 8 5 $1,200
$ J 6 6 C
$ K 5 3 $ 600
$ L*
TOTAL
* Activities on
critical path
3 3 C
$4,300

START
A
2
B
4
C
2
D
1
F
2
G
1
H
12
J
6
I
8
K
5
L
3
END
E
3
Network for a Software Purchasing Project using
Normal Times

IF ALL ACTIVITIES ARE CRASHED
STA
RT
A
1
B
2
C
2
D
1
F
2
G
1
H
8
J
6
I
5
K
3
L
3
END
E
1
(1,5,4)
(8,8,0)(6,6,0)(5,5,0)(0,0,0) (1,1,0) (3,3,0)
(26)
(23,23,0)
(17,18,1)
(17,17,0)
(9,20,11)
(9,9,0)
*What is the minimum amount of time to complete the project?
*What is the additional cost involved in achieving this reduction in time?

STA
RT
A
2
B
4
C
2
D
1
F
2
G
1
H
12
J
6
I
8
K
5
L
3
END
E
3
What is the minimum cost to achieve minimum time schedule for project
Total Cost
to Crash
Cost Per Unit
of Crash
Time
$ A 2 1 $1,000 $1,000
$ B 4 2 $ 500 $ 250
$ C 2 2 C C
$ D 1 1 C C
$ E 3 1 $ 200 $ 100
$ F 2 2 C C
$ G 1 1 C C
$ H 12 8 $ 800 $ 200
$ I 8 5 $1,200 $ 400
$ J 6 6 C C
$ K 5 3 $ 600 $ 300
$ L 3 3 C
$4,300
C

STA
RT
A
2
B
4
C
2
D
1
F
2
G
1
H
12
J
6
I
8
K
5
L
3
END
E
3
What is the minimum cost to achieve minimum time schedule for project
Total Cost
to Crash
Cost Per Unit
of Crash
Time
$ A 2 1 $1,000 $1,000
$ B 4 2 $ 500 $ 250
$ C 2 2 C C
1 1 C C
$ E 3 1 $ 200 $ 100
$ F 2 2 C C
$ G 1 1 C C
$ H 12 8 $ 800 $ 200
$ I 8 5 $1,200 $ 400
$ J 6 6 C C
$ K 5 3 $ 600 $ 300
$ L 3 3 C
$4,300
C

STA
RT
A
2
B
4
C
2
D
1
F
2
G
1
H
12
J
6
I
8
K
5
L
3
END
E
3
What is the minimum cost to reduce project time to 30 months
Total Cost
to Crash
Cost Per Unit
of Crash
Time
$ A 2 1 $1,000 $1,000
$ B 4 2 $ 500 $ 250
$ C 2 2 C C
1 1 C C
$ E 3 1 $ 200 $ 100
$ F 2 2 C C
$ G 1 1 C C
$ H 12 8 $ 800 $ 200
$ I 8 5 $1,200 $ 400
$ J 6 6 C C
$ K 5 3 $ 600 $ 300
$ L 3 3 C
$4,300
C

STA
RT
A
2
B
4
C
2
D
1
F
2
G
1
H
12
J
6
I
8
K
5
L
3
END
E
3
What is the optimal schedule if I incur a penalty of $280 for each month
above the absolute minimum project time of 26 months?
Total Cost
to Crash
Cost Per Unit
of Crash
Time
$ A 2 1 $1,000 $1,000
$ B 4 2 $ 500 $ 250
$ C 2 2 C C
1 1 C C
$ E 3 1 $ 200 $ 100
$ F 2 2 C C
$ G 1 1 C C
$ H 12 8 $ 800 $ 200
$ I 8 5 $1,200 $ 400
$ J 6 6 C C
$ K 5 3 $ 600 $ 300
$ L 3 3 C
$4,300
C

© 2007 Pearson Education
Calculating total CostCalculating total Cost
AddingAdding Direct, Penalty & Overhead CostsDirect, Penalty & Overhead Costs
The overhead (indirect) costs are $200 per day
There is a penalty of $100/day for completing project in
more than 12 days

Total Cost ProblemTotal Cost Problem

Assessing Risks
 Risk is a measure of the probability and
consequence of not reaching a defined
project goal.
 A major responsibility of the project
manager at the start of a project is to
develop a risk-management plan.
 A Risk-Management Plan identifies the
key risks to a project’s success and
prescribes ways to circumvent them.

ProbabilisticProbabilistic
Time EstimatesTime Estimates
MeanMean
mmaa bb TimeTime
ProbabilityProbability
Beta
Distribution
PessimisticOptimis
tic

TimeTime
NormalNormal
DistributionDistribution
MeanMean
aa bbmm
33σσ 33σσ
Area underArea under
curvecurve
between abetween a
and b isand b is
99.74%99.74%
ProbabilisticProbabilistic
Time EstimatesTime Estimates

te =
a + 4m + b
6
Mean
σσ22
== ( )bb –– aa
66
22
VarianceVariance
Probabilistic Time EstimatesProbabilistic Time Estimates
Calculating Means and Variances for a Beta
Distribution
Where:
a is the Optimistic
estimate
b is the pessimistic
estimate
m is the most likely
estimate

Optimistic Likely Pessimistic
Activity (a) (m) (b)
Time Estimates (wk)
A 11 12 13
B 7 8 15
C 5 10 15
D 8 9 16
E 14 25 30
F 6 9 18
G 25 36 41
St. John’s HospitalSt. John’s Hospital
A F
I
C G Finish
D
E
HB J
K
Start

Activity B
Most
Optimistic Likely Pessimistic
(a) (m) (b)
7 8 15
A F
I
C G Finish
D
E
HB J
K
Start
te = = 9 weeks
7 + 4(8) + 15
6
σ2
= = 1.78( )15 - 7
6
2
Calculating Means and Variances

Optimistic Likely Pessimistic Expected Variance
Activity (a) (m) (b) Time (te ) (σ2
)
Time Estimates (wk) Activity Statistics
A 11 12 13 12 0.11
B 7 8 15 9 1.78
C 5 10 15 10 2.78
D 8 9 16 10 1.78
E 14 25 30 24 7.11
F 6 9 18 10 4.00
G 25 36 41 35 7.11
H 35 40 45 40 2.78
I 10 13 28 15 9.00
J 1 2 15 4 5.44
K 5 6 7 6 0.11

K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
FinishStart
A
12
F
10
0 9
9 33
9 19 19 59
22 5712 22
59 63
12 27
12 22 63 690 12
48 63
53 63
59 63
24 59
19 59
35 59
14 24
9 19
2 14
0 9
63 69
Earliest start time Earliest finish time
Latest start time Latest finish time

σ2
= Σ (variances of activities) z =
T – TE
σ2
σ2
= 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89
z =
72 – 69
11.89
What is the Probability of finishing the
project in 72 weeks?Given that: Critical Path = B - D - H - J - K
T = 72 Weeks TE = 69 Weeks
Analyzing ProbabilitiesAnalyzing Probabilities
From Normal Distribution appendix
Pz = .8078 ≈ .81
= .87

.00 .01 .02 .03 .04 .05 .06 .07 .08 .09
.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359
.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5753
.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141
.3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517
.4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879
.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224
.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549
.7 .7580 .7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852
.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133
.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389
1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621
1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830
1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015
1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177
1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319
1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441
1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545
1.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633
1.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706
1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767
2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817
2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857
2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890
2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .9916
2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936
2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952
2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964
2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974
2.8 .9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .9981
2.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986
3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990
3.1 .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993
3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .9995
3.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997
3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998
NORMAL DISTRIBUTION TABLE
z0 +∞∞Ğ

Project duration (weeks)Project duration (weeks)
6969 7272
NormalNormal
distribution:distribution:
Mean = 69Mean = 69
weeks;weeks;
σσ = 3.45 weeks= 3.45 weeksProbabilityProbability
ofof
exceedingexceeding
72 weeks is72 weeks is
0.19220.1922
Probability of Completing Project On TimeProbability of Completing Project On Time
of meetingof meeting
thethe
scheduleschedule
is 0.8078is 0.8078
Length ofLength of
criticalcritical
pathpath

Optimistic Likely Pessimistic Expected Variance
Activity (a) (m) (b) Time (te ) (σ2
)
Time Estimates (Months) Activity Statistics
A 1 2 3
B 3 4 6
C 2 2 2
D 1 1 1
E 1 3 5
F 1 2 3
G 1 1 1
H 8 12 14
I 7 8 10
J 5 6 7
K 4 5 6
L 2 3 6
Software Purchasing ProjectSoftware Purchasing Project

START
A
2
B
4.17
C
2
D
1
F
2
G
1
H
11.67
J
6
I
8.17
K
5
L
3.33
END
E
3
Network for a Software Purchasing Project using the
Mean Times
Critical Path: A—B—C—D—F—G—H—I—L
Expected Time to complete the project:
2+4.17+2+1+2+1+11.67+8.17+3.33 = 35.33

What is the probability in
finishing in less than 37
months?

What is the probability in
finishing in less than 31
months?

Copyright 2009 John Wiley & Sons, Inc. 9-133
Lecture Outline
 Project Planning
 Project Scheduling
 Project Control
 CPM/PERT
 Probabilistic Activity Times
 Project Crashing and Time-Cost
Trade-off

What is a Project?
 Project
 unique, one-time operational activity or effort
 Examples
 constructing houses, factories, shopping malls, athletic stadiums
or arenas
 developing military weapons systems, aircrafts, new ships
 launching satellite systems
 constructing oil pipelines
 developing and implementing new computer systems
 planning concert, football games, or basketball tournaments
 introducing new products into market

Project Elements
 Objective
 Scope
 Contract requirements
 Schedules
 Resources
 Personnel
 Control
 Risk and problem analysis

Project Management Process
 Project planning
 Project scheduling
 Project control
 Project team
 made up of individuals from various areas and
departments within a company
 Matrix organization
 a team structure with members from functional areas,
depending on skills required
 Project Manager
 most important member of project team

Project Scope
 Scope statement
a document that provides an understanding,
justification, and expected result of a project
 Statement of work
written description of objectives of a project
 Work breakdown structure
breaks down a project into components,
subcomponents, activities, and tasks

Work Breakdown Structure for Computer Order
Processing System Project
Work Breakdown Structure for Computer Order
Processing System Project

 Organizational Breakdown Structure
 a chart that shows which organizational units are
responsible for work items
 Responsibility Assignment Matrix
 shows who is responsible for work in a project

Project Scheduling
 Steps
Define activities
Sequence activities
Estimate time
Develop schedule
 Techniques
Gantt chart
CPM
PERT
Microsoft Project

Gantt Chart
 Graph or bar chart with a bar for each
project activity that shows passage of
time
 Provides visual display of project
schedule
 Slack
 amount of time an activity can be delayed
without delaying the project

| | | | |
Activity
Design house
and obtain
financing
Lay foundation
Order and
receive
materials
Build house
Select paint
Select carpet
Finish work
00 22 44 66 88 1010
MonthMonth
MonthMonth
11 33 55 77 99
Example of Gantt Chart

Project Control
 Time management
 Cost management
 Quality management
 Performance management
 Earned Value Analysis
 a standard procedure for numerically measuring a
project’s progress, forecasting its completion date and
cost and measuring schedule and budget variation
 Communication
 Enterprise project management

CPM/PERT
 Critical Path Method (CPM)
 DuPont & Remington-Rand (1956)
 Deterministic task times
 Activity-on-node network construction
 Project Evaluation and Review Technique
(PERT)
 US Navy, Booz, Allen & Hamilton
 Multiple task time estimates
 Activity-on-arrow network construction

Project Network
 Activity-on-node (AON)
 nodes represent activities,
and arrows show
precedence relationships
 Activity-on-arrow (AOA)
 arrows represent activities
and nodes are events for
points in time
 Event
 completion or beginning of
an activity in a project
1 32
BranchBranch
NodeNode

AOA Project Network
for a House
33
22 00
11
33
11 11
11
1 2 4 6 7
3
5
LayLay
foundationfoundation
Design houseDesign house
and obtainand obtain
financingfinancing
Order andOrder and
receivereceive
materialsmaterials
DummyDummy
FinishFinish
workwork
SelectSelect
carpetcarpet
SelectSelect
paintpaint
BuildBuild
househouse

Concurrent ActivitiesConcurrent Activities
2 3
Lay foundationLay foundation
Order materialOrder material
(a)(a) Incorrect precedenceIncorrect precedence
relationshiprelationship
(b)(b) Correct precedenceCorrect precedence
relationshiprelationship
3
42
DummyDummy
LayLay
foundationfoundation
Order materialOrder material
11
22 00

AON Network for House
Building Project
1
3
2
2
4
3
3
1 5
1
6
1
7
1Start
Design
house and
obtain
financing
Order and
receive
materials
Select paint
Select carpet
Lay foundations Build house
Finish work

1
3
2
2
4
3
3
1 5
1
6
1
7
1Start
Critical Path
 Critical pathCritical path

Longest pathLongest path
through a networkthrough a network
 Minimum projectMinimum project
completion timecompletion time
A:A: 1-2-4-71-2-4-7
3 + 2 + 3 + 1 = 9 months3 + 2 + 3 + 1 = 9 months
B:B: 1-2-5-6-71-2-5-6-7
3 + 2 + 1 + 1 + 1 = 8 months3 + 2 + 1 + 1 + 1 = 8 months
C:C: 1-3-4-71-3-4-7
3 + 1 + 3 + 1 = 8 months3 + 1 + 3 + 1 = 8 months
D:D: 1-3-5-6-71-3-5-6-7
3 + 1 + 1 + 1 + 1 = 7 months3 + 1 + 1 + 1 + 1 = 7 months

Activity Start Times
1
3
2
2
4
3
3
1 5
1
6
1
7
1Start
Start at 3
months
Start at 6
months
Start at 5
months
Finish at 9
months
Finish

Mode Configuration
1 0 3
3 0 3
Activity number
Activity duration
Earliest start
Latest start
Earliest finish
Latest finish

Forward Pass
 Start at the beginning of CPM/PERT network to
determine the earliest activity times
 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

Earliest Activity Start
and Finish Times
1 0 3
1
2 3 5
2
3 3 4
1 5 5 6
1
4 5 8
3
6 6 7
1
7 8 9
1
Start
Design
house and
obtain
financing
Select pain
Lay foundations
Select
carpet
Build house
Finish
work
Order and receive
materials

Backward Pass
 Determines latest activity times by starting at
the end of CPM/PERT network and working
forward
 Latest Start Time (LS)
 Latest time an activity can start without delaying
critical path time
LS= LF - t
 Latest finish time (LF)
 latest time an activity can be completed without
delaying critical path time
 LS = minimum LS of immediate predecessors

Latest Activity Start
and Finish Times
1 0 3
1 0 3
2 3 5
2 3 5
3 3 4
1 4 5 5 5 6
1 6 7
4 5 8
3 5 8
6 6 7
1 7 8
7 8 9
1 8 9
Start
Design
house and
obtain
financing
Select pain
Lay foundations
Select
carpet
Build house
Finish
work
Order and receive
materials

* Critical Path
009999999988888888*7*7
11777788886666777766
11666677775555666655
008888888855555555*4*4
11444455553333444433
005555555533333333*2*2
003333333300000000*1*1
Slack SEFEFLFLFESESLSLSActivity
Activity Slack

Probabilistic Time Estimates
 Beta distribution
 a probability distribution traditionally used in
CPM/PERT
aa = optimistic estimate= optimistic estimate
mm = most likely time estimate= most likely time estimate
bb = pessimistic time estimate= pessimistic time estimate
wherewhere
Mean (expected time):Mean (expected time): tt ==
aa + 4+ 4mm ++ bb
66
Variance:Variance: σσ 22
==
bb -- aa
66
22

Examples of Beta DistributionsExamples of Beta Distributions
PP(time)(time)
PP(time)(time)
PP(time)(time)
TimeTime
aa mmtt bbaa mm tt bb
mm == tt
TimeTime
TimeTime
bbaa

Project Network with Probabilistic
Time Estimates: Example
Start Finish2
3,6,9
3
1,3,5
1
6,8,10
5
2,3,4
6
3,4,5
4
2,4,12
7
2,2,2
8
3,7,11
9
2,4,6
1
0
1,4,7
1
1
1,10,13
Equipment
installation
System
development
Position
recruiting
Equipment testing
and modification
Manual
testing
Job Training
Orientation
System
training
System
testing
Final
debugging
System
changeover

Activity Time EstimatesActivity Time Estimates
11 66 88 1010 88 0.440.44
22 33 66 99 66 1.001.00
33 11 33 55 33 0.440.44
44 22 44 1212 55 2.782.78
55 22 33 44 33 0.110.11
66 33 44 55 44 0.110.11
77 22 22 22 22 0.000.00
88 33 77 1111 77 1.781.78
99 22 44 66 44 0.440.44
1010 11 44 77 44 1.001.00
1111 11 1010 1313 99 4.004.00
TIME ESTIMATES (WKS)TIME ESTIMATES (WKS) MEAN TIMEMEAN TIME VARIANCEVARIANCE
ACTIVITYACTIVITY aa mm bb tt бб22

Activity Early, Late Times,Activity Early, Late Times,
and Slackand Slack
ACTIVITYACTIVITY tt бб22
ESES EFEF LSLS LFLF SS
11 88 0.440.44 00 88 11 99 11
22 66 1.001.00 00 66 00 66 00
33 33 0.440.44 00 33 22 55 22
44 55 2.782.78 88 1313 1616 2121 88
55 33 0.110.11 66 99 66 99 00
66 44 0.110.11 33 77 55 99 22
77 22 0.000.00 33 55 1414 1616 1111
88 77 1.781.78 99 1616 99 1616 00
99 44 0.440.44 99 1313 1212 1616 33
1010 44 1.001.00 1313 1717 2121 2525 88
1111 99 4.004.00 1616 2525 1616 2525 00

Start Finish
1 0 8
8 1 9
3 0 3
3 2 5
4 8 13
5 16 21
6 3 7
4 5 9
7 3 5
2 14 16
9 9 13
4 12 16
10 13 17
1 0 3
2 0 6
6 0 6
5 6 9
3 6 9
8 9 16
7 9 16
11 16 25
9 16 25
Critical Path
Earliest, Latest, and Slack

σ2
= б2
2 +
б5
2
+ б8
2
+ б11
2
σ = 1.00 + 0.11 + 1.78 + 4.00
= 6.89 weeks
Total project variance

Probabilistic Network Analysis
Determine probability that project isDetermine probability that project is
completed within specified timecompleted within specified time
wherewhere
µµ == ttpp = project mean time= project mean time
σσ == project standard deviationproject standard deviation
x =x = proposed project timeproposed project time
Z =Z = number of standard deviations xnumber of standard deviations x
is from meanis from mean
ZZ ==
xx -- µµ
σσ

Normal Distribution Of Project Time
µµ == ttpp TimeTimexx
Zσ

Southern Textile Example
What is the probability that the project is completedWhat is the probability that the project is completed
within 30 weeks?within 30 weeks?
σσ 22
= 6.89 weeks= 6.89 weeks
σσ = 6.89= 6.89
σσ = 2.62 weeks= 2.62 weeks
ZZ ==
==
= 1.91= 1.91
xx -- µµ
σσ
30 - 2530 - 25
2.622.62
From Table A.1, (appendix A) aFrom Table A.1, (appendix A) a ZZ score of 1.91 corresponds to ascore of 1.91 corresponds to a
probability of 0.4719. Thusprobability of 0.4719. Thus PP(30) = 0.4719 + 0.5000 = 0.9719(30) = 0.4719 + 0.5000 = 0.9719
µµ = 25= 25 Time (weeks)Time (weeks)xx = 30= 30
PP((xx ≤≤ 30 weeks)30 weeks)

Southern Textile Example
µµ = 25= 25 TimeTime
(weeks)(weeks)
xx = 22= 22
PP((xx ≤≤ 22 weeks)22 weeks)
What is the probability that the project is completedWhat is the probability that the project is completed
within 22 weeks?within 22 weeks?
σσ 22
= 6.89 weeks= 6.89 weeks
σσ = 6.89= 6.89
σσ = 2.62 weeks= 2.62 weeks
ZZ ==
==
= -1.14= -1.14
xx -- µµ
σσ
22 - 2522 - 25
2.622.62
From Table A.1 (appendix A) aFrom Table A.1 (appendix A) a ZZ score of -1.14 corresponds to ascore of -1.14 corresponds to a
probability of 0.3729. Thusprobability of 0.3729. Thus PP(22) = 0.5000 - 0.3729 = 0.1271(22) = 0.5000 - 0.3729 = 0.1271

Project Crashing
 Crashing
 reducing project time by expending additional
resources
 Crash time
 an amount of time an activity is reduced
 Crash cost
 cost of reducing activity time
 Goal
 reduce project duration at minimum cost

1
1
2
2
8
4
1
2
3
4 5
4
6
4
7
4
Project Crashing: Example

Project Crashing: Example
(cont.)
$7,000 –
$6,000 –
$5,000 –
$4,000 –
$3,000 –
$2,000 –
$1,000 –
–
| | | | | | |
0 2 4 6 8 10 12 14 Weeks
Normal activity
Normal time
Normal cost
Crash time
Crashed activity
Crash cost
Slope = crash cost per week

Normal Activity and Crash
Data
TOTALTOTAL
NORMALNORMAL CRASHCRASH ALLOWABLEALLOWABLE CRASHCRASH
TIMETIME TIMETIME NORMALNORMAL CRASHCRASH CRASH TIMECRASH TIME COST PERCOST PER
ACTIVITYACTIVITY (WEEKS)(WEEKS) (WEEKS)(WEEKS) COSTCOST COSTCOST (WEEKS)(WEEKS) WEEKWEEK
11 1212 77 $3,000$3,000 $5,000$5,000 55 $400$400
22 88 55 2,0002,000 3,5003,500 33 500500
33 44 33 4,0004,000 7,0007,000 11 3,0003,000
44 1212 99 50,00050,000 71,00071,000 33 7,0007,000
55 44 11 500500 1,1001,100 33 200200
66 44 11 500500 1,1001,100 33 200200
77 44 33 15,00015,000 22,00022,000 11 7,0007,000
$75,000$75,000 $110,700$110,700

1
12
2
8
3
4 5
4
6
4
7
4
$400
$500
$3000
$7000
$200
$200
$70012
4
Project Duration:
36 weeks
FROM …
1
7
2
8
3
4 5
4
6
4
7
4
$400
$500
$3000
$7000
$200
$200
$70012
4
Project Duration:
31 weeks
Additional Cost:
$2000
TO…

 Crashing costs increase as projectCrashing costs increase as project
duration decreasesduration decreases
 Indirect costs increase as projectIndirect costs increase as project
duration increasesduration increases
 Reduce project length as long asReduce project length as long as
crashing costs are less than indirectcrashing costs are less than indirect
costscosts
Time-Cost Relationship

Time-Cost TradeoffCost($)Cost($)
Project durationProject duration
CrashingCrashing TimeTime
Minimum cost = optimal project timeMinimum cost = optimal project time
Total project costTotal project cost
Indirect costIndirect cost
Direct costDirect cost

■ The Elements of Project Management
■ CPM/PERT Networks
■ Probabilistic Activity Times
■ Microsoft Project
■ Project Crashing and Time-Cost Trade-Off
■ Formulating the CPM/PERT Network as a Linear
Programming Model
Chapter Topics
Copyright © 2010 Pearson Education,
Inc. Publishing as Prentice Hall

■ Network representation is useful for project analysis.
■ Networks show how project activities are organized and are used to
determine time duration of projects.
■ Network techniques used are:
▪ CPM (Critical Path Method)
▪ PERT (Project Evaluation and Review Technique)
■ Developed independently during late 1950’s.
Overview

Elements of Project Management
■ Management is generally perceived as concerned with planning,
organizing, and control of an ongoing process or activity.
■ Project Management is concerned with control of an activity for a
relatively short period of time after which management effort ends.
■ Primary elements of Project Management to be discussed:
 Project Planning
 Project Team
 Project Control

Project Planning
■ Objectives
■ Project Scope
■ Contract Requirements
■ Schedules
■ Resources
■ Personnel
■ Control
■ Risk and Problem AnalysisCopyright © 2010 Pearson Education,

■ Project team typically consists of a group of individuals from various
areas in an organization and often includes outside consultants.
■ Members of engineering staff often assigned to project work.
■ Project team may include workers.
■ Most important member of project team is the project manager.
■ Project manager is often under great pressure because of uncertainty
inherent in project activities and possibility of failure. Potential
rewards, however, can be substantial.
■ Project manager must be able to coordinate various skills of team
members into a single focused effort.
The Project Team

Figure 8.1 The project management process
The Project Management Process

Scope Statement
■ Document providing common understanding of project.
■ Justification describing the factors giving rise to need for project.
■ Expected results and what constitutes success.
■ List of necessary documents and planning reports.
■ Statement of work (SOW) - a planning document for individuals,
team members, groups, departments, subcontractors and suppliers,
describing what are required for successful completion on time.

Work Breakdown Structure (WBS) (1 of 2)
■ WBS breaks down project into major components (modules).
■ Modules are further broken down into activities and, finally, into
individual tasks.
■ Identifies activities, tasks, resource requirements and relationships
between modules and activities.
■ Helps avoid duplication of effort.
■ Basis for project development, management , schedule, resources and
modifications.
■ Approaches for WBS development:
1. Top down process 2. Brainstorm entire project

Figure 8.2 WBS for Computer Order-processing System Project
Work Breakdown Structure (2 of 2)

Responsibility Assignment Matrix (1 of 2)
■ Project manager assigns work elements to organizational units,
departments, groups, individuals or subcontractors.
■ Uses an organizational breakdown structure (OBS).
■ OBS is a table or a chart showing which organizational units are
responsible for work items.
■ OBS leads to the responsibility assignment matrix (RAM)
■ RAM shows who is responsible for doing the necessary work in the
project

Responsibility Assignment Matrix (2 of 2)
Figure 8.3 A responsibility assignment matrix

Project Scheduling
■ Project Schedule evolves from planning documents, with focus on
timely completion.
■ Critical element in project management – source of most conflicts and
problems.
■ Schedule development steps:
1. Define activities, 2. Sequence activities,
3. Estimate activity times, 4. Construct schedule.
■ Gantt chart and CPM/PERT techniques can be useful.
■ Computer software packages available, e.g. Microsoft Project.

Gantt Chart (1 of 2)
■ Popular, traditional technique, also known as a bar chart -developed
by Henry Gantt (1914).
■ Direct precursor of CPM/PERT for monitoring work progress.
■ A visual display of project schedule showing activity start and finish
times and where extra time is available.
■ Suitable for projects with few activities and precedence relationships.
■ Drawback: precedence relationships are not always discernible.

Project Control
■ Process of ensuring progress toward successful completion.
■ Monitoring project to minimize deviations from project plan and
schedule.
■ Corrective actions necessary if deviations occur.
■ Key elements of project control
 Time management
 Cost management
 Performance management
 Earned value analysis.

Copyright © 2010 Pearson Education, Inc. Publishing as
Prentice Hall
■ A branch reflects an activity of a project.
■ A node represents the beginning and end of activities, referred to as
events.
■ Branches in the network indicate precedence relationships.
■ When an activity is completed at a node, it has been realized.
The Project Network
CPM/PERT
Figure 8.5 Nodes and Branches
Activity-on-Arc (AOA) Network

Prentice Hall
■ Network aids in planning and scheduling.
■ Time duration of activities shown on branches.
■ Activities can occur at the same time (concurrently).
■ A dummy activity shows a precedence relationship but reflects
no passage of time.
■ Two or more activities cannot share the same start and end nodes.
The Project Network
Concurrent Activities
Figure 8. 7 A Dummy Activity

The Project Network
House Building Project Data
No. Activity Activity Predecessor Duration (Months)
1. Design house and - 3
obtain financing
2. Lay foundation 1 2
3. Order Materials 1 1
4. Build house 2, 3 3
5. Select paint 2, 3 1
6. Select carpet 5 1
7. Finish work 4, 6 1

The Project Network
AOA Network for House Building Project
Figure 8.6
Expanded Network for Building a
House Showing Concurrent ActivitiesCopyright © 2010 Pearson Education,

The Project Network
AON Network for House Building Project
Activity-on-Node (AON) Network
 A node represents an activity, with its label and time shown on the node
 The branches show the precedence relationships
 Convention used in Microsoft Project software
Figure 8.8

The Project Network
Paths Through a Network
Table 8.1
Paths Through the House-Building NetworkCopyright © 2010 Pearson Education,
Path Events
A 1247
B 12567
C 1347
D 13567

The critical path is the longest path through the network; the
minimum time the network can be completed. From
Figure 8.8:
Path A: 1 → 2 → 4 → 7 3 + 2 + 3 + 1 = 9 months
Path B: 1 → 2 → 5 → 6 → 7 3 + 2 + 1 + 1 + 1= 8
months
Path C: 1 → 3 → 4 → 7 3 + 1 + 3 + 1 = 8 months
Path D: 1 → 3 → 5 → 6 → 7 3 + 1 + 1 + 1 + 1 = 7
The Project Network
The Critical Path

Prentice Hall
The Project Network
Activity Start Times
Figure 8.9 Activity start time

The Project Network
Activity-on-Node Configuration
Figure 8.10 Activity-on-Node ConfigurationCopyright © 2010 Pearson Education,

Prentice Hall
■ ES is the earliest time an activity can start: ES = Maximum (EF)
■ EF is the earliest start time plus the activity time: EF = ES + t
The Project Network
Activity Scheduling : Earliest Times
Figure 8.11 Earliest activity start and finish times

Prentice Hall
■ LS is the latest time an activity can start without delaying critical path time:
LS = LF - t
■ LF is the latest finish time. LF = Minimum (LS)
The Project Network
Activity Scheduling : Latest Times
Figure 8.12 Latest activity start and finish times

Prentice Hall
 Slack is the amount of time an activity can be delayed without
delaying the project: S = LS – ES = LF - EF
 Slack Time exists for those activities not on the critical path for
which the earliest and latest start times are not equal.
 Shared Slack is slack available for a sequence of activities.
The Project Network
Activity Slack Time (1 of 2)
Table 8.2
*Critical path
Activit
y
LS ES LF EF Slack,
S
*1 0 0 3 3 0
*2 3 3 5 5 0
3 4 3 5 4 1
*4 5 5 8 8 0
5 6 5 7 6 1
6 7 6 8 7 1

Prentice Hall
The Project Network
Activity Slack Time (2 of 2)
Figure 8.13 Activity slack

■ Activity time estimates usually cannot be made with certainty.
■ PERT used for probabilistic activity times.
■ In PERT, three time estimates are used: most likely time (m), the
optimistic time (a), and the pessimistic time (b).
■ These provide an estimate of the mean and variance of a beta
distribution:
variance:
mean (expected time):
6
b4mat ++=
2
6
a-b










=v
Probabilistic Activity Times

Prentice Hall
Example (1 of 3)
Figure 8.14 Network for Installation Order Processing System

Prentice Hall
Example (2 of 3)
Table 8.3 Activity Time Estimates for Figure 8.14

Prentice Hall
Example (3 of 3)
Figure 8.15 Earliest and Latest Activity Times

Prentice Hall
■ Expected project time is the sum of the expected times of the
critical path activities.
■ Project variance is the sum of the critical path activities’ variances
■ The expected project time is assumed to be normally distributed
(based on central limit theorem).
■ In example, expected project time (tp) and variance (vp) interpreted as
the mean (µ) and variance (σ2
) of a normal distribution:
µ = 25 weeks
σ2
= 62/9
= 6.9 (weeks)2
Expected Project Time and Variance

■ Using the normal distribution, probabilities are determined
by computing the number of standard deviations (Z) a
value is from the mean.
■ The Z value is used to find corresponding probability in
Table A.1, Appendix A.
Probability Analysis of a Project Network (1 of 2)

Probability Analysis of a Project Network (2 of 2)
Figure 8.16 Normal Distribution of Network DurationCopyright © 2010 Pearson Education,

What is the probability that the new order processing system will be
ready by 30 weeks?
µ = 25 weeks
σ2
= 6.9 σ = 2.63 weeks
Z = (x-µ)/ σ = (30 -25)/2.63 = 1.90
Z value of 1.90 corresponds to probability of .4713 in Table A.1,
Appendix A. Probability of completing project in 30 weeks or less:
(.5000 + .4713) = .9713.
Probability Analysis of a Project Network
Example 1 (1 of 2)

Example 1 (2 of 2)
Figure 8.17 Probability the Network Will Be Completed in 30 Weeks or LessCopyright © 2010 Pearson Education,

■ A customer will trade elsewhere if the new ordering system is not
working within 22 weeks. What is the probability that she will be
retained?
Z = (22 - 25)/2.63 = -1.14
■ Z value of 1.14 (ignore negative) corresponds to probability of .
3729 in Table A.1, appendix A.
■ Probability that customer will be retained is .1271
Example 2 (1 of 2)

Example 2 (2 of 2)
Figure 8.18 Probability the Network Will Be Completed in 22 Weeks or LessCopyright © 2010 Pearson Education,

CPM/PERT Analysis with
QM for Windows & Excel QM (1 of 2)

Prentice Hall
Exhibit 8.2
CPM/PERT Analysis with
QM for Windows & Excel QM (2 of 2)

Prentice Hall
Microsoft Project handles only AON networks.
Analysis with Microsoft Project (1 of 13)
Exhibit 8.3

Analysis with Microsoft Project (2 of
13)
Exhibit 8.4

Exhibit 8.5

Exhibit 8.6

Figure 8.8

Exhibit 8.10

Figure 8.12

Figure 8.13

Exhibit 8.15

■ Project duration can be reduced by assigning more resources to
project activities.
■ However, doing this increases project cost.
■ Decision is based on analysis of trade-off between time and cost.
■ Project crashing is a method for shortening project duration by
reducing one or more critical activities to a time less than normal
activity time.
Project Crashing and
Time-Cost Trade-Off Overview

Prentice Hall
Project Crashing and Time-Cost Trade-Off
Example Problem (1 of 5)
Figure 8.19 The Project Network for Building a House

Prentice Hall
Table 8.4

Prentice Hall
Figure 8.21 Network with Normal Activity Times and Weekly Crashing Costs

Prentice Hall
Figure 8.22
Revised Network with
Activity 1 Crashed
As activities are crashed, the critical path may change and
several paths may become critical.

Prentice Hall Exhibit 8.16
Project Crashing with QM for Windows

General Relationship of Time and Cost (1 of 2)
■ Project crashing costs and indirect costs have an inverse
relationship.
■ Crashing costs are highest when the project is shortened.
■ Indirect costs increase as the project duration increases.
■ Optimal project time is at minimum point on the total
cost curve.

General Relationship of Time and Cost (2 of 2)
Figure 8.23
The Time-Cost Trade-Off

General linear programming model with AOA convention:
Minimize Z = Σxi
subject to:
xj - xi ≥ tij for all activities i → j
xi, xj ≥ 0
Where:
xi = earliest event time of node i
xj = earliest event time of node j
tij = time of activity i → j
The objective is to minimize the project duration (critical path time).
The CPM/PERT Network
Formulating as a Linear Programming Model
i

Example Problem Formulation and Data (1 of 2)
Figure 8.24

Minimize Z = x1 + x2 + x3 + x4 + x5 + x6 + x7
subject to:
x2 - x1 ≥ 12
x3 - x2 ≥ 8
x4 - x2 ≥ 4
x4 - x3 ≥ 0
x5 - x4 ≥ 4
x6 - x4 ≥ 12
x6 - x5 ≥ 4
x7 - x6 ≥ 4
xi, xj ≥ 0
Example Problem Formulation and Data (2 of 2)

Exhibit 8.17
Example Problem Solution with Excel (1 of 4)
B6:B12

Exhibit 8.18

Exhibit 8.19

Exhibit 8.20

Minimize Z = $400y12 + 500y23 + 3000y24 + 200y45 + 7000y46
+ 200y56 + 7000y67
subject to:
y12 ≤ 5 y12 + x2 - x1 ≥ 12 x7 ≤ 30
y23 ≤ 3 y23 + x3 - x2 ≥ 8 xi, yij ≥ 0
y24 ≤ 1 y24 + x4 - x2 ≥ 4
y34 ≤ 0 y34 + x4 - x3 ≥ 0
y45 ≤ 3 y45 + x5 - x4 ≥ 4
y46 ≤ 3 y46 + x6 - x4 ≥ 12
y56 ≤ 3 y56 + x6 - x5 ≥ 4
y67 ≤ 1 x67 + x7 - x6 ≥ 4
xi = earliest event time of node I
xj = earliest event time of node j
y = amount of time by which activity i → j is crashed
Project Crashing with Linear Programming
Example Problem – Model Formulation
Objective is to
minimize the
cost of crashing

Excel Solution (1 of 3)
Exhibit 8.21

Prentice Hall
Given this network and the data on the following slide, determine the
expected project completion time and variance, and the probability
that the project will be completed in 28 days or less.
Example Problem
Problem Statement and Data (1 of 2)

Prentice Hall
Example Problem
Problem Statement and Data (2 of 2)

Prentice Hall
6
b4mat ++=
2
6
a-b










=v
Example Problem Solution (1 of 4)
Step 1: Compute the expected activity times and variances.

Prentice Hall
Step 2: Determine the earliest and latest activity times & slacks

Step 3: Identify the critical path and compute expected
completion time and variance.
 Critical path (activities with no slack): 1 → 3 → 5 → 7
 Expected project completion time: tp = 9+5+6+4 = 24 days
 Variance: vp = 4 + 4/9 + 4/9 + 1/9 = 5 (days)2

Step 4: Determine the Probability That the Project Will be
Completed in 28 days or less (µ = 24, σ = √5)
Z = (x - µ)/σ = (28 -24)/√5 = 1.79
Corresponding probability from Table A.1, Appendix A, is .4633 and
P(x ≤ 28) = .4633 + .5 = .9633.

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