History of Christianity—Lecture 7: The Gospel according to Luke (part 1)


This is a summary of the seventh part of twenty-four in the course on the New Testament presented by The Teaching Company.  The lectures in this course are by Prof. Bart D. Ehrman, the James A. Gray Distinguished Professor of Religious Studies at the University of North Carolina at Chapel Hill.  His expertise is in the Greco-Roman cultural environment of early Christianity and the textual criticism of the New Testament.  For those who are interested in purchasing this course and listening to the complete lectures, please go to http://www.thegreatcourses.com.

1.  Introduction

We have not yet begun to ask the question about what Jesus himself really said and did.  Instead, we have been looking at the distinctive portrayals of Jesus in each one of the Gospels.  We have seen that Mark portrays Jesus as the son of God who, contrary to widely held expectations, must suffer for the sins of the world.  Matthew agrees with this perspective, but adds a strong emphasis that Jesus was the Jewish Messiah sent in fulfillment of the Jewish scriptures, a new Moses who expected his followers to keep the Jewish Law.

Prof. Ehrman turns now to the third of the Synoptic Gospels, the Gospel of Luke, who like Matthew and Mark has a distinctive emphasis of his own.  On the other hand, like Mark, Luke will portray Jesus as the son of God whose death fulfilled the Scriptures, but he does not stress the failure of everyone to recognize Jesus the way that Mark did.  In fact, in Luke’s Gospel, Jesus is worshipped already as an infant.  Like Matthew, Luke will remain that Jesus is the Messiah, but he does not stress that Jesus is the new Moses who demanded that his followers adhere to the Jewish law.  Instead, Luke stresses that Jesus’ salvation comes not just to the Jews, but to all people.

Prof. Ehrman does not mean to say that Jesus is not portrayed as Jewish in the Gospel of Luke, for in fact he is portrayed as a Jewish prophet, that is, a man who knows God’s will and has been called by God to proclaim this will to his people.  Jesus in this Gospel is portrayed as a Jewish prophet sent to the Jewish people who was rejected by them.  Because he was rejected by the Jews, his message of salvation can then go to the non-Jews, that is, to the Gentiles.  That is the overriding thesis of the Gospel of Luke.

2.  Background Information

As with the other Gospels we have considered, this one too is anonymous; the other didn’t tell us his name.  Traditionally the Gospel has been ascribed to a man named Luke who is a Gentile physician who was a traveling companion of the Apostle Paul.  This tradition goes back to the 2nd century.  Whether or not we can trust the tradition is a matter of debate among competent scholars.  Like the other Gospels, this one was written in Greek.  Apparently, it was written at about the same time as the Gospel of Matthew, possibly around 80-85 AD.

There’s little to suggest that Matthew and Luke knew of each other’s work, but they do both appear to have had access to the Gospel of Mark, and to the lost source of Jesus’ sayings that scholars have called “Q”.  One of the things that makes the Gospel of Luke distinct is that this author wrote a second volume, the Book of Acts, which we will be discussing later in this series of lectures.  The Book of Acts, which is our only surviving account of the history of earliest Christianity after the death of Jesus up through the ministry of the apostle Paul.  In this later lecture, we’ll look at how this second volume, the Book of Acts, continues many of the themes and emphases of this first volume, the Gospel of Luke.  This lecture focuses exclusively on the Gospel of Luke.

3.  The Preface to Luke’s Gospel

One way of approaching Luke’s account is by comparing it with the narratives that we have already considered, those of Matthew and Mark.  Prof. Ehrman wants to compare these accounts not to conflate them, but precisely to show how they differ from one another, so we can see what the distinctive emphases are.

The first thing that strikes one when making a comparison between Luke and the other Gospels is that he begins in a completely different way from Matthew and Mark.  Luke begins by a kind of preface, an overview of his account.  It is a preface that is very much like that of  prefaces of other works that you find from ancient historians.  Luke begins by saying (Luke 1:1-4):  “whereas many have undertaken a narrative of the matters that have been fulfilled among us, just as they were handed on to us from the beginning from eyewitnesses and ministers of the Word, it seemed good to me, most excellent Theophilus, to produce an accurate account, having followed all things carefully so that you might know the certainty of the matters that had been fulfilled among us.”

It’s a very interesting preface for several reasons.  First, as mentioned before, this preface is like prefaces found in other works of other historians, which might suggest that Luke was taking the historical nature of his narrative a little more seriously than the other Gospel writers that we have.  He is trying to mimic the style of ancient historians.

Second, he tells us what his sources of information were.  This was a typical move among ancient historians.  His narrative will be based on accounts that he has seen based on written reports that others have made, and these written reports go back to the reports of eyewitnesses.  In other words, Luke has before him written Gospels and oral traditions.

4.  Luke’s implicit criticism of Mark

Third, it is striking that Luke does not think favorably of his predecessors.  He indicates that others have tried to write an account, but now he wants to write one that’s accurate so that the recipient will know the certainty of what happened before.  In other words, he is casting some slight aspersions perhaps on some of his predecessors, which is particularly interesting if in fact Mark was one of those predecessors, because that might suggest that Luke didn’t think Mark had done an adequate job.  Of course that’s implied by the fact that he has changed Mark so significantly.  If he had liked Mark the way it was, he would have simply copied Mark and published it as is.

5.  Luke’s Dedication

He dedicates this book to Theophilus, but we don’t’ know who Theophilus was.  It’s typical for historians to dedicate their work to a patron, someone who provides financial support for the author.  The author may have been a patron of Luke.  Some scholars have thought that Theophilus might have been some kind of Roman administrator who Luke is giving his book to.  The reason for thinking that is because he calls Theophilus “most excellent Theophilus” and that term “most excellent” is used in the Book of Acts for Roman administrators.  So possibly this is a pagan Roman who Luke is writing for.

While that is a possibility, and a number of scholars think that is what is going on here, it seems to other scholars somewhat unlikely that a book of this size is being handed over to some pagan Roman official as if he would have time or the desire to read it.  There’s another explanation of what “Theophilus” is.  The term “Theophilus” in fact comes from two Greek words meaning “beloved of God” or “lover of God.”  It’s possible that in fact Luke has devised a fictional recipient of this book, one who is loved of God.  In other words, he is writing for Christians in his own community who are loved of God or who are lovers of God.  That makes somewhat better sense since most of these early Christian writings, in fact, all of these Gospels, were probably directed to the Christians rather than to outsiders, say, as missionary literature.  And so it may be that Theophilus is simply a “code name” for the Christians who are receiving this book.

6.  Luke’s Genealogy of Jesus

Once we get beyond the preface, we can see other differences between Luke and the other Gospels.  First, let me point out a striking difference between the Gospel of Luke and the Gospel of Matthew.  It’s not that Luke used Matthew as a source, but they do have some similarities and so it is interesting to look at some of their differences.  One of the striking differences between Luke and Matthew has to do with the genealogy of Jesus that he uses in his Gospel.  Mark doesn’t have a genealogy; Matthew has one and it turns out Luke has one as well.  What is striking is that Luke’s genealogy is different from Matthew’s.

The genealogy that Luke gives is found in Chapter 3.  In Chapter 3 we are told that Jesus was supposedly the son of Joseph who was the son of Heli who was the son of Matthat who was the son of Levi, etc. and it keeps on going back.  Matthew’s genealogy, if you recall, traced Jesus back to King David, and from King David back to Abraham, the father of the Jews.  The stress in Matthew’s genealogy was that Jesus was Jewish, descended from the father of the Jews and the great King of the Jews, and is the Messiah from the Davidic line.

Interestingly, Luke doesn’t just go back to David and Abraham; he goes all the way back to Adam.  This is a terrific genealogy that traces Jesus all the way back to Adam, as in Adam and Eve.  But why?  If Matthew’s genealogy was meant to show the Jewishness of Jesus because he’s related to David and Abraham, Luke’s genealogy is designed to show Jesus’ humanity.  He is not just the Savior of the Jews.  He descends from the entire human race; he’s the Savior of all humankind.

This genealogy is different from Matthew’s not simply because it goes all the way back to Adam.  If you read the beginning part of this genealogy, you realize in fact that it is a completely different genealogy from the one in Matthew.  It traces Jesus’ lineage through Joseph, as does Matthew’s, but Joseph in Luke’s genealogy as a different father and a different grandfather and a different great-grandfather than does Joseph in Matthew’s genealogy.  The names are in fact all different from Joseph back to David.  Some people have tried to reconcile this by saying that Matthew is giving the genealogy of Joseph, whereas Luke is giving the genealogy of Mary.  This would be a clever solution which would explain why you have the different names.  Unfortunately for that thesis, when you read the text itself it is quite clear that Luke’s genealogy is also the genealogy of Joseph.

Apparently Matthew and Luke simply inherited their genealogies from different sources.

The next post will cover the second part of the lecture.

5th Edition PMBOK® Guide Chapter 7: Earned Value Management (part 2)


The most powerful of the tool & techniques of process 7.4 Control Costs is Earned Value Management or EVM. The whole point of earned value management is to find out how the project is performing as compared to the cost and schedule performance baselines. The last post discussed the quantities PV, EV, AC, which are the “building blocks” of the all the EVM variance formulas that I am going to discuss in this post.

1. Variances

A measure of how a project is doing is a variance, which is calculated by taking the earned value (EV) and subtracting either the actual cost (AC) or the planned value (PV).

Here are the variances that are used to measure the performance of a project, together with their definition and the formula of how they are calculated.

Variance

Definition

Formula

Cost Variance (CV)

 

The amount of budget deficit or surplus. CV = EV – AC
Schedule Variance (SV) The amount by which the project is ahead or behind schedule. SV = EV – PV
Variance at Completion (VAC) A projection of the amount of budget deficit or surplus at the end of the project. VAC = BAC – EAC

With all of these variances, if the result is positive, then that is good: the project is either under budget or ahead of schedule. If the result is negative, then that is bad: the project is either over budget or behind schedule.

2. Performance Indexes

Another measure of how a project is doing is a performance index, which is calculated by taking the earned value (EV) and dividing by either the actual (AC) or the planned value (PV). Here are the performance indexes that are used to measure the performance of a project, together with their definition and the formula of how they are calculated.

Performance Index

Definition

Formula

Cost Performance Index (CPI)

 

The amount of budget deficit or surplus. CPI = EV/AC
Schedule Performance Index (SPI) The amount by which the project is ahead or behind schedule. SPI = EV/PV

With all of these variances, if the result is greater than one, then that is good: the project is either under budget or ahead of schedule. If the result is less than one, then that is bad: the project is either over budget or behind schedule.

These variances or performance indexes are used to find out whether the project is performing better or worse than expected.

The next posts on this topic will show how they can be used to forecast the amount of money it will take to complete the project, as well as the amount of time it will take to complete it.

5th Edition PMBOK® Guide—Chapter 7: Earned Value Management (Part 1)


1. Introduction

Earned Value Management is the first technique listed in the 5th Edition PMBOK® Guide for the only time management knowledge area process in the Monitoring & Controlling Process Group, 7.4 Control Costs. It is also the most powerful in the extent of its use and implications for the proper management of a project. For those of you who are new to the concept, and are wondering “what is earned value management good for?”, let me tell you a story. There once was a young Native American brave who once asked his father, “I know that we’ve from the Halawi tribe, but where did the name come from.” “The chief came up that name. Last winter, when we moving our hunting grounds to this place, I went up to him and asked him the same question you asked me. What’s the name of our tribe? He was standing on a hill looking lost, when he looked up from his map, and said, “where the Halawi?” And that’s how we got our name. The purpose of that little story is to let you know that when you are working on a new project, at some point your “chief” or boss may come to ask you the same question, “where the hell are we?” In other words, is the project under budget and on schedule? That’s what earned value management can tell you.

2. Three Key Quantities: PV, EV, AC

There are three basic quantities you need to know when dealing with earned value analysis: Planned value, earned value, and actual cost. The PMBOK® Guide gives a definition which, although accurate, might be more simply expressed as I have attempted to do in the column marked “English Definition” next to the “PMBOK® Guide Definition.” The reason why earned value measurement works is because the quantity of “earned value” is a measure of both the schedule (“measure of work performed”) and the budget (“expressed in terms of budget authorized for that work”), and a combination of earned value and the planned value or actual cost can give an indication of how the project is doing with respect to the schedule or the budget, respectively.

Quantity Measures PMBOK® Guide Definition English Definition
Planned Value (PV) Schedule Authorized budget assigned to scheduled work. How much work was supposed to be done?
Earned Value (EV) Schedule AND Budget Measure of work performed expressed in terms of budget authorized for that work How much work was actually done?
Actual Cost (AC) Budget Realized cost incurred for the work performed on an activity during a specific time period How much did the work actually cost?

Now the planned value, earned value, and actual cost are measured at various times during the project and thus provide a “snapshot” of how the project is doing.

3. Budget at Completion

One additional quantity you need to be aware that is related to one of the key three quantities above is that of the Budget at Completion. The planned value or PV is the authorized budget assigned to the work scheduled up to that point. If you take the project all the way to its completion, then what should the planned value be at the end of the project? It should be equal to the budget at completion or BAC, in other words, the authorized budget assigned to ALL the work scheduled in the project. However, a word of caution! The actual PMBOK® Guide definition is “sum of all budgets established for the work to be performed”, and then in the chart on page 224 of the Guide, it says in the next column “the value of total planned work, the project cost baseline.” One of the problems about dealing with the project budget is that in reality, it is like a three layer cake, with the bottom layer being the project cost estimate, with a layer of contingency reserves or “filling” on top, which creates the middle layer called the project cost baseline, and a layer of management reserves or “filling” on top of that, which creates the top layer called the project budget. The BAC or budget at completion is, somewhat confusingly, NOT based on the project budget or the top layer, but on the middle layer of the project cost baseline, which includes both the cost estimates and the contingency reserves (but NOT the management reserves). So just be aware that although it says the budget at completion, this will be obtained by getting the project cost baseline for the project, and not the project budget. I guess we could all start calling it the “Baseline at Completion” to avoid confusion, but the terminology of Budget at Completion is so well firmly established, that it would be hard to change the term at this point. The next post shows how these four quantities, PV, EV, AC, and BAC (which is related to PV), can be used to show the variance of the project from its performance baseline of either the schedule or the budget. The fact that it can be used to handle both types of variance is part of the reason why earned value management has such tremendous utility as a technique for monitoring & controlling a project.

5th Edition PMBOK® Guide—Chapter 7: Process 7.4 Control Costs


1. Introduction

The three of the four processes devoted to cost management are in the Planning Process Group. The fourth process, 7.4 Control Costs, is in the Monitoring & Controlling Process Group. The performance baseline for costs, the cost baseline, which was determined in the last process, 7.3 Determine Budget, is what the performance of the project will be measured against when the actual costs of doing the work are calculated.

The purpose of this post is to give a general overview of the inputs, tools & techniques, and outputs of this process.

2. Inputs

The main inputs come from the cost management knowledge area, as you would expect. For those projects which are not totally funded in advance of the project, but at various stages during the project, project funding requirements will need to be paid attention to so that the project doesn’t get too far ahead of itself to the point that funding is temporarily not available for activities.

Work performance data is used which will be analyzed and processed into work performance information through this process. The ubiquitous OPAs inputs are also important as they give access to the company’s corporate knowledge base when it comes to cost control.

7.4 CONTROL COSTS
INPUTS
1. Project Management Plan The following elements of the Project Management Plan are inputs to the process.

  • Cost Baseline—This is an output of process 7.3 Determine Budget
  • Cost Management Plan–This is an output of process 7.1 Plan Cost Management.
2. Project Funding Requirements
This not only specifies the projected expenditures for the project, but also the schedule of when those expenditures will be periodically released for the project.
3. Work Performance Data The data that will be used in earned value management calculations are

  • which activities have been started and completed, and the degree of progress for those in process, and
  • the costs that have been planned for those activities and the actual costs incurred.
4. OPAs
  • Cost control-related policies, procedures, and guidelines
  • Cost control tools
  • Methods for monitoring and reporting costs
TOOLS & TECHNIQUES
1. Earned Value Management Combines scope, schedule, and resource measurements to assess the project performance and progress. Main EVMs are

  • planned value (PV),
  • earned value (EV), and
  • actual costs (AC).

These are used to calculate variances:

  • Schedule variance (SV = EV – PV)
  • Cost variance (CV = EV – AC)
  • Schedule performance index (SPI = EV/PV)
  • Cost performance index (CPI = EV/AC)
2. Forecasting Developing an estimate at completion (EAC) to see how far it varies from the budget at completion (BAC), VAC = BAC – EAC
3. To-complete performance index (TCPI) Measures the cost performance to be achieved in order to have the project completed within the budget at completion (BAC), or alternately, the estimate at completion (EAC). TCPI is calculated by taking the remaining work and dividing by the remaining funds, which can be taken from either the BAC or EAC:

TCPI = (BAC – EV)(BAC – AC)

TCPI = (BAC – EV)(EAC – AC)

4. Performance Reviews
  • EVM (earned value management): takes a snapshot of the performance of the project at any given time
  • Variance analysis: The cause of the cost or schedule variance found through EVM is analyzed to determine corrective or preventive actions required in order to eliminate or reduce that variance.
  • Trend analysis: Examines performance over time (as measured through EVM) to see if there is a trend towards improvement or deterioration.
5. Project Management Software This tool is often used to monitor PV, EV, and AC.
6. Reserve Analysis Monitors the status of contingency reserves and management reserves. Unused contingency reserves for probable risk events which do not occur may be removed from the project budget.
OUTPUTS
1. Work Performance Information The calculated values of CV, SV, CPI, SPI, TCPI, and VAC
2. Cost Forecasts The calculation of estimate at completion either based on a bottom-up recalculation or through one of the formulas.
3. Change Requests Based on the work performance information and cost forecasts, changes may be indicated in one of the following categories

  • Corrective action
  • Preventive action
  • Changes to the cost baseline itself
4. Project Management Plan Updates The same elements of the cost management plan that were inputs may be modified as a result of this process.

  • Cost baseline
  • Cost management plan
5. Project Documents Updates
  • Cost estimates
  • Basis of estimates
6. OPAs Updates
  • Causes of variances
  • Corrective actions to be taken
  • Financial Databases
  • Lessons learned

3. Tools & Techniques

The subject of earned value management, forecasting, the TCPI (To-Complete Performance Index), and performance reviews are the main techniques, with the project management software being the main tool. Earned value management takes a snapshot of the present moment to see how the project is doing. The techniques of forecasting and TCPI shows how the future of the project will evolve given how the project is doing now.

Finally, the performance reviews compare the past performance with the present performance to see how the progress of the project has evolved up until the present moment.

Reserve analysis takes into account the “extra layers” on top of the cost estimates, the contingency reserves (which are added to the cost estimates to get the cost baseline) and the management reserves (which are added to the cost baseline to get the project budget). It should be decided whether any unused reserves will simply be left in the project budget, thereby improving the performance of the project, or whether they will be taken out of the project budget to possibly be used on other projects.

4. Outputs

The work performance information and the cost forecasts are elements which need to be communicated to the project team and concerned stakeholders on a regular basis. If the analysis of these indicate that there is a variance in either the cost or schedule performance of the project that needs correcting, then a change request may be recommended.

The corrective action aims to reduce the variance, whereas preventive action aims to prevent the variance from growing larger in the future. It may happen, however, that the variance is so large that the cost baseline is determined to be unrealistic, in which case it may be suggested that the cost baseline itself is changed.

In any case, these change requests are outputs of this process, but then are inputs to the process in the Integration Management Knowledge area called process 4.5, Perform Integrated Change Control.

As usual with monitoring and controlling processes, the management plans, project documents, and OPAs may end up being updated as a result.

The inputs to this process are clear enough, but the technique of earned value management (EVM) and associated techniques (forecasting, TCPI) are so vital to project management that they deserve some posts of their own, which I will begin with starting tomorrow.

5th Edition PMBOK® GUIDE—Chapter 7: Contingency Reserves and Management Reserves


1. Contingency Reserves and Management Reserves

Every project faces risks that some event may occur which may impact the project’s schedule. That is why it is necessary to list the known or predictable risks before the start of a project and list them in the risk register. The next step in dealing with the risks is in devising a risk response strategy in case they occur.

To fund these risk responses, a project manager needs to set up contingency reserves, the contingency in this case being if a certain risk occurs at some point in the project. These contingency reserves are in control of the project manager, and the funds are spent out of these reserves if the predicted risk actually does comes about.

However, there may be risks that are unknown or not predicted in advance. You cannot develop a risk response in advance because you don’t know what the risks are going to be in advance. If a risk occurs that is not predicted, you need to develop a workaround or ad hoc solution to the problem. How are these workarounds funded? With management reserves. The amount of these reserves is determined before the project begins, but as opposed to contingency reserves, they are not under control of the project manager. The project sponsor must approve their use, and that is why a project sponsor must be notified if one of these “unknown” or unpredicted risks occurs, because that sponsor will have to

approve the use of funds from the management reserves in order to deal with the problem.

The two levels of reserves mean that there are three separate categories of cost aggregation to deal with on a project.

2. Cost Estimate, Cost Baseline, and Project Budget

The cost estimate for all the work packages is aggregated or “rolled up” the various levels of the WBS or Work Breakdown Structure, including the “control accounts,” until one gets to the level of the entire project, and this is the cost estimate for the project itself.

That is the first cost aggregation to be aware of. The contingency reserves mentioned in the first section are added to the cost estimate to get the cost baseline. This is the performance baseline against which the actual performance of the project will be measured. Note that, if certain risks do not occur during the project, then the contingency reserves to be used to respond to those risks will shrink during the course of the project, and the cost performance of the project will therefore improve automatically.

Then the management reserves are added to the cost baseline to yield the project budget. These funds are moved from the project budget into the cost baseline usually by the following procedure:

  1. An unknown or unpredicted risk occurs.
  2. A workaround to deal with the unknown risk is proposed.
  3. This proposal is put in the form of a change request, and is analyzed in the change control process, which must include the project sponsor.
  4. If the change is approved by the project sponsor in the change control process, then the funds from the management reserve are released from the project budget into the cost baseline.
  5. However, the performance of the project will continue to be measured not against the project budget, but the cost baseline.

The 5th Edition PMBOK® Guide not only does a better job of explaining the difference between contingency and management reserves than the 4th Edition did, but there is a helpful chart to show the difference on p. 213. If you purchase the 5th Edition in hardcover or download it electronically (which you can do if you are a member of PMI), you can refer to this chart which is more elaborate the conceptual scheme I have posted above.

The next post will go to the next process after the last process for Time Management in the Planning Process Group, 7.3 Determine Budget, namely the one in the Monitoring & Controlling Process Group, called process 7.4 Control Costs.

5th Edition PMBOK® Guide—Chapter 7: Process 7.3 Determine Budget


After all the estimation done in process 7.2, it is now time to determine the budget, and that’s what this process does. The purpose of this post is to give a general overview of the inputs, tools & techniques, and outputs associated with this process.

1. Inputs

Obviously the most important inputs to the process 7.3 Determine Budget are the estimates determined in the previous process 7.2 Estimate Costs. Other important inputs come from other knowledge areas such as Scope, Time, Human Resource, Risk, and Procurement Management.

7.3 DETERMINE BUDGET
INPUTS
1. Cost Management Plan This is an output of process 7.1 Plan Cost Management.
2. Scope Baseline The scope management plan has three components of the scope baseline:

  • Project Scope Statement (output of 5.3 Define Scope)
  • WBS (output of 5.4 Create WBS)
  • WBS Dictionary (output of 5.4 Create WBS)
3. Activity Cost Estimates The cost estimates of each activity within a work package are aggregated or “rolled up” to get a cost estimate for each work package as a whole. This is an output of process 7.2 Estimate Costs.
4. Basis of Estimates Details supporting the activity cost estimates (input #3). This is another output of process 7.3 Estimate Costs.
5. Project Schedule This is used to assign costs to the calendar period in which they are scheduled to occur. This is an output of process 6.6 Determine Schedule.
6. Resource Calendars This is used to indicate resource costs over the duration of the project.

This is an output of the Human Resources Management process 9.2 Acquire Project Team.

7. Risk Register Used to aggregate costs for risk responses to obtain the contingency reserves for the project. This is an output of process 11.2 Identify Risks.
8. Procurement Agreements This is used for products, services or results that are purchased from suppliers or vendors in order to complete the project. This is an output of Procurements Management process 12.
9. OPAs
  • Cost budgeting policies, templates, guidelines
  • Cost budgeting tools
  • Cost reporting formats
TOOLS & TECHNIQUES
1. Cost Aggregation Cost estimates of work packages in the WBS are aggregated or “rolled up” at higher levels (including control accounts) and then finally for the entire project.
2. Reserve Analysis This establishes the contingency reserves and management reserves for the project.
3. Expert Judgment Guidance in the area of determining the budget by those with expertise. This expertise can come from project team members, outside consultants, stakeholders (including customers), or professional or industry associations.
4. Historical Relationships These are used to develop analogous or parametric estimates.
5. Funding Limit Reconciliation The expenditure on the project needs to be reconciled with the funding limits on the commitment of funds to the project, and the timing of these commitments.
OUTPUTS
1. Cost Baseline The approved version of the time-phased project budget. Management reserves are not included in this cost baseline. The management reserves plus the cost baseline give the project budget.
2. Project Funding Requirements The funding for the project may occur in periodic increments, which may place time constraints on work to be done in the project schedule.
3. Product Documents Updates
  • Risk register
  • Activity cost estimates
  • Project schedule

2. Tools & Techniques

Cost aggregation of the work packages gets you to the cost estimate of the project. If you add the cost of risk responses or contingency reserves, you get the cost baseline of the project. If you add the management reserves, which are not controlled by the project manager but by management, to the cost baseline, you get the cost budget.

If the funding for the project is not entirely available at the beginning of the project, but is available in periodic increments, then these project funding requirements of how much funding is released and at what point in the project need to be paid attention to so that the project does not temporarily run out of funding. Thus if the project is ahead of schedule, which is normally a good thing, and it gets too far ahead of schedule, the project may temporarily run out of funding until the next increment is available. This in a way is similar to resource leveling, but in this case the resource is not the work of a specific person on the project, but the funding for the project itself.

3. Outputs

The cost baseline is the performance baseline for costs against which the actual performance of the project is measured when the actual costs of the project at any given time are known.

The project funding requirements are an important output, because they may require the project schedule to be adjusted to the necessities of the periodic project funding requirements.

For that reason, the project schedule may be updated as one of the outputs. The activity cost estimates may be adjusted to reflect contingency reserves, and this information may also be updated in the risk register.

In the next post, I will review the three different figures of the cost estimate, cost baseline, and project budget and how they relate to the contingency and management reserves.

History of Christianity—Lecture 6: The Gospel according to Matthew (part 2)


This is a summary of the sixth part of twenty-four in the course on the New Testament presented by The Teaching Company. The lectures in this course are by Prof. Bart D. Ehrman, the James A. Gray Distinguished Professor of Religious Studies at the University of North Carolina at Chapel Hill. His expertise is in the Greco-Roman cultural environment of early Christianity and the textual criticism of the New Testament. For those who are interested in purchasing this course and listening to the complete lectures, please go to http://www.thegreatcourses.com.

This post covers the second part of the lecture; see the previous post for the first part.

10. Matthew’s editing of the Genealogy according to 1 Chronicles

Why would Matthew change the genealogy that he inherited from 1 Chronicles? Apparently because he wanted to show that something significant happened every 14 generations. If he included all the generations between Joram and Uzziah, then he would no longer have the sequence of 14 generations.

There are other problems with this sequence of 14 generations, one of which being that the final sequence of 14 actually contains only 13 names. Matthew, though, is trying to make a point, and the point is not really about the historical accuracy of his genealogy; the point is about Jesus. He’s trying to say that Jesus really was the Jewish Messiah descended from the venerable Jewish line of David. His genealogy is constructed in order to show that there was divine Providence behind the appearance of Jesus at this particular point in time.

11. Matthew’s account of Jesus’ birth

Jesus’ Jewishness continues to be at the forefront in the stories that come next in Matthew’s Gospel, stories that again are not found in Mark, stories of Jesus’ miraculous birth.

Probably the most striking thing about these stories as found in Matthew is that they mirror the accounts of the birth of Moses in the Hebrew Bible. You can compare the accounts of Luke and Matthew about Jesus’ birth because they both give narratives of Jesus’ birth, but they are both very different from one another. The stories found in Luke are not the stories found in Matthew and vice versa. In Matthew’s account, there is no word about Jesus’ parents, Mary and Joseph, taking a trip from Nazareth to Bethlehem because there is a tax that Caesar Augustus has levied, and the entire world has to go register for a census, and so they just happen to be in Bethlehem that weekend. In Matthew’s account, Mary and Joseph are just in Bethlehem and Jesus is born there. There is no account in Matthew of the shepherds coming to worship Jesus. In Matthew’s account instead there are the wise men who come to worship Jesus.

The way the story goes in Matthew’s Gospel after the recounting of the genealogy is that Jesus is born in Bethlehem, there are wise men who are following a star who eventually come to Bethlehem apparently some months later, because we find out that King Herod learns that these wise men have come, and he decides that he wants to kill this child who has been born. And so he sends his soldiers out, and they kill every child two years and under in Bethlehem. Well, why two years and under? If Jesus was born just last night, surely the soldiers would recognize that some toddler running around in the yard wasn’t born last night. It’s because these wise men in fact have taken months to come to Bethlehem.

Joseph learns in a dream, though, that Herod is sending out the troops, and is warned to flee, so they flee to Egypt. We are told that they flee to Egypt, so that God can fulfill a scripture about Jesus, “out of Egypt have I called my son” (Hosea 11:1). When Joseph and Mary learn then that King Herod has eventually died, they return. Where are they going to return? In Matthew’s Gospel, they want to return to Bethlehem, presumably because it’s their home town. But they learn that the ruler now in Bethlehem is Archelaus, Herod’s son, who is even worse than his father, so they decide to relocate in Nazareth. And so the reason Jesus is raised in Nazareth is because his parents have to relocate there after fleeing back out of Egypt.

These stories of Jesus’ birth in Matthew, unlike in Luke, are interesting because they mirror the accounts of Moses’ birth. With Moses, again a child is born under a hostile regime, Egypt rather than Rome. In Moses’ case as well, the ruling power wants to destroy him. In Moses’ case too, he is divinely protected. He sojourns in Egypt. He leaves Egypt. He goes through the water. In Moses’ case, of course, it’s the water of the Red Sea during the Exodus. In Jesus’ case, immediately after the stories of his birth, he is baptized. In other words, it skips all of those years from his infancy and his adulthood. The next story is that he goes through the waters of baptism. And then, he goes out into the wilderness to be tempted, just like how Moses and the children of Israel went into the wilderness. In their case, it was for 40 years; in the case of Jesus, it was for 40 days. And then , Jesus comes from the wilderness and goes up onto the mountain to deliver his teaching, his new Law, just as Moses went up on Mt. Sinai to deliver God’s law.

12. Matthew’s Jesus: The New Moses

Matthew has told the stories about Jesus’ birth precisely in order to call into mind the birth of Moses. Why the birth of Moses? Because for Matthew’s Gospel, Jesus is a new Moses, a new Savior of the people of Israel. Not one who stands in contradiction to or in tension with Moses himself, but a new Moses who fulfills the Law of Moses and delivers its correct interpretation. Matthew doesn’t understand the choice for people in his day to between Moses and Jesus. Matthew, as we are going to see, is not propounding that followers of Jesus have to reject Judaism. On the contrary, followers of Jesus, according to Matthew, have to affirm Judaism. But it is Judaism as interpreted by Jesus. It’s not a choice between Moses and Jesus; it’s a choice between Moses without Jesus and Moses with Jesus. And according to the Gospel of Matthew, it’s only Moses with Jesus that is the proper interpretation of the Law of Moses.

Some people have pointed out the striking fact that in Matthew’s Gospel, unlike Mark and unlike Luke, there are five major blocks of Jesus’ teaching, the first of which is the Sermon on the Mount in chapters 5 through 7. Much of this material is not found in Mark; most of it is found in “Q”. But why are five blocks of his teaching? Is it to make a parallel to the five books of Moses, the Pentateuch? It’s a possibility.

13. Jesus and the Fulfillment of Jewish Law

It’s important further to recognize that these stories of Jesus’ birth in Matthew’s Gospel are all explicitly said to fulfill the Scripture. We’re told by Matthew that Jesus was born of a virgin and we’re told why, because according to Isaiah 7:14, “a virgin shall conceive and bear a child and you shall call him Emanuel.” There’s a question of whether Isaiah itself was referring to the birth of a child through a virgin. When you read the text in Hebrew, it doesn’t in fact say a virgin will conceive and bear a child, it says a young woman will conceive and bear a child, but the Christian quotation of it in Matthew indicates that she was to be a virgin; Jesus’ birth therefore fulfills Scripture.

He’s born in Bethelem. Why? Well, Matthew says it is because it is according to the prophet Micah, who says that the Savior will come from Bethlehem. He flees to Egypt. Why? Because Scripture says in Hosea 11:1: “out of Egypt have I called my son.”

At every point, the events surrounding Jesus’ birth are said to fulfill Scripture. Why this emphasis, which is found only in Matthew? Precisely because Matthew is trying to show that Jesus fulfills everything that God predicted in the Scriptures. Jesus in other words is the Jewish fulfillment of the Jewish law given by the Jewish God. He is the one who, like Moses, will deliver God’s Law to his people. This emphasis on the Law that Jesus gives is particularly to be found in the first block of his teaching, the so-called Sermon on the Mount.

14. The Sermon on the Mount: The Antitheses

Jesus goes up on a mountain, much as Moses went to Mt. Sinai and then delivers his teaching. He begins the Sermon on the Mount, not by espousing an entirely new teaching, but interpreting for his hearers the teachings of Moses in the so-called “Antitheses,” the Antitheses of the Sermon on the Mount.

The Sermon on the Mount is chapters 5 through 7 of Matthew. The Antitheses come after he has given the Beatitudes, where he begins to interpret what Moses said, and gives his own reading of what Moses means. Jesus says, for example, “you have heard it said that you shall not murder, and that whoever murders shall be liable to judgment. But I say to you that everyone who gets angry with his brother shall be liable to judgment. You have heard it said that you shall not commit adultery. I say to you, you should not even lust after a woman in your heart. You have heard it said ‘an eye for an eye and a tooth for a tooth’. I say to you, turn the other cheek.”

Jesus gives the Law of Moses and then gives his interpretation of the Law. These teachings are called the Antitheses because Jesus sets his own understanding of his teaching in opposition to other understandings of the teaching. It’s not that Jesus is contradicting what Moses himself says. In other words, Jesus doesn’t say, “Moses says you shall not murder, but I say you should.” These Antitheses instead are giving alternative interpretations of the Law of Moses which go beyond the literal level down to the point of the spirit of the Law. “Moses said don’t kill; I say don’t even get angry.” “Moses said don’t commit adultery; I say don’t even lust.” Jesus wants his followers to not only follow the letter of the Law, but it’s very spirit.

Some readers have assumed that Jesus can’t really be serious: Jesus can’t really expect people not to get angry or not to lust. Prof. Ehrman says, however, that Matthew in fact seems to think that Jesus is quite serious. Matthew gives no indication that he thinks that these are impossible commandments, quite the contrary. Matthew indicates that Jesus’ followers are to keep the Law even better than the Jewish leaders of his own day. Jesus says in the Sermon on the Mount, verses 17-20, found only in Matthew, “don’t suppose that I came to destroy the Law and the prophets; I did not come to destroy them, but to fulfill them. Truly I say to you, until Heaven and Earth pass away, not one letter, not even a small part of a letter, will pass away from the Law until it all takes place.” Whoever loosens the least of these Commandments and teaches others to do likewise will be called least in the Kingdom of Heaven.” Then he concludes by saying “truly I tell you, unless your righteousness exceeds that of the scribes and the Pharisees, you will never enter the Kingdom of Heaven.” Jesus insists that his followers keep the Law and keep it even better than the scribes and Pharisees.

Well, how is that possible? Matthew evidently does not think it is possible simply by making a list of do’s and don’ts that everyone has to follow. To some extent, following the Law of God for Matthew is a very simple affair, as we learn later in the Gospel in chapter 22, where a Jewish teacher comes up to Jesus and says to him, “what is the heart of the Law?”, and Jesus quotes two of the Law’s commandments, “you shall love the Lord your God with all your heart, your soul, and your strength, and you shall love your neighbor as yourself. Anyone who truly follows those two commandments fulfills the Law and does so better than the scribes and the Pharisees.

15. Jesus’ criticism of Jewish leaders

In fact, in this Gospel, the emphasis on following the Jewish Law and the emphasis on the Jewishness of Jesus himself is counterbalanced by Jesus’ forceful opposition to the Jewish leaders, whom Jesus does not think follow the Law very well. In fact, Jesus portrays them as hypocrites who demand that people follow the Law but don’t do so themselves. Particularly striking is chapter 23, which shows Matthew’s vehement opposition to the scribes and the Pharisees, where Jesus calls his opponents, the Jewish leaders, “white-washed sepulchers”, meaning they look clean on the outside, but filled with rot and corruption within. He calls them “hypocrites” who don’t practice what they preach. He says that they stress what is picayune, they don’t keep what is central, but keep only little bits of the law, they strain out gnats but they swallow camels. They are portrayed as godless and heartless blind leaders who know the right thing to do, but don’t raise a finger to do it themselves.

Matthew’s Gospel is sometimes thought of as being anti-Semitic because of this harsh opposition to the Jewish leaders. Prof. Ehrman stresses, however, that there is nothing in this Gospel itself that condemns Jews per se, only the Jewish leaders. Even in the most vitriolic attack on the Jewish leaders, Jesus does not condemn the Jewish people per se.

Probably the most poignant scene is at Jesus’ own trial before Pilate, where Pilate claims that Jesus is innocent and he washes his hands of Jesus’ blood, which is found only in Matthew. The Jewish crowds cry out, “his blood be upon us and our children.” Some people have taken this as a condemnation of the Jewish people. But it’s worth noting that in the context, it’s the Jewish leaders that have urged the people to say this. It’s the Jewish leaders who are at fault for leading the Jewish people astray.

16. Conclusion

This Gospel does not condemn Judaism or Jews; it condemns the Jewish leaders of Jesus’ day. In conclusion, this Gospel is a lot like Mark. Here too, Jesus dies as the son of God for the sins of the world, but the emphasis here is a lot more on the Jewishness of Jesus. Jesus here is the Jewish Messiah, sent from the Jewish God, in fulfillment of the Jewish Law. Jesus as the Messiah gives the true interpretation of the Jewish Scriptures to his Jewish followers and he expects these followers to keep the Jewish law even better than the scribers at the Pharisees.

History of Christianity–Lecture 6: The Gospel according to Matthew (part 1)


This is a summary of the sixth part of twenty-four in the course on the New Testament presented by The Teaching Company. The lectures in this course are by Prof. Bart D. Ehrman, the James A. Gray Distinguished Professor of Religious Studies at the University of North Carolina at Chapel Hill. His expertise is in the Greco-Roman cultural environment of early Christianity and the textual criticism of the New Testament. For those who are interested in purchasing this course and listening to the complete lectures, please go to http://www.thegreatcourses.com.

1. Introduction: Jesus, the Jewish Messiah

At this point in our study, we have begun to examine the individual Gospels of the New Testament to see how they each portray Jesus. Our assumption has been that each Gospel is distinctive, and that it is important to see how each author individually portrays Jesus.

We began with Mark, since by common assent it was the earliest of the Gospels to be written. Mark portrays Jesus as the powerful but almost universally misunderstood son of God who, despite common expectations, had to suffer and die.

2. Matthew—One of the Synoptic Gospels

We can now move on to Matthew, a Gospel widely thought to be the most Jewish in its understanding of Jesus. In many ways, both Matthew and Luke are very similar to Mark. In fact, there are entire passages that the three Gospels share, sometimes telling the very same stories word for word the same. For this reason, scholars have long called these three books the Synoptic Gospels. The word “Synoptic” comes from two Greek words which mean “seen together”. It’s possible to lay these Gospels—Matthew, Mark and Luke–side by side and see them together. They tell many of the same stories, often in the same words.

As we will see, this is not the case with the Gospel of John, which has very few stories in common with the other three Gospels. For centuries, scholars have agreed that the Synoptic Gospels have so many stories in common because they used the same sources for their information about Jesus. The reason why they tell the same stories, and the reason why these stories are sometimes word for word the same, is because they are using the same sources. More specifically, it’s now generally thought that Matthew and Luke both had a copy of Mark available to them, and that they borrowed from Mark many of the stories that they give, while changing the stories as they deemed desirable. The stories are often told in the same sequence, but sometimes Matthew will relocate the story to another part of the Gospel, sometimes Luke will do that, or sometimes either one of them may change the words. Often the three Gospels will agree with one another, sometimes two of the Gospels with one another, and sometimes all three are different, depending on who changed what.

3. The Hypothetical “Q” Document

Matthew and Luke, however, have a number of stories in common between themselves that are not found in Mark. Obviously for these stories Mark was not the source. For the most part, these stories involve sayings of Jesus, for example, the Lord’s Prayer and the Beatitudes, which are found in Matthew and Luke, but not in Mark. These stories, that are shared by Matthew and Luke, but not found in Mark, come from a Gospel document that no longer survives, which scholars since the 19th century have called “Q”. The “Q” Document is a hypothetical source, in other words, it no longer exists, and scholars have to reconstruct it, that provided Matthew and Luke with many of their traditions about Jesus, especially the sayings of Jesus. The document is called “Q” because the scholars who devised this theory in the 19th century were German scholars, and, somewhat lacking in ingenuity, they called this special source for Matthew and Luke the “Source“, which in German is “Quelle“, and hence gave it the short designation of “Q”. So when people talk about the “Q” source, they are referring to this hypothetical source of Matthew and Luke.

4. The Special Sources “M” and “L”

For stories that Matthew and Luke have that are unique to each Gospel, scholars hypothesize additional sources. They like Matthew’s special sources “M” and Luke’s special sources “L”. And so, for example, Matthew alone tells the story of the wise men following the star to the baby Jesus; that story would have come from “M”. Luke alone tells the stories of the Good Samaritan and the Prodigal Son. Both parables are found only in Luke, and they would have come from “L.”

As a result, behind our three Synoptic Gospels, Matthew, Mark, and Luke, in the opinion of most scholars, there were 4 sources, only one of which, Mark, we still have, the others being “Q”, “M”, and “L”.

5. Redaction Criticism

Since it appears that Matthew used Mark as one of his sources, one of the ways to study Matthew’s gospel (and Luke’s as well, when we get to it) is by seeing how it differs from its source. This is a way of studying the Gospels of Matthew and Luke which is sometimes called “redaction criticism.” Redaction criticism tries to look at how an author has redacted or edited his sources. And so, if Mark was one of the sources, we can see how Matthew has changed Mark. The idea behind redaction criticism is that if an author likes the way a story already was, he wouldn’t change it. If he has added something to it, taken something away from it, or changed its wording, then it’s because there’s something about the story he wanted to change. So by looking at the changes, you can see what the author’s vested interests were. That’s the approach we’ll take in this lecture towards the Gospel of Matthew, trying to see how Matthew differs from Mark in order to see what Matthew’s distinctive emphases were.

6. Authorship of the Gospel of Matthew

By way of background, Prof. Ehrman reminds us that this Gospel has been attributed traditionally to Matthew, the disciple of Jesus who was known to be a tax collector. We don’t actually know what the actually identity of the author was. He doesn’t appear, though, to have been an eyewitness to Jesus’ life. This book was written anonymously. There are no first-person narratives in this account. And if scholars are right to say that the author used Mark for many of his stories, it’s hard to imagine that the author himself was an eyewitness, if he had to rely on somebody else for recounting what Jesus had done. Scholars are fairly unified in thinking that, whoever the author was, he was not one of the disciples. He appears to have been a Greek-speaking Christian writing around 80-85 AD, about a half century or so after the events that he narrated.

7. Matthew’s portrayal of Jesus—the Jewish Messiah

Matthew’s Gospel provides a distinctive portrayal of Jesus. On the one hand, as you might expect, Matthew has a view that is similar to Mark. Here too as in Mark, Jesus is the Messiah, the son of God, whose entire life looked forward to his death, which was necessary to bring about salvation. Matthew has many of the same stories and therefore much of the same theology as Mark, but there are different emphases in this Gospel as well. It becomes apparent at the very outset. In brief, the distinctiveness of this Gospel has to do with its stress both on the Jewishness of Jesus and on his opposition to Judaism as he found it. This Gospel emphasizes far more than Mark that Jesus was the Jewish Messiah sent from the Jewish God to the Jewish people in fulfillment of the Jewish scripture. He gathered Jewish disciples and taught them that they had to follow the Jewish law. At the same time, Jesus opposed the Jewish teachers of his own day and condemned the way that they practiced their own religion. It’s this combination of a strong affirmation of Judaism as it ought to be, and a vitriolic condemnation of Judaism as it was actually practiced, that makes Matthew’s portrayal of Jesus so distinctive.

8. The Beginning of Matthew—the Genealogy of Jesus

Matthew’s emphasis on Jesus’ own Jewishness can be seen in passages that are found in Matthew that are not found in his earlier source Mark. Prof. Ehrman stresses again this methodological point. By adding stories to his source, Matthew has altered somewhat the overarching perspective. We saw that Mark began his Gospel with the baptism of Jesus by John the Baptist. Matthew doesn’t begin his Gospel that way. Instead, Matthew begins his Gospel with a genealogy that traces the descent of Jesus.

Genealogies are not the most favorite readings of students of the Bible. However, the genealogy in Matthew, which is only 16 verses long, doesn’t compare at all with some of the genealogies you get in the Hebrew Bible, like 1 Chronicles which begins with 9 chapters of genealogy.

The 16 verses in Matthew are well chosen and are a key to understanding Matthew’s own emphasis as comes clear at the very beginning: “the genealogy of Jesus Christ, the son of David, the son of Abraham.” He begins his Gospel by stressing the intimate connection between Jesus and David and Abraham. David, of course, was the great King of the Jews who lived a thousand years before Jesus, the great King whose descendant was supposed to be another King, a ruler of the Jews, commonly known as the “son of David,” the Messiah. Abraham was the Father of the Jews, from whom all Jews trace their lineage.

In other words, the very first verse is stressing that Jesus, because he is descended from Abraham, and that he is the Messiah, descended from David. The genealogy itself goes on then to establish Jesus’ credentials as standing in the Messianic line of the Jews, and it does so in a striking way.

The genealogy begins: Abraham begot Isaac, Isaac begot Jacob, Jacob begot Judah and his brothers, then it goes on down to Jesse begot David the King, David begot Solomon through the wife of Uriah, Solomon begot Rehoboam, etc. It goes on down to Jeconiah, who was begotten along with his brothers by Josiah at the time of captivity to Babylon. After the captivity to Babylon Jeconiah begot Shealtiel, Shealtiel begot Zerubbabel, etc., on down to Matthan, who begot Jacob, who begot Joseph, who was the husband of Mary, from whom was born Jesus, the Messiah. It’s who begot whom from Abraham to David to the captivity in Babylon down to Joseph, who is married to the woman who begot Jesus. It doesn’t say that Joseph begot Jesus.

9. Key Events in the Genealogy of Jesus according to Matthew

But then comes the most striking verse of all, verse 17. “So, all of the generations from Abraham to David were 14 generations.” Those from David to the captivity in Babylon were 14 generations. And those from the captivity in Babylon to the Messiah were 14 generations.” 14 generations between the Father of the Jews, the great King of the Jews, the Babylonian captivity, and the Messiah. This genealogy seems to be showing that at every 14th generation a significant event happened in the history of Israel: its greatest King, its greatest disaster, the Babylonian captivity, and then its Messiah. 14 generations separated all of the key events in the history of Israel; this almost sounds too good to be true, as if the Messiah had to come precisely when Jesus was born.

The problem, though, is that in order to make the sequence of 14, 14, and 14 work, Matthew had to do some creative editing. A comparison with the Hebrew Bible shows in fact that Matthew has dropped out some of the names from his genealogy. Mark 1:8 says that Asa begot Jehosephat, Jehosephat begot Joram, and Joram begot Uzziah. According to this then Uzziah was the son of Joram. But when you read the Hebrew Bible, according to 1 Chronicles, the nine chapter long genealogy, you find Joram and Uzziah again, but in that case it turns out that Joram was not Uzziah’s father, but his great-great-grandfather.

The next post will give the second part of the lecture.

5th Edition PMBOK® Guide—Chapter 7: Comparison of Estimating Techniques


1. Introduction

In the chart below are the tools & techniques used in process 7.2 Estimating Costs. I am discussing the tools & techniques listed in red in the post today; the ones listed in gray are not covered in the post.

7.2 ESTIMATE COSTS
TOOLS & TECHNIQUES
1. Expert Judgment Expert judgment can be used by using historical information to give duration estimates from similar projects. It can also used to reconcile different estimating methods.
2. Analogous Estimating Uses a measure from a previous similar project to estimate the duration or cost of the current project in a top-down approach.
3. Parametric Estimating Uses an algorithm to estimate the duration or cost of the current project based on historical data from previous similar projects.
4. Bottom-Up Estimating Estimates costs of individual work packages, and these estimates are then totaled or “rolled up” to higher levels.
5. Three-Point Estimating Accuracy of estimates may be improved by considering risk in order to create three estimates: the most-likely (cM), optimistic (cO), and pessimistic (cP) cost estimate. These three estimates are combined in either the triangular or beta distribution.
6. Reserve Analysis Duration estimates can use “contingency reserves” for risks in the risk register that the “known-unknowns” of the project.
7. Cost of Quality (COQ) Assumptions about the cost of quality may affect the cost estimates.
8. Project Management Software Automated tools used to create cost estimates.
9. Vendor Bid Analysis Responsive bids from qualified vendors should be analyzed to create cost estimates.
10. Group Decision-Making Techniques Team-based approaches can be useful for improving duration estimates.

Estimates made by individual experts use the technique of expert judgment (tool #1), and opposed to this are group decision-making techniques (tool #10), which create estimates in a brainstorming fashion by a group. This post will contrast the four estimating techniques of analogous (tool #2), parametric (tool #3), bottom-up estimating (tool #4) , and three-point estimating (tool #5). The remaining reserve analysis technique (tool #6) is particularly useful in conjunction with three-point estimating.

2. Analogous, parametric, bottom-up, and three-point estimating

The reason why I am creating this post is because the PMBOK® Guide definitions of analogous and parametric estimating both use the words “parameters” and I thought, well, there’s a potential source of confusion right there. So I am going to compare these definitions below to help the reader distinguish between them.

Estimating

Technique

Explanation Kind of projects used for
1. Analogous Uses actual duration of previous, similar projects as basis for estimate of duration of current project. Previous activities are similar in fact.
2. Parametric Uses statistical relationship between historical data and other variables. Previous activities are similar in appearance.
3. Bottom-up Uses greatest level of detail to estimate cost of individual work packages. Can be used for projects that are new.
4. Three-point Improves single-point estimates by using three estimates: most likely, optimistic, and pessimistic. Can be used for projects that are new.

Analogous and parametric estimates are examples of top-down estimates, the first being on the basis of the entire project and the second being on the basis of some sort of unit measure (dollars per square foot, hours per line of code, etc.). They both use historical data, with parametric estimates taking longer, but being more accurate than, analogous estimates.

Bottom-up estimates take more time to complete, but they also are more accurate than either analogous or parametric estimates. Three-point estimates are example of bottom-up estimates, which are obtained from analyzing individual work packages, that are refined through risk analysis. The single-point estimates are enhanced using risk analysis by figuring out how much each estimate would take in a best-case (optimistic) and worst-case basis (pessimistic).

They are even more accurate than bottom-up estimates, because they take into account the various risk factors which may effect the cost of the project. It is entirely possible that you could use all four techniques in different stages of planning, the analogous and then parametric estimates to get a preliminary estimate, and then the bottom-up estimate to get a more refined estimate, with the final estimate coming from the three-point estimates.

3. Three-point estimates

The three-point estimate relies on three different estimates:

Estimate Explanation
1. cO Optimistic Based on realistic analysis of the resources likely to be assigned, their availability, and their productivity.
2. cM Most Likely Based on analysis of the best-case scenario.
3. cP Pessimistic Based on analysis of the worst-case scenario

However, they can be combined into the three-point estimate in two different ways:

Estimation distribution type Expected Duration (cE)
1. Triangular distribution (cO + cM + cP)/3
2. Beta distribution (PERT technique) (cO + 4cM + cP)/6

The triangular distribution is simply the average or mean of the three separate estimates. The beta distribution, based on PERT (Program Evaluation and Review Technique), assumes a great deal of confidence that the most likely estimate cM is accurate. This allows the distribution to give 4 times more weight to cM than to either cO or cP. The way to remember the denominator of this formula is to realize that there are the equivalent of six terms rather than three in the numerator, if you consider the 4cM to be the equivalent of four terms, cM + cM + cM + cM.

After a brief interlude this weekend, I will continue next week with a summary of the last planning process, 7.3 Determine Budget, which puts together all of the other planning processes in the Cost Management knowledge area to form the project budget.

5th Edition PMBOK® Guide—Chapter 7: Process 7.2 Estimate Costs


This process develops an estimate of the monetary resources needed to complete the project. The estimate should be reviewed and refined during the course of the project.

1. Inputs

The inputs come from other knowledge areas such as scope, time, human resource, and even risk management.

6.2 DEFINE ACTIVITIES
INPUTS
1. Cost Management Plan
  • Estimation method used
  • Level of accuracy required

This is an output of process 7.1 Plan Cost Management.

2. Human Resource Management Plan Provides personnel rates, and specifies rewards/recognition.

This is an output of process 9.1 Plan Human Resource Management.

3. Scope Baseline The scope management plan has three components of the scope baseline:

  • Project Scope Statement (output of 5.3 Define Scope)
  • WBS (output of 5.4 Create WBS)
  • WBS Dictionary (output of 5.4 Create WBS)
4. Project Schedule The quantity of resources required and the amount of time required are major factors in determining their cost. This is an output of process 6.6 Determine Schedule
5. Risk Register Used to estimate costs for risk responses. This is an output of process 11.2 Identify Risks.
6. EEFs
  • Market conditions
  • Published commercial information
7. OPAs
  • Cost estimating policies, templates
  • Lessons learned, historical information
TOOLS & TECHNIQUES
1. Expert Judgment Expert judgment can be used by using historical information to give duration estimates from similar projects. It can also used to reconcile different estimating methods.
2. Analogous Estimating Uses a measure from a previous similar project to estimate the duration or cost of the current project in a top-down approach.
3. Parametric Estimating Uses an algorithm to estimate the duration or cost of the current project based on historical data from previous similar projects.
4. Bottom-Up Estimating Estimates costs of individual work packages, and these estimates are then totaled or “rolled up” to higher levels.
5. Three-Point Estimating Accuracy of estimates may be improved by considering risk in order to create three estimates: the most-likely (cM), optimistic (cO), and pessimistic (cP) cost estimate. These three estimates are combined in either the triangular or beta distribution.
6. Reserve Analysis Duration estimates can use “contingency reserves” for risks in the risk register that the “known-unknowns” of the project.
7. Cost of Quality (COQ) Assumptions about the cost of quality may effect the cost estimates.
8. Project Management Software Automated tools used to create cost estimates.
9. Vendor Bid Analysis Responsive bids from qualified vendors should be analyzed to create cost estimates.
10. Group Decision-Making Techniques Team-based approaches can be useful for improving duration estimates.
OUTPUTS
1. Activity Cost Estimates Quantitative assessments of the probable costs to complete project.
2. Basis of Estimates Details supporting the activity cost estimates (output #1).
3. Project Documents Updates The risk register will be updated to include the estimated costs of risk responses.

2. Tools & Techniques

Many of these techniques used in the Cost Management knowledge area are similar to those used in creating the duration estimates in the Time Management knowledge areas. Some additional techniques not used in Time Management are the Cost of Quality and Vendor Bid Analysis, from the Quality and Procurements knowledge areas, respectively.

3. Outputs

The outputs are the estimates and the supporting data used to create the estimates. These outputs are then used in the next process 7.3 Determine Budget.

The tools & techniques used in this estimating process are important enough to require some posts to review them. The next post will cover those tools & techniques which are also used in Time Management, analogous estimating, parametric estimating, bottom -up estimating, and three-point estimating.