Math 441 Section 201
Mathematical Modeling: Discrete Optimization Problems
|Online Course Material
Hope you had a great summer. This course should be a lot of fun for students. It can be
considered a capstone course, giving students an opportunity to use their
mathematical maturity to work on `real world' problems. It also serves a Arts degree `research intensive approved course' which is a degree requirement for a B.A. If you are in a joint degree with another specialty in Arts such as Economics, you may be taking `research intensive approved course' in that other department but you are more than welcome to take this course.
The course has a
reasonable amount of work and certainly the project takes a lot of time but
students typically enjoy the experience. Also there is no final exam!
This course does have MATH 340 as a prerequisite. You can discuss with me if this is missing.
This course uses discrete optimization techniques such as Linear programming
and Integer Programming. We will be using software (LINDO, LINGO) for
assignments and possibly the project. The course is organized with 50% for
assignments and 50% for a project. The project is done in a groups of at most 3
and a polished write up is expected. There is no final exam. Contact me if you
have questions before selecting this course.
The Course Outline gives a timeline for projects. It is important that groups
and projects are chosen early. I will expect project proposals by Friday Oct 3.
Some changes are possible but I wish the groups to begin exploring their
project early. In particular, I expect a written report and verbal report
on or before Monday October 27. It is a chance for you to see how your group
should be organized to produce a report. Hopefully you will have some initial computations done and are aware of the difficulties you might encounter. You should contemplate the scope
of your project. Consultation with me
is essential. I can help you identify the questions that you might focus on and
indicate parts of the project that are likely to be hopeless. It is your
responsibility to make the project interesting for me. There is no `right'
answer. You might find useful information in the handout Project Information.
We will have about 15 minute group presentations as progress reports on Friday October 24 and Monday October 27. Aim to have a nice overview of the problem (this will probably be useful later on when you are doing your write up) and give some sample input/output to indicate your progress to date. The final project is due Friday November 21.
Grading this course can be a challenge. It is disconcerting for students that
they won't get 100% for the correct answer. We give the top marks only to those
with clear and interesting writeups. The average in the course will probably be
in the low 70's. The overall grading distribution will be reminiscent of an
Arts course. I expect many good results but only the occasional stellar
Some LINDO data files LINDO files
The notes look authoritative when typed so be wary. They may look perfect but
may still contain errors! I don't have an editor.
I arrive most days by 9:00. I am scheduled to teach 10:00-11:00 MWF. I typically do not read my email from home (i.e.
evenings and weekends).
Outline: grading scheme etc.
Assignment 1 due Wednesday Sept 10. > Solutions
Assignment 2 due Friday Sept 19.
Hiring Firing input files
, LINDO file,
Slick Oil (vertically integrated oil company). Slick oil file
Slick oil solution file,
LINDO file for
Slick Oil , LINDO file for
Slick Oil with a number of variables as a constant
Absorptivity files LINDO file,
of data , LINGO
Vista Properties Vista Property Development data,
We will explore this in class. LINDO input file,
Branch and bound examples showing how to use
this to solve an integer (or mixed integer) programming problem.
Modeling Piecewise linear cuves whose constraints are called SOS2: Specially ordered sets of size two.
Various Reference files. Some are some nice and short descriptions from the AMS but also other information as well. If you suggest a link, I'll add it.
discussion of Travelling Salesman problem
website with an enormous amount of information on the Travelling Salesman problem including the Concorde algorithm in a phone app!
version of the travelling salesman problem for the New York Subway
website on unusual TSP algorithm, a bit too small to be useful.