URBS 609 PERT, Unit 2
Basic Techniques Using MS Excel
And Manual Calculation

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This Unit of Instruction was crafted by Robert Hugg For Minnesota State University, Mankato Urban and Regional Studies Institute - 2004
Urban and Regional Studies
Institute 2

• This module will provide:
– Introduction to manually calculating key Project
Management functions (both PERT and CPM)
– Introduction to using MS Excel to calculate key functions (PERT and Risk analysis)
– Step-by step instruction on building a PERT risk analysis calculator using MS Excel
– Use of PERT and CPM traditional techniques to manually lay out a project
• This module is constructed as the second block in a building block approach
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• Simple steps in a logical order
– Step 1: Define tasks
– Step 2: Place Tasks in a logical order, find the critical path
• The longest time path through the task network.
The series of tasks
(or even a single task) that dictates the calculated finish date
– Step 3: Generate estimates
• Optimistic, pessimistic, likely and PERT- expected
• Standard Deviation and variance
– Step 4: Determine earliest and latest dates
– Step 5:Determine probability of meeting expected date
• Steps 1 and 2 are logic and legwork, not calculation – these require a clear goal
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• Assuming steps 1 and 2 have been completed begin calculations – use a table to organize your calculations
• Simple calculations to estimate project durations
• Based on input of 3 estimated durations per task
– Most Optimistic (T
O
) – best case scenario
– Most Likely (T
L
) “normal” scenario
– Most Pessimistic (T
P
) Worst case scenario
• Formula derives a probability-based expected duration (T
E
– ( T
O x 1 + T
L x 4 + T
P x 1 ) / 6 = T
E
– Read this formula as the sum of (optimistic x 1 + likely x 4 + pessimistic x 1) divided by 6 = expected task duration
• Complete this calculation for all tasks
)
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• Standard deviation and variance
– Standard deviation (SD) is the average deviation from the estimated time
• SD=(T
P
-T
0
)/6 { read as (pessimistic-optimistic)/6}
• As a general rule, the higher the standard deviation the greater the amount of uncertainty
– Variance (V) reflects the spread of a value over a normal distribution
• V=SD 2 (Standard deviation squared)
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• When doing manual PERT Calculations it is helpful to construct a table to stay organized
• Consider the sample project in Unit 1 – planting trees and flowers, set up using a list
– Rough estimates and no risk analysis
• No Range, simply rough estimates - unreliable?
– PERT Analysis will better refine estimates
• Start by setting up a table to organize data
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Start
Set up in tabular form, it might look like this…
7
Buy Edging
TASK ID
1
Description
Mark Utilities
2
3
Dig Holes
Buy Trees
4
5
Buy Flowers
Plant Trees
6
7
8
Plant Flowers
Buy Edging
Install Edging
Duration (Days)
?
?
?
?
?
?
?
?
3
Buy Trees
1 2
Mark Utilities Dig Holes
5
Plant Trees
6
Plant Flowers
8
Install Edging Finish
4
Buy Flowers
Set up in visual form it might look like this…
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Institute 8

In considering all tasks on the previous slide, a table might look like this
T
O
T
L
CRITICAL PATH TASKS (Longest Duration)
T
P
T
E
TASK
1
2
5
6
8
TOTAL
T
O
T
L
T
P
OTHER PROJECT TASKS
T
E
TASK
3
4
7
TOTAL
T
O
-Optimistic T
M
-Likely T
P
-Pessimistic T
E
-Expected (Derived by PERT)
Remember – tasks 3, 4 and 7 are concurrent and do not add to the timeline
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After generating estimates using the formula, the table might look like this
TASK
1
2
5
6
8
TOTAL
TASK
3
4
7
TOTAL
1
1
7
T
O
1
2
1
T
O
.5
.5
.5
1.5
T
L
1
1
1
3
T
L
3
4
3
3
2
15
CRITICAL PATH TASKS (Longest Duration)
T
P
5
T
E
3
7 4.17
6 3.17
5 3
4 2.17
28 15.6
OTHER PROJECT TASKS
T
P
T
E
3 1.25
3 1.25
3 1.25
9 3.75
SD
.67
.83
.83
.67
.5
3.5
SD
.42
.42
.42
1.26
V
.44
.69
.69
.44
.25
2.51
V
.17
.17
.17
.51
T
O
-Optimistic T
M
-Likely T
P
-Pessimistic T
E
-Expected (Derived by PERT)
SD=Standard Deviation V=Variance
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Institute 10

For each task, determine the latest allowable time for moving to the next task
The difference between latest time and expected time is called slack time
Tasks with zero slack time are on the critical path
TASK
1
2
5
6
8
TOTAL
T
O
1
2
1
1
1
7
T
L
3
4
3
3
2
15
CRITICAL PATH TASKS (Longest Duration)
T
P
5
7
6
5
T
3
E
4.17
3.17
3
ES
0
3
7
10
EF
3
7.17
10.17
13
LS
0
3
7
10
LF
3
7.17
10.17
13
4 2.17
13 15.17 13 15.17
28 15.51
OTHER PROJECT TASKS
Slack SD
0
0
0
0
0
.67
.83
.83
.67
.5
3.5
V
.444
.694
.694
.444
.254
2.530
TASK
3
4
7
TOTAL
T
O
.5
.5
.5
1.5
T
L
1
1
1
3
T
P
T
E
3 1.25
3 1.25
ES
0
0
EF
1.25
1.25
LS
3
3
LF
4.25
4.25
3 1.25
1.25
2.50 4.25 5.50
9 3.75
FLOAT
3
3
3
SD
.42
.42
.42
1.26
V
.17
.17
.17
.51
ES=Earliest Start EF= Earliest Finish LS=Latest Start LF=Latest Finish
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Manually computing probability using data compiled in your table
• Determine probability of meeting a date by using the table data
– Denote the sum of all expected durations on the critical path as S
– Denote the sum of all variances on the critical path as V
– Select a desired completion time, denote this as D
– COMPUTE : (D-S)/square root (V) = Z ( the number of std. deviations that the due date is away from the expected date))
• Enter a standard normal table to find a probability that corresponds with Z or go online to:
– http://math.uc.edu/statistics/statbook/tables.html
) to enter a z number the application will retrieve the probability from the lengthy table
• For our project, figure a probability based on the most likely time, 15 days: (15-15.51)/square root(2.53) = (15-15.51)/1.59=-.3207 (Z)
• A corresponding probability is 37.7% (Rounded)
• This process can be repeated for any date desired
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Institute 12

Computing probability in Excel using data compiled in your table
• Excel has normal distribution functions built in and can compute PERT probabilities
• By creating a table as a spreadsheet, the addition of a few simple formulae will do the rest of the work
• Create a table as a template that can be used over and over again – simply change the input
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Computing probability in Excel using data compiled in your table
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Constructing the Spreadsheet
Step 1 - Create a spreadsheet that resembles the table used earlier
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Constructing the Spreadsheet
Step 2 – Use formulae as shown to calculate PERT Expectations
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Cell Formulae used for PERT Analysis- expected durations
• Computing PERT Expected duration
– For each task cell: (Optimistic + 4x Typical +
Pessimistic)/6
– Adjust cell address for each task
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Constructing the Spreadsheet
Step 3 – Use formulae as shown to calculate variances
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Cell Formulae used for PERT Analysis – Variances
• Computing Variances
– For each task cell:
• ((Pessimistic-Optimistic)/6) 2
– Adjust cell address for each task
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Constructing the Spreadsheet
Step 4 – Use formulae as shown to calculate STD. Deviations
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Cell Formulae used for PERT Analysis – Standard Deviations
• Computing Standard Deviations
– For each task cell:
• Square root of the variance for that task
– Adjust cell address for each task
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Constructing the Spreadsheet
Step 5 – Use formula as shown to sum PERT expectations
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Institute 22

Cell Formula used for PERT Analysis – Summing PERT Expectations
• Sum Pert Expectations using either autosum feature or sum formula
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Constructing the Spreadsheet
Step 6 – Use formula as shown to sum variances
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Cell Formula used for PERT Analysis – Summing Variances
• Sum Variances using either auto-sum feature or sum formula
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Institute 25

Constructing the Spreadsheet
Step 6 – Use formula as shown to compute probability
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Institute 26

Cell Formula used for PERT Analysis – Completion Probability
• Excel uses a formula designed to compute the probability of placement of a combination of elements in a normal distribution – very accurate
• NORMDIST(x,mean,standard_dev,cumulative)
– X is the value for which you want the distribution
(desired date)
– Mean is the arithmetic mean of the distribution (summed
PERT expected durations)
– Standard_dev is the standard deviation of the distribution (square root of the summed variances)
– Cumulative is a logical value that determines the form of the function. If cumulative is TRUE , NORMDIST returns the cumulative distribution function (probability of completion on the date entered)
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Cell Formula used for PERT Analysis – Hints and Tips
• Be sure to adjust formulae as necessary when adding additional tasks
– If a error message shows up check cell addresses in the formulae first – formulae must reflect intent
• This set of formulae mirrors the manual calculations but takes less time for the user
• Because PERT is a probabilistic approach, these formulae can deliver a 100% probability – but no plan is perfect – these are always estimates
• Never feel there is a 100% probability of a project completing on the estimated date
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Thoughts, Philosophy and Lessons Learned
• All Plans are estimates and are only as good as the task estimates – unrealistic estimates equal unrealistic plans
• If the scope of a plan changes, all estimates must change – adding tasks equals added time and cost
• PERT Analysis is a good way to “what if” before a project is launched – helps determine if it is needed at all
– What tasks will it take to do the project?
– What is the optimum order of the project tasks?
– How long will it take to do the project?
– How likely is the project to succeed?
– What if “ The Boss ” wants it earlier, what is the likelihood then?
• A great way to get organized and stay organized
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• In comparison to PERT, CPM analysis is simple
• CPM Analysis is a series of easy steps
1. Develop time and cost data ("normal" and "crashed") for all tasks
2. Develop cost-per-week for crashing ( crashed costs divided by time saved)
3. Develop project network (PERT)
4. Crash the activity crashing on the critical path with the lowest cost-for-
5. Recalculate the project network (the critical path might change!)
• Repeat steps 4 & 5 until all the paths have been crashed.
• Ease up on all non-critical paths, just to the point that all paths are critical.
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Institute 30

CPM Analysis
• A typical CPM table might have the following structure:
Activity Begin End
Time
(Crashed)
Time
(Normal)
Cost
(Crashed)
Cost
(Normal)
Time
Saved
Cost
Increase
Cost /
Week
Foundation
Frame
1
2
2
3
1
1
2
4
4000
8000
3000
4000
1
3
1000
4000
1000
1333 cost-per-week for crashing = crashed costs divided by time saved
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Institute 31

Thoughts, Philosophy and Lessons Learned
• All Plans are estimates and are only as good as the task estimates – unrealistic estimates equal unrealistic plans
• If the scope of a plan changes, all estimates must change – adding tasks equals added time and cost
• CPM Analysis is a good way to “what if” before a project is launched – helps control expectations
– How much will it cost?
– How long will it take?
– How long will it take if it needs to be done sooner?
– How much will it cost if it needs to be done sooner?
• A great way to get organized and stay organized
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Institute 32

• PERT & CPM are totally complementary both require the same preparation:
1. Define the Project and all of its significant activities or tasks. The
Project should have only a single start activity and a single finish activity.
2. Develop the relationships among the activities; decide which activities must precede and which must follow others.
3. Draw a Network Diagram connecting all the activities (each activity should have a unique number).
4. Assign time and/or cost estimates to each activity.
5. Compute the longest time path through the network. (The critical path)
6. Use the Network to help plan, schedule, monitor & control the project.
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Institute 33

• PERT and CPM can be used together
• Calculations are based on a few simple formulae:
– PERT Derived duration estimates
– Standard Deviation
– Variance
– Probability of meeting expectation
– Crash costs and time & normal costs and time
• Calculations can be done manually or using
Excel – same formulae, different tools
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Institute 34

• Bonini, Charles, et al, Quantitative
Analysis for Management, Columbus:
McGraw Hill, 1997
• Dr. Anthony Filipovitch
• Goldratt, Eli, Dr., The Goal: A Process of
Ongoing Improvement, Great
Barrington: New River Press, 1996
• Mednick, Barry, PERT-CPM on
Excel,Fullerton: Cal State, 2000
• MS Project, by Microsoft Corporation
• MS Excel, by Microsoft Corporation
• PM Body of Knowledge (PMBOK),
Philadelphia: PMI, 2000
• Project Management Institute (PMI)
Resource Center
– Project Management Institute Website
• ProjeX, by WAA, Inc
• Systema, Sid, Probabilistic Solutions to
Project Scheduling, Ferris State, 1999
• US National Performance Survey, The
Standish Group, 1998
• Verma, Vijay K., Managing the Project
Team: The Human Aspects of Project
Management, Philadelphia: PMI, 1997
• Wiest, Jerome D., and Levy, Ferdinand
K., A Management Guide to
PERT/CPM, New Delhi: Prentice-Hall of
India Private Limited, 1974
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You have completed
URBS 609 PERT Unit 2
Please proceed to
URBS 609 Project Management Using MS
Project Block
This Unit of Instruction was crafted by Robert Hugg For Minnesota State University, Mankato Urban and Regional Studies Institute - 2004
Urban and Regional Studies
Institute 36