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PERT/CPM CALCULATIONS

URBS 609 PERT, Unit 2

- Basic Techniques Using MS Excel
- And Manual Calculation

About This Training Module

- This training module was crafted using

PowerPoint by Microsoft Corporation. It has been

packaged with PowerPoint Viewer, a standalone

Microsoft product that allows a user to view this

module without use of PowerPoint.

- Left mouse-click or enter to go to next slide
- Right mouse-click or backspace to go to previous

slide - ESC to exit this module

This Unit of Instruction was crafted by Robert

Hugg For Minnesota State University, Mankato

Urban and Regional Studies Institute - 2004

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

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 5Determine probability of meeting expected

date - Steps 1 and 2 are logic and legwork, not

calculation these require a clear goal

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 1 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

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 - VSD2 (Standard deviation squared)

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

Our Project A Refresher

Set up in tabular form, it might look like this

Set up in visual form it might look like this

PERT Step 3 First Get Organized

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 3 Durations

- After generating estimates using the formula, the

table might look like this

TO-Optimistic TM-Likely TP-Pessimistic

TE-Expected (Derived by PERT) SDStandard

Deviation VVariance

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

ESEarliest Start EF Earliest Finish

LSLatest Start LFLatest Finish

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 - http//math.uc.edu/statistics/statbook/tables.htm

l) 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

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

PERT Step 5 Probabilities Computing

probability in Excel using data compiled in your

table

Constructing the Spreadsheet

Step 1 - Create a spreadsheet that resembles the

table used earlier

Constructing the Spreadsheet

Step 2 Use formulae as shown to calculate PERT

Expectations

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

Constructing the Spreadsheet

Step 3 Use formulae as shown to calculate

variances

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

Constructing the Spreadsheet

Step 4 Use formulae as shown to calculate STD.

Deviations

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

Constructing the Spreadsheet

Step 5 Use formula as shown to sum PERT

expectations

Constructing the Spreadsheet Cell Formula used

for PERT Analysis Summing PERT Expectations

- Sum Pert Expectations using either auto-sum

feature or sum formula

Constructing the Spreadsheet

Step 6 Use formula as shown to sum variances

Constructing the Spreadsheet Cell Formula used

for PERT Analysis Summing Variances

- Sum Variances using either auto-sum feature or

sum formula

Constructing the Spreadsheet

Step 6 Use formula as shown to compute

probability

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)

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

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

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.

CPM Analysis

- A typical CPM table might have the following

structure

cost-per-week for crashing crashed costs

divided by time saved

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

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.

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

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

- 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

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