Project Paper Assignment
(Linear Programming Models)
This is a chance to perhaps incorporate some of your
experience, interests, and career business/management goals and ambitions
within the context of an individual project paper. Make-up your own problem and apply the linear
programming tools and techniques we have been learning (Chapters 7 and 8). You do not need to use real data here;
instead, a reasonable and plausible objective function and constraints will
suffice.
Pretend your instructor is your boss or your client (i.e.,
you are a consultant). Your paper should
be 100% professional (neat, typed, error-free, descriptive, easy to read and
follow, etc.) in nature. You are in
college and, for most of you, English is your native language; that should be
reflected in the quality of your writing (spelling, punctuation, grammar,
etc.). At this point in your life and
academic career this is assumed; i.e., you get no credit for writing at an
acceptable level… instead, you incur severe sanctions if you do not.
Your problem will have exactly two variables (an X1 and an
X2) and will incorporate a maximization (either profit or revenue)
objective. You will include at least
four constraints (not including the X1?
0 and
X2 ? 0 [i.e., the
“Non-negativity” or “Duh!”] constraints).
At least one of these four must be a“?” constraint, and at least one
other must be a“?” constraint; do not include any “= only” constraints. You must have a unique Optimal Solution
Point; i.e., no unboundedness or infeasibility problems and no alternative
optimal solutions.
You will make up the context, the particular numbers
(objective function coefficient values), and the relationships (constraint
equations and values) for your problem.
Your model should be reasonable, plausible, and thoughtfully derived and
explained—but not necessarily an accurate reflection of reality (i.e., you can
make up the numbers).
Make sure you incorporate all of the topics we have gone
over. Of course, it is clearly not good
enough to just “mention and briefly define” any of these topics and leave it at
that; instead, you need to incorporate each in your paper within the context of
your problem/situation. Present and
discuss your problem (background, objective, constraints, etc.) in “English”
and then supplement that in “Math” (linear programming) language.(This is an
extremely important part of your paper, and something that you will have to do
a lot when you graduate and start a career.)
The overwhelming majority of your paper will be written in “English,” with
a bit of “Math” language stuff thrown in (as opposed to lots of “Math” language
with a bit of “English” thrown in).
Draw each constraint equation’s own individual graph. Then draw one “final” graph that includes the
feasible region, the optimal objective function line (you need to actually
graph it; do not just estimate where it goes!), and the optimal solution
point. Perhaps the best way to draw
these graphsis using a computer program such as EXCEL.
Make sure you incorporate (as discussed above) your
objective function, constraints, slack and surplus values, optimal solution,
optimal objective function value, sensitivity analysis, range of optimality,
range of feasibility, dual prices, shadow prices, reduced costs, and anything
else that we have discussed that is relevant to your project’s
problem/situation.
While much of your work will be narrative, of course you
should feel free to draw pictures, construct tables, use (and explain!) math
equations and “math language,” etc., as you think appropriate and
necessary. Re-stating some or all of
your computer output in some other form is certainly ok; in fact, that is a big
part of this project.
Make sure you include a page number for all pages.
Project Paper Assignment
(Linear Programming Models)
This paper is due by the last day of class. Of course, you can turn in your paper early
if you so desire. No late papers will be
accepted. If you get started soonthen
you should haveplenty of time to do a good job here.
My advice is to write the paper in sections, one or two at a
time. In the interests of organization
and reading ease, give each section a title (and maybe include some sub-titles
too where appropriate). Double-space the
text. Print on onlyone side of the paper
(i.e., single-sided, not “duplex”; nothing on the back of any sheet of
paper). Include a cover sheet/title
page. Write your name(s) on the cover
sheet only, nowhere else.
I know that you are all wondering “How long should this
paper be?” Well, the answer is, “Long
enough to get the job done!” I would
expect most papers to be about seven to ten or so pages in length—but that is
just a very general ballpark estimate.
Of course in the real business world, which I want you to simulate here,
there is seldom a minimum page length requirement for projects and papers. You will simply be expected to write enough
to “get the job done”; no less, no more.
This is your chance to shine and to be evaluated in a
context other than pencil-and-paper exams.
Report/Project writing is a skill that you will need throughout your
business career. Remember, your bottom-line
mission here is to impress me with your ability to implement, incorporate, and
professionally communicate your knowledge and understanding of linear
programming as a business/ management tool, as opposed to a more purely
mathematical and mechanical comprehension of it.
As with all of your other work, your paper will be evaluated
from an absolute, not a relative, perspective.
In other words, I do not grade “on the curve” by comparing your paper to
the work of any other paper in this or any previous semester’s Quant Methods
course—instead, your grade is based upon your adherence to all prescribed
dimensions of this assignment this semester and the excellence with which you
implement this assignment. Of course,
everything you submit needs to be your (or you and your partner’s) work; i.e.,
you need to produce your own submitted work-product.
Remember, discussing and explaining your problem and your
findings via sufficient incorporation (not just mere mention or token
definition!) of the topics we discussed is a MAJOR part of this project and,
therefore, of your grade. This is the
kind of stuff you might do in your business career.
