Project and Resource Management Track
Two things in common
with many of them are management of resources and management of projects. The
projects for this course focus on the mathematics of those areas.
By management of resources, we mean getting the most out
of raw materials, labor, space, money or people. This might occur in the course
of building a bridge, keeping the utilities in a city running properly, or
meeting Federal guidelines for water quality.
In calculus I and IV you encountered max/min
problems. The idea of these was to find
the greatest or least value of a function and the conditions that would cause
this to occur. This first project is
conceptually quite similar. You will
again have a function you are trying to maximize. You will also have a
set of conditions that this must be done under, called constraints. In
the world of civil engineering, this might correspond to having so much water,
sand, cement and mixing volume and deciding what the optimal quantities of each
might be while mixing cement.
For this project, please
use the textbook and work out the following
· read
sections 11.1 and 11.2 in Kolman Linear Algebra with Applications
(on reserve in the library or borrow a copy from many
students who own it)
·
page 503 problems 1-23
·
page 520 problems 5-11, 15. You
can do these both
Sloppy management of a large project can result in
considerable added expense, time, and even lawsuits. A companies
reputation may be damaged and customers lost.
In the 1950s, both the defense and chemical engineering
industries successfully applied mathematics to project management, seeking to identify
the key or limiting components and to optimize the time taken for completion.
The foundation of this was recognition of something called the critical path of
a project. The algorithms involved are called PERT and CPM, the latter short
for Critical Path Method. The goal of this project is to study CPM from
a mathematical point of view.
In practice, construction companies use software to
perform the many computations required by CPM. You will need to find out what
software the Civil Engineering Department at WPI currently uses so you may
compare the answers you generate by hand.
Project Management is also the name of the course CE 3020
in the Civil Engineering Department.
Please see me for
handouts for this project. Due to the heavily graphical nature of projects, the
material is not
on line. The material has been changed
to that from Chapter 11 of Quantitative
Models for Business Decisions
.
Read the chapter material (pp. 436-462)
On pages 463-465 please work out problems 1 through
5. You many find it helpful to put the
data into an Excel spreadsheet and have
it compute TE, TL and TS and ET by putting the formulas for these into
a cell and copying them.
Finding the critical path is an optimization problem
which may be solved with linear programming methods (see Project #1). Please do problems
13 and
15 on page 468. Once you have formulated
them, you may use Maple to solve them (as opposed to doing it by hand your
choice)
Next,
within the Civil Engineering department, find out what there is for Project
Management software. Use it to solve
problems 1 and 2 using the software.
Compare your results and comment.
Finally, find 3 sites on the
Internet which discuss PERT/CPM and its use in Civil Engineering and summarize
what you found
What you hand in should include the
following:
·
cover page title, group #, members etc
·
Introduction
·
Summary of what Pert and CPM are
·
Work and Solutions to Problems (see above)
·
Conclusion summary
of what you learned
·
References (books, people, web,
)
Project #3
The purpose of this
project is to review and summarize your work done from the first two
projects. What you turn in should be a
mix of writing and mathematics, with more of the former.
Part One
Summarize what Linear
Programming is. Include two potential
applications of it within the realm of Civil Engineering, not including
PERT/CPM.
Part Two
Summarize
PERT/CPM. Be sure to include a
conceptual description of what a critical
path is.
Part Three
The "Big
Dig" in
Part Four
Summarize what things
you have learned as individuals and as a group about project work during this
course, especially as it might be applicable to future work in IQPs and MQPs. Areas to include are