Math 441 Section 201
Mathematical Modeling: Discrete Optimization Problems
|Online Course Material
Happy New Year. 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 is a Arts degree `research intensive approved course' which is a degree requirement for a B.A.
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.
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.
Computer Lab access.
The Course Outline gives a timeline for projects. It is important that groups
and projects are chosen early. I will accept project proposals on Friday Feb 4.
Some changes are possible but I wish the groups to begin exploring their
project early. In particular, I would like a written report and verbal report
on or before Friday February 25. It is a chance for you to see how your group
should be organized to produce a report and a chance to contemplate the scope
of your project and the difficulties you might encounter. 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 15 minute group presentations as progress reports on Monday Feb ?? and Wednesday March ??. 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.
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 also scheduled to teach 15:00-16:00 MWF. I typically do not read my email from home (i.e.
evenings and weekends).
Outline: grading scheme etc.
Slick Oil (vertically integrated oil company). Slick oil file
problem file, LINDO file for
Hiring Firing problem files
statement, LINDO file,
Absorptivity files LINDO file,
of data , LINGO
Branch and bound example showing how to use
this to solve an integer (or mixed integer) programming problem.
Piecewise Linear Curves The SOS2
formulation (specially ordered sets of size 2)
Jobshop Files Machine
Shop job scheduling problem. , LINDO file
Fano Plane and Projective Planes by Integer Linear Programming LINGO
Network Flow template LINGO
PERT network template (Chemical Laboratory Remodelling) LINGO file
Dynamic programming notes for basic formulation without or with discounting.
spreadsheets for the two cases. Sheet 1 has the basic formulation. Sheet 2 has the discounting version.
Cosntruction Speedup Problem how to spend $70,000 effectively. Cosntruction Speedup Spreadsheet
spreadsheets for stochastic dynamic programming.
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!
A version of the travelling salesman problem for the New York Subway
website on unusual TSP algorithm, a bit too small to be useful.