Civil engineering is a very diverse profession, being the foundation for career paths from
architects to city planners or environmental engineers. Yet one thing they all have in
common is that they either manage or appraise projects.
Some of the noteworthy projects in the last 60 years have included the Lunar project to
put a man on the Moon, the development of the Hydrogen bomb during World War II,
the development of an Interstate highway system in the 50s and 60s, public water
supplies in states like Massachusetts, and, of course, the highly publicized Big Dig of
Whether one is a person or a company, the ability to manage a project is essential.
Both cost and time overruns can be disastrous. On the other hand, the ability to make an
accurate proposal or bid can lead to much success.
Still, this has not told you what a project is, except something big and having a lot of
money and time involved.
We will use something of modest size to refer to and trust the reader so supply some
imagination as to how the same concepts adapt to larger projects. Let's say we are
building a house. Since the housing industry is an important part of the US economy as
well as a domain of civil engineering from many different points of view, this is a
reasonable place to start.
For sake of discussion let's say we are building a rural home and hence that the only
public utility involved is electricity. The following areas all need to be addressed:
Problem 1 Which of these areas can be done in parallel (at the same time) with others?
Which must be done sequentially?
Problem 2 Which of these may involve getting legal permits?
So we see one of the first characteristics of projects, that they involve subprojects which
go on both in parallel and in sequence. The building can't be framed until there is a
foundation and it can't have a roof put on until there is a frame to put it on. On the other
hand, the landscapers do not care what the roofers are doing unless they drop something
Further, projects may be thought of as having events and activities. An event signifies
the start or completion of an activity. The activity is the work needed to bring about
completion. You might put a mark on the calendar to remind you of when an event
occurs. You might put a horizontal line on the calendar from the start to finish of the
This all has a quantitative aspect to it. In planning a project you make estimates of how
long activities will take. This is based on experience among other things. It is not an exact
science and has variability associated with it. You might estimate that it will take a week
to pour the foundation for the house but factors such as cold weather, the cement truck
getting stuck in the mud or someone being sick might delay this from being completed
when you planned. There are more reasons things take longer than expected then there
are reasons that they get done quickly. In fact they tend to follow a Beta Distribution,
which is skewed to the right. In more everyday terms, Murphy's Law is often hiding in
the shadows of your project.
Let's suppose we have the following collection of information and data about the
construction of a house.
First we have three time completion parameters for each activity: a,m and b. They can
be thought of as best case scenario, most likely, and worst case scenario. From the
background on a Beta Distribution the Expected Time, ET, of completion for that
activity is then given by
which is the 5th column. The quantity 2
σ ET is the variance of the times of completion
for the activity. It is a measure of how scattered or spread the possible times are and is
useful mostly in a relative sense when compared to other activities. (you learn more about
it in a Statistics course).
The columns TE and TL are very important to us. They tell us, relative to the entire
project, what the earliest and latest possible times of completion for this particular
activity are. If they are the same then the activity is critical. If there is a difference then
there is flexibility in when they may begin and end without impact to the overall project.
The difference is computed in the last column.
While this is useful, it is easier to understand if in a graphical format called a Network
Graph for the project. This may appear as follows:
The graph greatly helps to illustrate the combination of sequential and parallel activities.
A Fundamental Concept
If all of the activities of a project were sequential then it would be easy to estimate how
long the project would take – it would be the sum of the times for each activity. When
things are progressing in parallel, a little more thought is needed.
Suppose a subproject consists of finishing the exterior of the house once it has been
framed and covered (with plywood, let's say). The two jobs needed would then be siding
and roofing. These subcontractors can work independently of each other (assuming no
one unplugs anyone else's power tools). So you have a subproject which has two
activities and it is not done until both are done. We can only mark on the calendar
"exterior finished" when both the roof and siding are done. So how long will it take? The
answer is important: it will take however long the slower of the two activities is. If the
roofers take 3 weeks and the siding people take 5 weeks then the subproject will take 5
weeks. The fact that the roofers take 3 weeks has no impact on the overall length. They
can either put off starting for 2 weeks or leave 2 weeks early. They have "slack time". On
the other hand every minute that the siding people take or save impacts the length of the
The result of this is: when activities are in parallel, the slowest one is critical in
determining the length of time to completion of a subproject. This is an important
concept in project management.
This is now quantitatively shown by adding the values of TE and TL for each event:
Going back to our example, there are a number of paths between the start of the project
and the completion of it that are in parallel. If we add up the times along all of them, we
find that 1-2-4-5-6-7-8-9 is the path with the longest time. We note two things
the length of the project is then 39.5 weeks
the path is 1-2-4-5-6-7-8-9 the Critical Path of the project
The phrase Critical Path is a formal one in Project Management and well worth
Since the activities on the critical path determine the length of the project, managing
them is very important. If any of them should increase (see earlier discussion on
variability) then the length of the project will increase. Conversely if the time for any of
them can be made to decrease then the length of the project will decrease. Thus Critical
Path Management is a key concern of project managers!
Problem 3 For the house construction project above, find three other paths from Start
to Finish and visually determine the length of time associated with them.
PART TWO – Mathematical Considerations
In "real life" no one finds the Critical Path by eyeballing the Network Graph. It would be
impossible as a real construction project has thousands of activities and events. In the
1950s, people working on chemical plant construction and defense projects managed to
apply modern mathematics to such problems and turn them into "max/min" problems
such as you did in Calculus I. It figures out all paths from Start to Finish and then finds
the one with maximum time associated; the critical path. The specific branch of
mathematics is Linear Programming. Once they got the algorithm down pat, they wrote
computer code to do it automatically so project managers would not have to "re-invent
the wheel". Any construction company has a version that they use regularly.
Your goal in the second part of this work is to learn how to use current software at WPI
Problem 4 View the 4 introductory films on Primavera which are located at
Use Primavera to study the house building project developed on Part One. Enter all
necessary data. Compare the results generated by the software with the results gotten
above by hand. Summarize your findings.