Math 364 (Dec S 344)  -- Principles of Optimization

Course Description
Mathematical programming techniques are widely used to model and solve optimization problems from business, engineering, and several other areas. This course will give an introduction to linear optimization. Emphasis will be given to model formulation, basic theory behind solution techniques and algorithms, and to the use of modeling software. Specifically, the topics covered will include linear programming formulations, the simplex algorithm, transportation problems, network models, and integer programming. The software called AMPL will be introduced, and students will learn how to create models using this tool and to interpret the solutions. The targeted audience is junior or senior undergraduate students. A basic background in linear algebra will be required to follow the contents of the course.

Syllabus   (PS file)
Tentative Course Schedule   (PS file)

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Topics covered in each class

Announcements

Thursday, Jan 27: I will be out of town the whole of next week. Prof. Bob Mifflin and
Yuntao Zhu will give the lectures on Tuesday, Feb 1, and Thursday, Feb 3, respectively.
You can email me if you have questions.

Thursday, Jan 27: There is a typo in the book on one of the problems in Homework 3.
In Problem 3 in page 98 (which is the 4th problem in Homework 3), it should read
"Suppose that in example 13,.." and not "..example 11..".

Monday, Mar 7: The AMPL model and data files for the inventory problem discussed
in class (WV-IMP problem 1 from page 104), have been added (see bottom of page).

Tuesday, Mar 22: A new handout on AMPL has been posted. Go through the same and
re-submit problems 3,4, and 5 from HW 6 (the ones involving AMPL) by
Friday, March 25, 1:00 pm.

Handouts
Handout   (PS file)
Further Tips on AMPL (for HW 6)   (PS file)  
Simplex method in matrix form   (PS file)  Complete

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Homeworks
Homework 1     (PS file)   -- Due on Thursday, Jan 20.
     Solutions to Homework 1   (PS file)
Homework 2     (PS file)   -- Due on Thursday, Jan 27.
     Solutions to Homework 2   (PS file)
Homework 3     (PS file)   -- Due on Thursday, Feb 10.
     Solutions to Homework 3   (PS file)
Homework 4     (PS file)   -- Due on Thursday, Feb 17.
     Solutions to Homework 4   (PS file)
Homework 5     (PS file)   -- Due on Thursday, Feb 24.
     Solutions to Homework 5   (PS file)
Homework 6     (PS file)   -- Due on Thursday, Mar 10. Re-submit AMPL problems by Friday, March 25, 1:00 pm.
     Solutions to Homework 6   (PS file)      Check under the AMPL section for model and data files.
Homework 7     (PS file)   -- Due on Thursday, Mar 31.
     Solutions to Homework 7   (PS file)
Homework 8     (PS file)   -- Due on Thursday, Apr 7.
     Solutions to Homework 8   (PS file)
Homework 9     (PS file)   -- Due on Thursday, Apr 14.
     Solutions to Homework 9   (PS file)
Homework 10     (PS file)   -- Due on Thursday, Apr 21.
     Solutions to Homework 10   (PS file)
Homework 11     (PS file)   -- Due on Thursday, Apr 28.
     Solutions to Homework 11   (PS file)

Exams
Practice Midterm     (PS file)
     Solutions to Practice Midterm   (PS file)
Midterm Exam     (PS file)
     Solutions to Midterm   (PS file)

Practice Final     (PS file)
     Solutions to Practice Final   (PS file)

Software

AMPL
Handout I   (PS file)
Further Tips on AMPL (for HW 6)   (PS file)

   Farmer Jones example: model file   data file
       Dual to the Farmer Jones LP: model file   data file
   Inventory model (WV-IMP problem 1, pg 104): model file   data file    Output from AMPL
   Leary Chemicals (WV-IMP problem 3, pg 63): model file   data file
   Solodrex bonds investment (WV-IMP problem 9, pg 93): model file   data file
   James Cakes problem (WV-IMP problem 3, pg 104): model file   data file
   Sugarco problem (WV-IMP problem 6, pg 288): model file   data file
   Bloomington police problem (WV-IMP problem 6, pg 76): model file   dual model file   data file
   Balanced transportation problem: model file    data file for problem 1 from page 371.
      Shoe problem (Problem 3, pg 371) as balanced transportation problem: data file
      Bank checks problem (Problem 6, pg 372) as balanced transportation problem: data file
   Fixed Charge MIP (WV-IMP problem 3, pg 502-503) : model file    data file
   Momiss Pollutant MIP (WV-IMP problem 2, pg 502) : model file    data file

Xpress-Mosel - Optimization modeling program produced by Dash Optimization


Last modified: Tue Aug 21 01:39:02 PDT 2007