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Integer Programming: Polyhedral Theory and Algorithms

Topic

Integer programming is concerned with optimization problems where some of the variables are restricted to take only integral values. There are numerous applications of integer programming in various areas such as facility location, network design, vehicle routing and so on.

Topics included in the lecture are:

Lecture Dates

The lecture takes place on

Tutorials

The tutorials start on Tuesday, November 2, and Wednesday, November 3 with in-class exercises!

Tutorials are held on

The tutorials are managed by Sabine Büttner. Questions will be answered by mail (buettner(at)mathematik.uni-kl.de) or in room 14-432.

The application for the groups has to be done in the URM-system until Friday, October 29.

Homework Assignments

The Exercise Sheets are available on Thursday and have to be delivered to the boxes in building 48 (next to room 210) on Thursday of the next week before the lecture.

The first sheet will be online on Thursday, October 28, and will contain in-class exercises for the first tutorials as well as the homework which is due next week.

Exercises should be turned in in groups of 2 to 3 students.

 

Number

Due Date

PDF

additional information

1

November 4 

Exercise 1 corrected

in Exercise 5: '+' for two sets X and Y means here: a in X+Y iff a=x+y for some x in X and y in Y

2

November 11

Exercise 2

3

November 18

Exercise 3

4

November 25

Exercise 4

5

December 2

Exercise 5

6

December 9

Exercise 6

7

December 16

Exercise 7

8

January 6

Exercise 8

see below for information concerning the computer exercise

9

January 13

Exercise 9

in Exercise 2 a): the correct (nontrivial) exercise is: Show that the problem always has an optimal solution with at most one fractional entry.

10

January 20

Exercise 10

11

January 27

Exercise 11

data for the two-dimensional Knapsack in Exercise 4: knapsack.dat

Note in Exercise 3: the resources should be nonnegative.

12

February 3

Exercise 12

Computer Exercises

There will be some Computer Exercises during the second part of the lecture, giving you the opportunity to get to know some basics in solving optimization problems with the help of an LP-solver. You should inform yourself about the basics, but the exercises can be done without a lot of programming experience.You should use the optimization software AMPL to solve the LPs. An introduction to the program can be found e.g. at 'http://www.ampl.com/DOWNLOADS/index.html' where you can download an introductory chapter of a manual. There are also some examples.  Another short introduction is available at http://www.unc.edu/~pataki/hhh/ampl/amplhandout.pdf.

 

You have the following options to be able to use AMPL:

- There is a student version of AMPL on the computers of the Department of Mathematics accessible in rooms 48-419, 48-421 and 48-521.

- If you want to use the program on your personal computer, you can download the free student version (see also 'http://www.ampl.com/DOWNLOADS/index.html').

- If you are only interested in trying some basic things, you can test your models with the web interface at 'http://www.ampl.com/TRYAMPL/'.We will also give a short example of the functioning of AMPL in the first tutorials of the New Year, i.e. on January 11 and January 12 respectively.

Exam Information

In order to get a "Schein" you have to participate actively in the tutorials. This includes at least 50% of the points for the homework assignments, attendance of the tutorial and the presentation of own solutions in class.

Lecture Notes

Lecture notes will be provided here chapterwise during the course.

Be warned that these notes are still under construction and should not be trusted too easily. 

Literature