Math 441 Section 101
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 but you are bringing other strengths.

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 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 Wednesday Oct 5. We will have about 15 minute group presentations as progress reports the week of October 28. 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.

Some changes are possible but I wish the groups to begin exploring their project early. 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.

Group Projects for 2015
  • Rohin, Judah and Brandon will work on the Markowitz Portfolio model.
  • Yuanyuan, Bassem and Matthias are working together exploring a game Tarneeb (a Middle Eastern game).
  • Liuke, Jiaqi and Jianfei will work together.
  • Lei, Hui Shen and Wanqi will work on a production problem with a embedded transshipment problem. Toys. Presentation Oct 31.
  • Daniel, Jane (Hua) and Eric (ShiQi) may be exploring optimal exam scheduling.
  • Xiaomeng, JiaJun and Daniyar are interested in exploring a diet problem. McD or Sushi?. They will present Oct 31.
  • Guanfeng, Yidan and Ziwei will work on a diet problem; optimal grocery selection.
  • Chloe, Manni and Natasha are interested in exploring the game 2048.
  • Silvia, Beini and Tianwen are interested in exploring bus schedules.
  • Sylvester, Naqsh and Billy will work together on the gangster problem. Oct 31.

  • The final project is due Friday November 25.

    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 writeup.

    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).
  • Course Outline: grading scheme etc. 
  • Assignment 1 question , Paper on Property valuation due Monday September 12 Assignment 1 solutions ,
  • Assignment 2 , Vista Properties due Friday September 23 Assignment 2 solutions
  • Assignment 3 , due Wednesday October 5 Assignment 3 solutions
  • Assignment 4 , due Friday October 21

  • Slick Oil (vertically integrated oil company). Slick oil file problem file, Slick oil solution file, LINDO file for Slick Oil , LINDO file for Slick Oil with a number of variables as a constant

    Hiring and Firing Problem   Hiring Firing input files , LINDO file, or LINGO file

    Absorptivity files LINDO file, or speadsheet of data , LINGO file,

    An integer Linear Program selecting for chemicals to provide coverage over a range of wavelength. Chemical Coverage  

    Fano Plane and Projective Planes by Integer Linear Programming LINGO file

    Jobshop Files Machine Shop job scheduling problem. , LINDO file , LINGO file

    Network Flow template LINGO file, LINDO file

    Pit Mining Problem Cross section , Arcs ,Max Flow problem An intermediate flow and augmenting path , Max Flow , Min Cut identified as nodes that can be reached by augmenting paths, Optimal Pitmine  

    Chemical Laboratory Remodelling Project. LINDO input file to determine longest paths using Network Flows. Excel spreadsheet to use Dynamic Programming to compute longest paths.

    Various Reference files. Some are some nice and short descriptions from the AMS (The American Mathematical Society not the Alma Mater Society) but also other information as well. If you suggest a link, I'll add it.

  • Cookie recipe
  • Linear Programming Theorems  
  • Brief 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!  
  • Brief version of the travelling salesman problem for the New York Subway 
  • Studying Sudokus  
  • Bin Packing  
  • website on unusual TSP algorithm, a bit too small to be useful.