Pert2

PERT/CPM CALCULATIONSPERT/CPM CALCULATIONS

Basic Techniques Using MS Basic Techniques Using MS Excel Excel

And Manual CalculationAnd Manual Calculation

URBS 609 PERT, Unit 2

Urban and Regional Studies Institute Urban and Regional Studies Institute 22

About This Training ModuleAbout 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 - 2004


Training Module PreviewTraining Module Preview

• This module will provide:This module will provide:– Introduction to manually calculating key Introduction to manually calculating key

Project Management functions (both PERT and Project Management functions (both PERT and CPM)CPM)

– Introduction to using MS Excel to calculate key Introduction to using MS Excel to calculate key functions (PERT and Risk analysis)functions (PERT and Risk analysis)

– Step-by step instruction on building a PERT risk Step-by step instruction on building a PERT risk analysis calculator using MS Excelanalysis calculator using MS Excel

– Use of PERT and CPM traditional techniques to Use of PERT and CPM traditional techniques to manually lay out a projectmanually lay out a project

• This module is constructed as the second This module is constructed as the second block in a building block approachblock in a building block approach


PERT Calculations - PERT Calculations - SimplicitySimplicity

• Simple steps in a logical orderSimple steps in a logical order– Step 1: Define tasksStep 1: Define tasks– Step 2: Place Tasks in a logical order, find the Step 2: Place Tasks in a logical order, find the critical pathcritical path

• The longest time path through the task network.The longest time path through the task network. The series of The series of tasks (or even a single task) that dictates the calculated tasks (or even a single task) that dictates the calculated finish datefinish date

– Step 3: Generate estimatesStep 3: Generate estimates• Optimistic, pessimistic, likely and PERT- expectedOptimistic, pessimistic, likely and PERT- expected • Standard Deviation and varianceStandard Deviation and variance

– Step 4: Determine Step 4: Determine earliest and latest datesearliest and latest dates– Step 5:Determine Step 5:Determine probabilityprobability of meeting expected date of meeting expected date

• Steps 1 and 2 are logic and legwork, not calculation Steps 1 and 2 are logic and legwork, not calculation – these require a clear goal– these require a clear goal

http://en.wikipedia.org/wiki/Critical_path


PERT Calculations – Step 3PERT Calculations – Step 3• Assuming steps 1 and 2 have been completed begin Assuming steps 1 and 2 have been completed begin

calculations – use a table to organize your calculationscalculations – use a table to organize your calculations• Simple calculations to estimate project durationsSimple calculations to estimate project durations• Based on input of 3 estimated durations Based on input of 3 estimated durations per taskper task

– Most Optimistic (TMost Optimistic (TOO) – best case scenario) – best case scenario– Most Likely (TMost Likely (TLL) “normal” scenario) “normal” scenario– Most Pessimistic (TMost Pessimistic (TPP) Worst case scenario) Worst case scenario

• Formula derives a probability-based expected duration Formula derives a probability-based expected duration (T(TEE))– ((TTO O x 1 x 1 ++ TTLL x 4 x 4 + + TTP P x 1 x 1) / 6 = ) / 6 = TTEE

– Read this formula as the sum of (optimistic x 1 + likely x 4 + Read this formula as the sum of (optimistic x 1 + likely x 4 + pessimistic x 1) divided by 6 = expected task durationpessimistic x 1) divided by 6 = expected task duration

• Complete this calculation for all tasksComplete this calculation for all tasks


PERT Calculations – Step 3PERT Calculations – Step 3

• Standard deviation and varianceStandard deviation and variance– Standard deviation (SD) is the average Standard deviation (SD) is the average

deviation from the estimated timedeviation from the estimated time•SD=(TSD=(TPP-T-T00)/6 {)/6 {read as read as

(pessimistic-optimistic)/6}(pessimistic-optimistic)/6}•As a general rule, the higher the standard As a general rule, the higher the standard

deviation the greater the amount of uncertaintydeviation the greater the amount of uncertainty

– Variance (V) reflects the spread of a value Variance (V) reflects the spread of a value over a normal distributionover a normal distribution•V=SDV=SD2 2 (Standard deviation squared)(Standard deviation squared)


PERT Calculations – Step 3PERT Calculations – Step 3

• When doing manual PERT Calculations it is When doing manual PERT Calculations it is helpful to construct a table to stay organized helpful to construct a table to stay organized

• Consider the sample project in Unit 1 – Consider the sample project in Unit 1 – planting trees and flowers, set up using a listplanting trees and flowers, set up using a list– Rough estimates and no risk analysisRough estimates and no risk analysis

•No Range, simply rough estimates - unreliable?No Range, simply rough estimates - unreliable?

– PERT Analysis will better refine estimatesPERT Analysis will better refine estimates

• Start by setting up a table to organize dataStart by setting up a table to organize data


Our Project – A RefresherOur Project – A RefresherTASK 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 ?

Plant TreesMark Utilities Dig Holes

Buy Flowers

Buy Trees

Buy Edging

FinishStart

2 6

7

8Install EdgingPlant Flowers

5

4

1

3

Set up in visual form it might look like this…

Set up in tabular form, it might look like this…


PERT Step 3PERT Step 3– First Get Organized– First Get Organized

CRITICAL PATH TASKS (Longest Duration)TASK TO TL TP TE

12568

TOTALOTHER PROJECT TASKS

TASK TO TL TP TE

347

TOTAL

In considering all tasks on the previous slide, a table might look like this

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


PERT Step 3PERT Step 3– Durations– DurationsAfter generating estimates using the formula, the table might look After generating estimates using the formula, the table might look

like thislike thisCRITICAL PATH TASKS (Longest Duration)

TASK TO TL TP TE SD V

1 11 33 55 33 .67.67 .44.442 22 44 77 4.174.17 .83.83 .69.695 11 33 66 3.173.17 .83.83 .69.696 11 33 55 33 .67.67 .44.448 11 22 44 2.172.17 .5.5 .25.25

TOTAL 77 1515 2828 15.615.6 3.53.5 2.512.51OTHER PROJECT TASKS

TASK TO TL TP TE SD V

3 .5.5 11 33 1.251.25 .42.42 .17.174 .5.5 11 33 1.251.25 .42.42 .17.177 .5.5 11 33 1.251.25 .42.42 .17.17

TOTAL 1.51.5 33 99 3.753.75 1.261.26 .51.51

TO-Optimistic TM-Likely TP-Pessimistic TE-Expected (Derived by PERT)

SD=Standard Deviation V=Variance


PERT Step 4 PERT Step 4 – Dates– Dates

CRITICAL PATH TASKS (Longest Duration)TASK TO TL TP TE ES EF LS LF Slack SD V

1 11 33 55 33 00 33 00 33 00 .67.67 .444.4442 22 44 77 4.174.17 33 7.177.17 33 7.177.17 00 .83.83 .694.6945 11 33 66 3.173.17 77 10.110.1

7777 10.1710.17 00 .83.83 .694.694

6 11 33 55 33 1010 1313 1010 1313 00 .67.67 .444.4448 11 22 44 2.172.17 1313 15.115.1

771313 15.1715.17 00 .5.5 .254.254

TOTAL 77 1515 2828 15.5115.51 3.53.5 2.5302.530OTHER PROJECT TASKS

TASK TO TL TP TE ES EF LS LF FLOAT SD V

3 .5.5 11 33 1.251.25 00 1.251.25 33 4.254.25 33 .42.42 .17.174 .5.5 11 33 1.251.25 00 1.251.25 33 4.254.25 33 .42.42 .17.177 .5.5 11 33 1.251.25 1.251.25 2.502.50 4.254.25 5.505.50 33 .42.42 .17.17

TOTAL 1.51.5 33 99 3.753.75 1.261.26 .51.51ES=Earliest Start EF= Earliest Finish LS=Latest Start LF=Latest Finish

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


PERT Step 5 PERT Step 5 – Probabilities– Probabilities

• Determine Determine probabilityprobability of meeting a date by using the table data of meeting a date by using the table data – Denote the sum of all expected durations on the critical path as Denote the sum of all expected durations on the critical path as SS – Denote the sum of all variances on the critical path as Denote the sum of all variances on the critical path as VV – Select a desired completion time, denote this as Select a desired completion time, denote this as DD – COMPUTECOMPUTE: : (D-S)/square root (V) = Z(D-S)/square root (V) = Z ( the number of std. ( the number of std.

deviations that the due date is away from the expected date))deviations that the due date is away from the expected date))• Enter a standard normal table to find a probability that Enter a standard normal table to find a probability that

corresponds with Z or go online to:corresponds with Z or go online to:– http://math.uc.edu/statistics/statbook/tables.htmlhttp://math.uc.edu/statistics/statbook/tables.html) to enter a z ) to enter a z

number - the application will retrieve the probability from the number - the application will retrieve the probability from the lengthy tablelengthy table

• For our project, figure a probability based on the most likely For our project, figure a probability based on the most likely time, 15 days: (15-15.51)/square root(2.53) = time, 15 days: (15-15.51)/square root(2.53) = (15-15.51)/1.59=-.3207 (Z)(15-15.51)/1.59=-.3207 (Z)

• A corresponding probability is 37.7% (Rounded)A corresponding probability is 37.7% (Rounded)• This process can be repeated for any date desiredThis process can be repeated for any date desired

Manually computing probability using data compiled in your table

http://math.uc.edu/statistics/statbook/tables.html


PERT Step 5 PERT Step 5 – Probabilities – Probabilities Computing probability in Excel using data compiled in your

table

• Excel has normal distribution Excel has normal distribution functions built in and can compute functions built in and can compute PERT probabilitiesPERT probabilities

• By creating a table as a spreadsheet, By creating a table as a spreadsheet, the addition of a few simple formulae the addition of a few simple formulae will do the rest of the workwill do the rest of the work

• Create a table as a template that can Create a table as a template that can be used over and over again – simply be used over and over again – simply change the inputchange the input


PERT Step 5 PERT Step 5 – Probabilities – Probabilities Computing probability in Excel using data compiled in your

table


Constructing the Constructing the SpreadsheetSpreadsheet

Step 1 - Create a spreadsheet that resembles the table used earlier



Step 2 – Use formulae as shown to calculate PERT Expectations



Cell Formulae used for PERT Analysis- expected durations

• Computing PERT Expected durationComputing PERT Expected duration– For each task cell: (Optimistic + 4x For each task cell: (Optimistic + 4x

Typical + Pessimistic)/6Typical + Pessimistic)/6– Adjust cell address for each taskAdjust cell address for each task


Constructing the Constructing the SpreadsheetSpreadsheetStep 3 – Use formulae as shown to calculate variances



Cell Formulae used for PERT Analysis – Variances

• Computing VariancesComputing Variances– For each task cell: For each task cell:

•((Pessimistic-Optimistic)/6)((Pessimistic-Optimistic)/6)22

– Adjust cell address for each taskAdjust cell address for each task


Constructing the Constructing the SpreadsheetSpreadsheetStep 4 – Use formulae as shown to calculate STD. Deviations



Cell Formulae used for PERT Analysis – Standard Deviations

• Computing Standard DeviationsComputing Standard Deviations– For each task cell: For each task cell:

•Square root of the variance for that taskSquare root of the variance for that task

– Adjust cell address for each taskAdjust cell address for each task


Constructing the Constructing the SpreadsheetSpreadsheetStep 5 – Use formula as shown to sum PERT expectations



Cell Formula used for PERT Analysis – Summing PERT Expectations• Sum Pert Expectations using either Sum Pert Expectations using either

auto-sum feature or sum formulaauto-sum feature or sum formula


Constructing the Constructing the SpreadsheetSpreadsheetStep 6 – Use formula as shown to sum variances



Cell Formula used for PERT Analysis – Summing Variances

• Sum Variances using either auto-sum Sum Variances using either auto-sum feature or sum formulafeature or sum formula


Constructing the Constructing the SpreadsheetSpreadsheetStep 6 – Use formula as shown to compute probability



Cell Formula used for PERT Analysis – Completion Probability• Excel uses a formula designed to compute the probability of placement of a Excel uses a formula designed to compute the probability of placement of a combination of elements in a normal distribution – very accuratecombination 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)



Cell Formula used for PERT Analysis – Hints and Tips

• Be sure to adjust formulae as necessary when Be sure to adjust formulae as necessary when adding additional tasksadding additional tasks– If a error message shows up check cell addresses If a error message shows up check cell addresses

in the formulae first – formulae must reflect intentin the formulae first – formulae must reflect intent• This set of formulae mirrors the manual This set of formulae mirrors the manual

calculations but takes less time for the usercalculations but takes less time for the user• Because PERT is a probabilistic approach, Because PERT is a probabilistic approach,

these formulae can deliver a 100% probability these formulae can deliver a 100% probability – but no plan is perfect – these are always – but no plan is perfect – these are always estimatesestimates

• NeverNever feel there is a 100% probability of a feel there is a 100% probability of a project completing on the estimated dateproject completing on the estimated date


PERT AnalysisPERT Analysis Thoughts, Philosophy and Lessons Learned

• All Plans are All Plans are estimatesestimates and are only as good as the and are only as good as the task estimates – task estimates – unrealistic estimates equal unrealistic unrealistic estimates equal unrealistic plansplans

• If the scope of a plan changes, all estimates must If the scope of a plan changes, all estimates must change – change – adding tasks equals added time and costadding tasks equals added time and cost

• PERT Analysis is a good way to “what if” before a PERT Analysis is a good way to “what if” before a project is launched – helps determine if it is needed at project is launched – helps determine if it is needed at allall– What tasks will it take to do the project?What tasks will it take to do the project?– What is the optimum order of the project tasks?What is the optimum order of the project tasks?– How long will it take to do the project?How long will it take to do the project?– How likely is the project to succeed?How likely is the project to succeed?– What if “What if “The BossThe Boss” wants it earlier, what is the likelihood then?” wants it earlier, what is the likelihood then?

• A great way to get organized and stay organizedA great way to get organized and stay organized


CPM AnalysisCPM Analysis

• In comparison to PERT, CPM analysis is simpleIn comparison to PERT, CPM analysis is simple• CPM Analysis is a series of easy stepsCPM Analysis is a series of easy steps

1.1. Develop time and cost data ("normal" and "crashed") for all Develop time and cost data ("normal" and "crashed") for all tasks tasks

2.2. Develop cost-per-week for crashing (Develop cost-per-week for crashing (crashed costs divided by crashed costs divided by time saved) time saved)

3.3. Develop project network (PERT) Develop project network (PERT) 4.4. Crash the activity Crash the activity on the critical pathon the critical path with the lowest cost-for- with the lowest cost-for-

crashing crashing 5.5. Recalculate the project network (the critical path might Recalculate the project network (the critical path might

change!) change!) • Repeat steps 4 & 5 until all the paths have been Repeat steps 4 & 5 until all the paths have been

crashed. crashed. • Ease up on all non-critical paths, just to the point that Ease up on all non-critical paths, just to the point that

all paths are critical.all paths are critical.


CPM AnalysisCPM Analysis

• A typical CPM table might have A typical CPM table might have the following structure: the following structure:

ActivityBegi

nEnd

Time(Crashed

)

Time (Normal

)

Cost (Crashed

)

Cost (Normal)

Time Saved

Cost Increase

Cost / Week

Foundation

1 2 1 2 4000 3000 1 1000 1000

Frame 2 3 1 4 8000 4000 3 4000 1333

cost-per-week for crashing = cost-per-week for crashing = crashed costs divided by time savedcrashed costs divided by time saved


CPM AnalysisCPM Analysis Thoughts, Philosophy and Lessons Learned

• All Plans are All Plans are estimatesestimates and are only as good as the and are only as good as the task estimates – task estimates – unrealistic estimates equal unrealistic estimates equal unrealistic plansunrealistic plans

• If the scope of a plan changes, all estimates must If the scope of a plan changes, all estimates must change – change – adding tasks equals added time and costadding tasks equals added time and cost

• CPM Analysis is a good way to “what if” before a CPM Analysis is a good way to “what if” before a project is launched – helps control expectationsproject is launched – helps control expectations– How much will it cost?How much will it cost?– How long will it take?How long will it take?– How long will it take if it needs to be done sooner?How long will it take if it needs to be done sooner?– How much will it cost 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 organizedA great way to get organized and stay organized


Use PERT and CPM TogetherUse PERT and CPM Together

• PERT & CPM are totally PERT & CPM are totally complementary - both require the complementary - both require the same preparation: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.


PM Calculations OverviewPM Calculations Overview

• PERT and CPM can be used togetherPERT and CPM can be used together• Calculations are based on a few simple Calculations are based on a few simple

formulae:formulae:– PERT Derived duration estimatesPERT Derived duration estimates– Standard DeviationStandard Deviation– VarianceVariance– Probability of meeting expectationProbability of meeting expectation– Crash costs and time & normal costs and timeCrash costs and time & normal costs and time

• Calculations can be done manually or Calculations can be done manually or using Excel – same formulae, different using Excel – same formulae, different toolstools


Resources Used in This UnitResources Used in This Unit

• Bonini, Charles, et al, Quantitative Bonini, Charles, et al, Quantitative Analysis for Management, Analysis for Management, Columbus: McGraw Hill, 1997Columbus: McGraw Hill, 1997

• Dr. Anthony FilipovitchDr. Anthony Filipovitch• Goldratt, Eli, Dr., The Goal: A Goldratt, Eli, Dr., The Goal: A

Process of Ongoing Improvement, Process of Ongoing Improvement, Great Barrington: New River Press, Great Barrington: New River Press, 19961996

• Mednick, Barry, PERT-CPM on Mednick, Barry, PERT-CPM on Excel,Fullerton: Cal State, 2000Excel,Fullerton: Cal State, 2000

• MS Project, by Microsoft MS Project, by Microsoft CorporationCorporation

• MS Excel, by Microsoft CorporationMS Excel, by Microsoft Corporation• PM Body of Knowledge (PMBOK), PM Body of Knowledge (PMBOK),

Philadelphia: PMI, 2000Philadelphia: PMI, 2000

• Project Management Institute Project Management Institute (PMI) Resource Center(PMI) Resource Center– Project Management Institute WebProject Management Institute Web

sitesite• ProjeX, by WAA, Inc ProjeX, by WAA, Inc • Systema, Sid, Probabilistic Systema, Sid, Probabilistic

Solutions to Project Scheduling, Solutions to Project Scheduling, Ferris State, 1999Ferris State, 1999

• US National Performance Survey, US National Performance Survey, The Standish Group, 1998The Standish Group, 1998

• Verma, Vijay K., Managing the Verma, Vijay K., Managing the Project Team: The Human Aspects Project Team: The Human Aspects of Project Management, of Project Management, Philadelphia: PMI, 1997Philadelphia: PMI, 1997

• Wiest, Jerome D., and Levy, Wiest, Jerome D., and Levy, Ferdinand K., A Management Ferdinand K., A Management Guide to PERT/CPM, New Delhi: Guide to PERT/CPM, New Delhi: Prentice-Hall of India Private Prentice-Hall of India Private Limited, 1974Limited, 1974

http://www.pmi.org/

http://www.pmi.org/


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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

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