Civil engineers have
many, diverse, career paths. You have
two possible project tracks to pick from this term. One is below and culminates
in the mathematics of project management (PERT/CPM). The other is in Truss Analysis. See me if you wish to work
on Truss Analysis.
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
·
page 503 problems 1-23
·
page 520 problems 5-11, 15
by hand
using Maple refer to the maximize function in the simplex
library
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.
Please see me for
handouts for this project. Due to the heavily graphical nature of projects, the
material is not on line. (Nov 18) By now, each
group
should have one copy of materials (Chapter 8 from Management Science by
What you want to do once you
have all read over the material is go to the problems on page 340
a)
problems 1-6 by
hand (paper/pencil)
b)
pick 3 of the first 6 and set them up as linear
programming problems and then use Maple
or paper/pencil to do them. Obviously you should
get the same answer. In doing this,
for those variables with slack in the optimal
solution, give an interpretation of the slack
c)
problems 8,9,10,20 by hand or with Maple your choice
Next, within the Civil
Engineering department, find out what there is for Project Management
software. Using it, pick three of the
problems that you worked on, including 9 and 20 and solve them using the
software. Compare your results and
comment.
What you hand in should include the
following:
·
cover page
·
introduction
·
Summary of what Pert
and CPM are
·
Work and Solutions
to Problems
·
Summary of what how
you compare the three approaches (paper, Maple or Linear Programming, Software
from Civil Dept)
·
References (books,
people, web,
)
due date: December 5. Please
do not leave all of this until a day or two before. Apply good project
management techniques to
your own work!