Thinking in Project Management Terms.docx

8/14/2019 Thinking in Project Management Terms.docx

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Thinking in Project Management TermsBasicMethods and Calculations

By Bob Hugg

In Unit 1 Project Management (PM) was discussed as a management philosophy. Within thatphilosophy there are many methods and techniques; most are industry specific and are designed toprovide performance metrics meaningful to that industry. This unit will discus the three chiefmethods in wide use with the most focus paid to the most commonly used technique, PERT/CPM.PERT and CPM, though separate techniques, are commonly used in tandem because together theyprovide a stronger tool and will be discussed accordingly in this chapter.

A central weakness of both PERT and CPM is the inability to deal with resourcedependencies As discussed in chapter 1, resource dependencies are those that concern theavailability of resources whether they are human, mechanical or fiscal (PERT/CPM considers onlycausal dependencies, the completion of a prior task). PERT/CPM also assumes that additionalresources can be shifted to a project as required. Because, in the real world, all projects have finiteresources to draw on the estimates and expectations are frequently skewed. Because of thisweakness, a significant portion of the PM community believes that PERT/CPM creates unrealisticexpectations, at best. As a result, management of projects using only PERT/CPM can be difficultand frustrating for worker, Project Managers and stakeholders alike.

A newly emerging (within the last 10 years) methodology is Critical Chain ProjectManagement (CCPM), also referred to asTheory of Constraints. In essence, CCPM focuses onmanaging constraints, the relationship between tasks within a project and resources withinproject. By actively managing these hotspotsit is believed that CCPM decreases project conflictand tension and provides a more balanced expectation. Though an interesting theory, CCPM islargely unproven and appears to be most applicable in projects concerning highly dynamic tasks thatcan be grouped in modules. Module structure groups tasks where the completion of a moduledelivers some degree of function that can be used regardless of the status of the remainder of theproject. An example would be software development, where a subroutine that is common to many

applications can be completed and useful without the entire project is completed. Because therelationship between modules is not as critical, the modules themselves can be re-planned and re-scheduled as necessary, adding a degree of efficiency and decreasing conflict within a project orbetween projects. CCPM also focuses on overall project progress instead of individual task progress.A perceived strength of CCPM is that it is based on an absence of multi-tasking; a single resource isonly assigned to a single task/project. A relatively humanistic approach, CCPM calculations alsoaccount for the inconsistent nature of human performance (good days, bad days, sick time, trainingneeded, etc). CCPM estimates are much broader (50% probability, 90% probability, etc) and deal


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exclusively with a single normal completion date of the project as a whole. As such, it is believedthat by identifying and grouping tasks and limiting constraints the project becomes moremanageable while providing incremental value. Critics of CCPM argue that its assumptions (absenceof multitasking, tasks may be grouped into semi-independent yet value-filled groups) createunrealistic expectations. In any event, CCPM seems applicable only in those industries where

incremental progress can deliver incremental value or function. Clearly, only completing one wing ofan airplane, 2 walls of a house or 1/3 of a city-wide traffic risk assessment would provide little value,so CCPM has found little acceptance outside of very specific hi-tech business areas.

The second method in use is a variation of PERT called Earned Value Method, introducedby the Department of Defense in the mid 60s. In the business world this method is synonymouswith ROI (Return On Investment).Simply put, it examines the relationship between the cost ofdoing something and the value received by doing it. Earned value does not concentrate onprobability of completion at a specific time, nor does it deal with a specific time or range of times,though a byproduct of the analysis is a constantly moving completion projection. It tracks tasks

and the project as a whole in terms of money by analysis that answers 3 specific questions:

1) How does the cost of work performed compare to the value of the workperformed?

2) What is the value (in dollars) of work performed so far?

3) How does the amount of money spent so far on a project compare to what shouldhave been spent?

Using answers to those questions, Earned Value Method generates a variety of productivityindices that can be used to forecast a project completion date. Because Earned Method focuses onwork performance in terms of cost and value, it is used extensively throughout the Department ofDefense in contracts administration and in industries where significant amounts of work areperformed either under contract or through contractors. It is not commonly used in Social andBehavioral sciences or technical production (software development, healthcare, etc) because, inthose disciplines, the tangiblevalueof the process and result is much more difficult to identify.Earned Value Method employs many fundamentals of WBS and PERT and is commonly found as

an analysis tool in most mainstream PM software packages, including MS Project.

By far, the most common method used is PERT/CPM. The remainder of this unit will focuson introducing basic methods and calculations in use. As discussed in Unit 1, PERT is based on abeta distribution that is useful in real-world planning because it accounts for a degree of randomness(that all humans bring to the table). Based on its theoretical model, PERT delivers a task or project


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completion estimatebased on pessimistic, optimistic and most likely estimates provided by theuser. PERT also provides a probability of completion on any date selected by the user. PERTcalculations are simple and straightforward, but tend to get lengthy when many tasks areused. Before the task calculations can be made, however, 2 steps must be taken in any projectplanning:

1) Define the goal of the project and the tasks required to complete it2) Place tasks in a logical order and determine the critical path(it is helpful to diagram

the tasks)a. The critical pathis the longest time path through the network of tasks

When these steps are complete, generate a set of duration estimates for each task; each setshould contain a pessimistic, most likely and optimistic estimate. To keep the estimates straight, it isuseful to labelpessimisticestimates asTP, optimisticestimates asTOand most likelyestimates asTL(any labeling system can be used, but these are fairly intuitive).For each task, calculate the PERTderived expected duration (TE) based on a formula, (TP +4TL +TO) / 6 =TE

1) Read this formula as the sum of pessimistic plus 4 times likely plus optimisticdivided by 6 equals the expected duration

2) Compete this calculation for all tasks; making sure to group tasks on the critical pathseparately

a. The critical pathis the longest time path through the network of tasksb. The sum of duration of tasks on the critical path will determine the project

duration

A second set of calculations are necessary to determine information that will be useful later

in the process. These calculations will yield the Standard Deviation (SD) and Variance (V) for eachtask duration. The SD is the average deviation form the estimated time; as a general rule, the higherthe SD is the greater amount of uncertainty exists. The V reflects the spread of a value over anormal distribution. The SD and V will be useful in determining the probability of the projectmeeting a desired completion date. The formulae for calculating SD and V are:


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1) SD=(TP-T0)/6 {read as (pessimistic-optimistic)/6}2) V=SD2(Standard Deviation squared)3) Compete this calculation for all tasks; making sure to group tasks on the critical path

separately

c. The critical pathis the longest time path through the network of tasksd. The sum of duration of tasks on the critical path will determine the project

duration

Since most projects involve several tasks, it is helpful to construct a table to stay organized. A tablemight look like:

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

TOTALOTHER PROJECT TASKS

TASK TO TL TP TE SD V

TOTALTable 1, Sample table of estimates

Consider a sample project, planting flowers and trees. This project could involve 8 tasks;when diagramed it would look like:


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Figure 1, PERT Diagram for sample project

For this sample project a table would be helpful in getting organized, and would yield moreusable information than the PERT diagram.. This sample project, with 8 tasks, complete withoptimistic, pessimistic and likely estimates could then populate the table. When PERT expecteddurations and SD and V are added using the formulae, the table would look like:

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

1 1 3 5 3 .67 .442 2 4 7 4.17 .83 .695 1 3 6 3.17 .83 .696 1 3 5 3 .67 .448 1 2 4 2.17 .5 .25

TOTAL 7 15 28 15.51 3.5 2.51OTHER PROJECT TASKS

TASK TO TL TP TE SD V3 .5 1 3 1.25 .42 .174 .5 1 3 1.25 .42 .177 .5 1 3 1.25 .42 .17

TOTAL 1.5 3 9 3.75 1.26 .51Table 2, Sample Project populating a table of estimates

This table now provides a wealth of information. It contains a list of required tasks andseparates those tasks in critical path and non-critical path tasks. It also lists the best and worst caseestimates and the expected duration for each task and the project as a whole (the sum of the


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expected critical path tasks). This table also lists the Standard Deviations and Variances for each taskand the project as a whole, a valuable (but not intuitive) indicator of the probability of projectcompletion by a desired date. A manual method to calculate the probability of meeting a desireddate is somewhat more complicated than the other formulae used so far, but would look like:

1) Denote the sum of all expected durations on the critical path as S

2) Denote the sum of all variances on the critical path asV

3) Select a desired completion time, denote this as D

4) COMPUTE: (D-S)/square root (V) = Z( Read as the result of D minus Sdivided by the square root of V equals Z)

5) Enter a standard normal table to find a probability that corresponds with Z or goonline to:

a. http://math.uc.edu/statistics/statbook/tables.html)to enter a z number -the application will retrieve the probability from the very lengthy table

For our sample project, figure a probability based on a desired time, 15 days: ((D-S)/sqrt{V} =Z)

a. (15-15.51)/square root(2.51) = (15-15.51)/1.59=-.321 (Z) (Rounded)b. A corresponding probability is 37.7% (Rounded)c. In other word, there is a 37.7% probability that the project will be completed within

15 days of the start date

It is also helpful to determine the earliest and latest dates a task can start to highlight areasthat may be improved upon. For each task, determine the latest allowable time for moving to thenext task. Think of these tasks as flexible tasks that can be started earlier or later in the process with

no effect on the project duration. The difference between latest time and expected time is calledslack time; Tasks with zero slack time are on the critical path. For our sample project, these dateswould look like:

CRITICAL PATH TASKS (Longest Duration)TASK TO TL TP TE ES EF LS LF Slack SD V
http://math.uc.edu/statistics/statbook/tables.htmlhttp://math.uc.edu/statistics/statbook/tables.htmlhttp://math.uc.edu/statistics/statbook/tables.html


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1 1 3 5 3 0 3 0 3 0 .67 .442 2 4 7 4.17 3 7.17 3 7.17 0 .83 .695 1 3 6 3.17 7 10.17 7 10.17 0 .83 .696 1 3 5 3 10 13 10 13 0 .67 .448 1 2 4 2.17 13 15.17 13 15.17 0 .5 .25

TOTAL 7 15 28 15.51 3.5 2.51OTHER PROJECT TASKS

TASK TO TL TP TE ES EF LS LF Slack SD V3 .5 1 3 1.25 0 1.25 3 4.25 3 .42 .174 .5 1 3 1.25 0 1.25 3 4.25 3 .42 .177 .5 1 3 1.25 1.25 2.50 4.25 5.50 3 .42 .17

TOTAL 1.5 3 9 3.75 1.26 .51ES=Earliest Start EF= Earliest Finish LS=Latest Start LF=Latest Finish

Table 3, Sample Project populating a table of estimates with start dates

The table is now complete and is a treasure trove of project information, but has provenlabor intensive due to the number of manual calculations (imagine a project with dozens orhundreds of tasks!). The same results can be obtained in much less time with much less effort usingMS Excel.

Open a new workbook in Excel and structure a spreadsheet to resemble the table for thesample project. This spreadsheet can become a template for future project calculations and, ineffect becomes a PERT calculator. It may look like:
http://krypton.mankato.msus.edu/~tony/courses/PERT/pertcalc.xlshttp://krypton.mankato.msus.edu/~tony/courses/PERT/pertcalc.xlshttp://krypton.mankato.msus.edu/~tony/courses/PERT/pertcalc.xls


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Figure 2, PERT Analysis Calculator layout

Notice how the spreadsheet resembles the table used so far, with a notable addition. This

calculator will include a function to calculate the probability of completing a project on a desireddate. Use the dame formulae discussed so far to write equations for each cell address. To start, beginwriting equations for the cell addresses for calculating the PERTexpected duration.

Figure 3, PERT Analysis Calculator layoutPERTExpected durationequations

1) For each task cell: (Optimistic + 4x Typical + Pessimistic)/62) Adjust cell address for each task

Next, write equations to calculate theVariancesfor each task:


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Figure 4, PERT Analysis Calculator layoutPERTVarianceequations

1) For each task cell: ((Pessimistic-Optimistic)/6)22) Adjust cell address for each task

Next, write equations to calculate the Standard Deviationsfor each task:


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Figure 5, PERT Analysis Calculator layoutPERT Standard Deviationequations

1) For each task cell: sqrt (V) ( the square root of V for that task)2) Adjust cell address for each task

Next, write an equation to sum the PERT Expected Date for the project:

Figure 6, PERT Analysis Calculator layoutSumming Pert Expected Dates

Next, write an equation to sum theVariancesfor the project:


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Figure 7, PERT Analysis Calculator layoutSumming Variances

Finally, write the equation to calculate the Probability of Completion for a desired projectdate:

Figure 8, PERT Analysis Calculator layoutProbability of Completion


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Excel uses a formula designed to compute the probability of placement of a combination ofelements in a normal distribution that is very accurate for use in real-world situations. The equationis NORMDIST(x, mean, standard_dev, cumulative) in which:

1) X is the value for which you want the distribution (desired date)2) Mean is the arithmetic mean of the distribution (summed PERT expected

durations)3) Standard_dev is the standard deviation of the distribution (square root of the

summed variances)4) 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)

Somethings to consider when setting up this equation:

1) Be sure to adjust formulae as necessary when adding additional tasksa. If a error message shows up check cell addresses in the formulae first

formulae must reflect intent2) This set of formulae mirrors the manual calculations but takes less time for the

user3) Because PERT is a probabilistic approach, these formulae can deliver a 100%

probabilitybut no plan is perfectthese are always estimates4) Never feel there is a 100% probability of a project completing on the estimated

date

Armed with a substantial tool to compute PERT expectations and probabilities, all thatremains is to complete a few simple CPM calculations. As discussed in Unit 1, and earlier in thisunit, CPM deals with a single expected date and anticipates that a project may be crashed. Crashinga project is reducing the project to its shortest duration by adding resources. It is important to notethat the effort required to complete a task or project remains the same, only the duration may be


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shortened. By its nature, crashing a project is disruptive (it pulls resources from other tasks) andincreases the project cost. Careful consideration must be made whether the effects of crashing aproject are worth completing a project earlier. The answer will vary from project to project andsituation to situation. Again, using a table to get organized, a very simple example might look like:

The basic steps in completing a CPM analysis are: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 on the critical pathwith the lowest cost-for-crashing

5) Recalculate the project network (the critical path might change!)

6) Repeat steps 4 & 5 until all the paths have been crashed.

7) Ease up on all non-critical paths, just to the point that all paths are critical

Table 4, Sample Project populating a table of CPM estimates of time and costs

In this example the time saved (4 weeks) is substantial but the cost increase is alsosubstantial ($5,000). At an aggregate increase of $2,333 per week for crashing this project, this wouldbe a course of action not lightly taken. Sometimes crashing a project is unavoidable but a seriousconsideration of the tangible and intangible costs must be undertaken.

When used together, PERT and CPM can provide:

1) A range of time estimates (PERT)

Activity BeginEnd Time(Crashed)

Time(Normal) Cost(Crashed) Cost(Normal)

TimeSaved

CostIncrease Cost /Week

Foundation 1 2 1 2 4000 3000 1 1000 1000Frame 2 3 1 4 8000 4000 3 4000 1333

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


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2) Likely time estimates (PERT and CPM)3) Cost estimates (CPM)4) Time and costs if crashed (CPM)5) Probabilities of completion on time for a range of times (PERT)6) A clear path of tasks that are critical to the project (PERT and CPM)7) A central focus for solid communications on project issues (PERT and CPM)

All plans are estimates and should be viewed as such. When used together, PERT and CPMprovide a valuable tool for organizing and tracking projects as well as providing a usable what ifforum. Care must be taken in collecting estimates used in planningany plan is only as good as themost unrealistic estimate. By using simple but complementary formulae, managers at all levels canget, and keep, a good handle on a project or its tasks.

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