1. PERT/CPM CALCULATIONS
URBS 609 PERT, Unit 2
Basic Techniques Using MS Excel
And Manual Calculation

2. About This Training Module
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This Unit of Instruction was crafted by Robert Hugg For Minnesota State University, Mankato Urban and Regional Studies Institute
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3. Training Module Preview
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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4. PERT Calculations - Simplicity
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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5. PERT Calculations – Step 3
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 (TO) – best case scenario
Most Likely (TL) “normal” scenario
Most Pessimistic (TP) Worst case scenario
Formula derives a probability-based expected duration (TE)
(TO x TL x 4 + TP x 1) / 6 = TE
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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6. PERT Calculations – Step 3
Standard deviation and variance
Standard deviation (SD) is the average deviation from the estimated time
SD=(TP-T0)/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=SD2 (Standard deviation squared)
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7. PERT Calculations – Step 3
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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8. Our Project – A Refresher
TASK ID
Description
Duration (Days) 1
Mark Utilities ? 2
Dig Holes 3
Buy Trees 4
Buy Flowers 5
Plant Trees 6
Plant Flowers 7
Buy Edging 8
Install Edging
Set up in tabular form, it might look like this…
Set up in visual form it might look like this…
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9. PERT Step 3– First Get Organized
In considering all tasks on the previous slide, a table might look like this
CRITICAL PATH TASKS (Longest Duration)
TASK TO TL TP TE 1 2 5 6 8
TOTAL
OTHER PROJECT TASKS 3 4 7
TO-Optimistic TM-Likely TP-Pessimistic TE-Expected (Derived by PERT)
Remember – tasks 3, 4 and 7 are concurrent and do not add to the timeline
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10. CRITICAL PATH TASKS (Longest Duration)
PERT Step 3– Durations
After generating estimates using the formula, the table might look like this
CRITICAL PATH TASKS (Longest Duration)
TASK TO TL TP TE SD V 1 3 5
.67
.44 2 4 7
4.17
.83
.69 6
3.17 8
2.17 .5
.25
TOTAL 15 28
15.6
3.5
2.51
OTHER PROJECT TASKS
1.25
.42
.17
1.5 9
3.75
1.26
.51
TO-Optimistic TM-Likely TP-Pessimistic TE-Expected (Derived by PERT)
SD=Standard Deviation V=Variance
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11. PERT Step 4 – Dates
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
CRITICAL PATH TASKS (Longest Duration)
TASK TO TL TP TE ES EF LS LF
Slack SD V 1 3 5
.67
.444 2 4 7
4.17
7.17
.83
.694 6
3.17
10.17 10 13 8
2.17
15.17 .5
.254
TOTAL 15 28
15.51
3.5
2.530
OTHER PROJECT TASKS
FLOAT
1.25
4.25
.42
.17
2.50
5.50
1.5 9
3.75
1.26
.51
ES=Earliest Start EF= Earliest Finish LS=Latest Start LF=Latest Finish
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12. PERT Step 5 – Probabilities
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:
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: ( )/square root(2.53) = ( )/1.59= (Z)
A corresponding probability is 37.7% (Rounded)
This process can be repeated for any date desired
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13. Urban and Regional Studies Institute
PERT Step 5 – Probabilities 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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14. Urban and Regional Studies Institute
PERT Step 5 – Probabilities Computing probability in Excel using data compiled in your table
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15. Constructing the Spreadsheet
Step 1 - Create a spreadsheet that resembles the table used earlier
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16. Constructing the Spreadsheet
Step 2 – Use formulae as shown to calculate PERT Expectations
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17. Urban and Regional Studies Institute
Constructing the Spreadsheet 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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18. Constructing the Spreadsheet
Step 3 – Use formulae as shown to calculate variances
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19. Urban and Regional Studies Institute
Constructing the Spreadsheet 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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20. Constructing the Spreadsheet
Step 4 – Use formulae as shown to calculate STD. Deviations
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21. Urban and Regional Studies Institute
Constructing the Spreadsheet 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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22. Constructing the Spreadsheet
Step 5 – Use formula as shown to sum PERT expectations
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23. Urban and Regional Studies Institute
Constructing the Spreadsheet Cell Formula used for PERT Analysis – Summing PERT Expectations
Sum Pert Expectations using either auto-sum feature or sum formula
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24. Constructing the Spreadsheet
Step 6 – Use formula as shown to sum variances
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25. Urban and Regional Studies Institute
Constructing the Spreadsheet Cell Formula used for PERT Analysis – Summing Variances
Sum Variances using either auto-sum feature or sum formula
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26. Constructing the Spreadsheet
Step 6 – Use formula as shown to compute probability
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27. Constructing the Spreadsheet 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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28. Urban and Regional Studies Institute
Constructing the Spreadsheet 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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29. PERT Analysis 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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30. Urban and Regional Studies Institute
CPM Analysis
In comparison to PERT, CPM analysis is simple
CPM Analysis is a series of easy steps
Develop time and cost data ("normal" and "crashed") for all tasks
Develop cost-per-week for crashing (crashed costs divided by time saved)
Develop project network (PERT)
Crash the activity on the critical path with the lowest cost-for-crashing
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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31. Urban and Regional Studies Institute
CPM Analysis
A typical CPM table might have the following structure:
Activity
Begin
End
Time
(Crashed)
Time (Normal)
Cost (Crashed)
Cost (Normal)
Saved
Cost Increase
Cost / Week
Foundation 1 2
4000
3000
1000
Frame 3 4
8000
1333
cost-per-week for crashing = crashed costs divided by time saved
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32. CPM Analysis 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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33. Use PERT and CPM Together
PERT & CPM are totally complementary - both require the same preparation:
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.
Develop the relationships among the activities; decide which activities must precede and which must follow others.
Draw a Network Diagram connecting all the activities (each activity should have a unique number).
Assign time and/or cost estimates to each activity.
Compute the longest time path through the network. (The critical path)
Use the Network to help plan, schedule, monitor & control the project.
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34. PM Calculations Overview
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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35. Resources Used in This Unit
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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36. URBS 609 Project Management Using MS Project Block
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
Urban and Regional Studies Institute