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## PERT/CPM CALCULATIONS

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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 Urban and Regional Studies Institute**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 Urban and Regional Studies Institute**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 Urban and Regional Studies Institute**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 Urban and Regional Studies Institute**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) Urban and Regional Studies Institute**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 Urban and Regional Studies Institute**Our Project – A Refresher**Set up in tabular form, it might look like this… Set up in visual form it might look like this… Urban and Regional Studies Institute**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 Urban and Regional Studies Institute**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) SD=Standard Deviation V=Variance Urban and Regional Studies Institute**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 iscalledslack time Tasks with zero slack time are on the critical path ES=Earliest Start EF= Earliest Finish LS=Latest Start LF=Latest Finish Urban and Regional Studies Institute**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.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 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 Urban and Regional Studies Institute**PERT Step 5 – Probabilities Computing probability in Excel**using data compiled in your table Urban and Regional Studies Institute**Constructing the Spreadsheet**Step 1 - Create a spreadsheet that resembles the table used earlier Urban and Regional Studies Institute**Constructing the Spreadsheet**Step 2 – Use formulae as shown to calculate PERT Expectations Urban and Regional Studies Institute**Constructing the SpreadsheetCell 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 Urban and Regional Studies Institute**Constructing the Spreadsheet**Step 3 – Use formulae as shown to calculate variances Urban and Regional Studies Institute**Constructing the SpreadsheetCell Formulae used for PERT**Analysis – Variances • Computing Variances • For each task cell: • ((Pessimistic-Optimistic)/6)2 • Adjust cell address for each task Urban and Regional Studies Institute**Constructing the Spreadsheet**Step 4 – Use formulae as shown to calculate STD. Deviations Urban and Regional Studies Institute**Constructing the SpreadsheetCell 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 Urban and Regional Studies Institute**Constructing the Spreadsheet**Step 5 – Use formula as shown to sum PERT expectations Urban and Regional Studies Institute**Constructing the SpreadsheetCell Formula used for PERT**Analysis – Summing PERT Expectations • Sum Pert Expectations using either auto-sum feature or sum formula Urban and Regional Studies Institute**Constructing the Spreadsheet**Step 6 – Use formula as shown to sum variances Urban and Regional Studies Institute**Constructing the SpreadsheetCell Formula used for PERT**Analysis – Summing Variances • Sum Variances using either auto-sum feature or sum formula Urban and Regional Studies Institute**Constructing the Spreadsheet**Step 6 – Use formula as shown to compute probability Urban and Regional Studies Institute**Constructing the SpreadsheetCell 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) Urban and Regional Studies Institute**Constructing the SpreadsheetCell 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 Urban and Regional Studies Institute**PERT AnalysisThoughts, 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 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. Urban and Regional Studies Institute**CPM Analysis**• A typical CPM table might have the following structure: cost-per-week for crashing = crashed costs divided by time saved Urban and Regional Studies Institute**CPM AnalysisThoughts, 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 Urban and Regional Studies Institute**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. Urban and Regional Studies Institute**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 Urban and Regional Studies Institute**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 Resources Used in This Unit Urban and Regional Studies Institute**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