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Combinatorial Optimization, MA4502 (in English)



%SBICON% Ca. 48% aller Hilfskräfte in der Mathematik im Wintersemester 2010/2011 werden aus Studienbeiträgen finanziert.

Dozent: Prof. Dr. Raymond Hemmecke
Übungsleitung: Dr. Michael Ritter (teilweise %SBICON%)

News Dates of lectures/exercise classes and office hours Lecture notes Exercise sheets Literature FAQ

Recommendations for students of this course

Students of this course will be interested in these additional courses:
  • computer lab course: learn to use modern optimization software and implement some of the topics you have learned during this course (2-4 days during the semester break)
  • Case Studies in Combinatorial Optimization: Get hands-on practice and use you optimization skills to work on real-world projects. This master's course will be taught in the summer term of 2011.


  • (Apr 11, 2011) The exam on April 18, 2011 will take place at 10:00 a.m. in room MI 00.07.011. Please refer to Exam for details.
  • (Mar 9, 2011) Grading of the exam is finished, you can find your results at TUMOnline . If you want to review your exam, please see Exam for details.
  • (Feb 23, 2011) Please refer to Exam below for information concerning the written exam on March 1, 2011 and April 18, 2011.
  • (Feb 23, 2011) Sheet 9 is available for download. This is the second multiple choice sheet designed to help you recap some of the contents of the lecture.
  • (Feb 2, 2011) Students of this course interested in getting some hands-on experience in combinatorial optimization will be interested in the case studies course in the summer term of 2011. There will also be a computer lab course before the start of the summer term which will get you acquainted with state-of-the-art optimization software. This course is especially recommended as a preparation for the case studies.
  • (Jan 14, 2011) Sheet 6 is now available for download. This sheet is a special multiple choice sheet designed to help you recap some of the contents of the lecture. You can check your answers online (see the link next to the download). In the next exercises classes, we will talk about the questions on this exercise sheet and any other questions you might have. In order to allow for preparation of some examples or additional material, please email problems/questions/suggestions to m.ritterma.tum.de. For this next exercise classes there will be no prepared student presentations. Also, there will be a similar multiple choice sheet at the end of the semester to help you prepare for the exam (which might also contain some multiple-choice exercises).
  • (Jan 13, 2011) The written exam to this lecture will take place on March 1, 2011 at 10:00am and (for the repeat exam) on April 18, 2011 at 10:00am. More details will be posted when available. Please register for the exam on TUMOnline as soon as possible.
  • (Nov 2, 2010) Due to an assembly of the student body (FVV) the exercise class 3, originally scheduled for Nov 3, 10:15-11:45, will have to be rescheduled for this one date. The class will take place one week later on Nov 10 10:15 - 11:45. The rest of the schedule will not change!
  • (15.10.2010) BE AWARE: Regular time for lectures has been changed to Wednesday 2.15-3.45 p.m.!!!

TUM-Online pages

Dates of lectures/exercise classes and office hours

  day time room teacher/tutor dates
lecture Wednesday 2:15 - 3:45 p.m. MI HS 3 Hemmecke weekly, starting on Oct. 20
exercise class 1 (German) Wednesday 4:00 - 5:30 p.m. MI HS 3 Ritter Oct 27, Nov 10, Nov 24, Dec 8, Dec 22, Jan 19, Feb 2
exercise class 2 (English) Wednesday 4:00 - 5:30 p.m. MI HS 3 Ritter Nov 3, Nov 17, Dec 1, Dec 15, Jan 12, Jan 26, Feb 9
exercise class 3 (English) Wednesday 10:15 - 11:45 am MI 02.04.011 Ritter Nov 10, Nov 17, Dec 1, Dec 15, Jan 12, Jan 26, Feb 9

Registration for the exercise classes is closed. For problems/questions concerning the exercise classes, please contact Michael Ritter.

Person Office hours (during semester)
Raymond Hemmecke by appointment
Michael Ritter tba


The dates for the written exam can be found below. The exam is closed-book - no utilities, book, etc. beyond a pen will be allowed, the exam will take 60 minutes. Please do not forget to bring your student ID card and an additional photo ID (the student ID card cannot be accepted as a photo ID!). Please show up at the room indicated below 10 minutes before the start of the exam.

  date time room exam sheet suggested solutions
exam March 1, 2011 10:00 a.m. MI HS 1 exam.pdf exam-lsg.pdf
repeat exam April 18, 2011 10:00 a.m. MI 00.07.011 exam2.pdf exam2-lsg.pdf

If you want to review your graded exam, please contact m.ritterma.tum.de for an appointment. Note that the grades will be final by Friday, March 18, 2011, so please make your appointment before that date. For any questions regarding the exam, please contact m.ritterma.tum.de.

Lecture notes

Exercise sheets

date file solution and notesSorted ascending
Feb 23, 2011 sheet09.pdf: exercise sheet 9 online version of this multiple choice exercise sheet
Oct 21, 2010 sheet01.pdf: exercise sheet 1 sheet01-lsg.pdf: suggested solution for sheet 1
Nov 02, 2010 sheet02.pdf: exercise sheet 2 sheet02-lsg.pdf: suggested solutions for sheet 2
Nov 11, 2010 sheet03.pdf: exercise sheet 3 sheet03-lsg.tex: LaTeX-Template for the solutions
Nov 26, 2010 sheet04.pdf: exercise sheet 4 sheet04-lsg.pdf: suggested solutions for sheet 4
Dec 10, 2010 sheet05.pdf: exercise sheet 5 sheet05-lsg.pdf: suggested solution for sheet 5
Jan 14, 2011 sheet06.pdf: exercise sheet 6 sheet06-lsg.pdf: suggested solutions for sheet 6
Jan 21, 2011 sheet07.pdf: exercise sheet 7 sheet07-lsg.pdf: suggested solutions for sheet 7

tex-files.zip: LaTeX style files for use with the solution templates

Sheet 9 is a multiple choice sheet designed to test your knowledge of some of the terms covered in the lecture. An online version is available that will help you check your answers. Should you have any problems with the online version or with the questions on the sheet, please contact m.ritterma.tum.de.


  • Cook, Cunningham, Pulleyblank, Schrijver, Combinatorial Optimization, Wiley 1998
  • Korte, Vygen, Combinatorial Optimization: Theory and Algorithms, Springer 2002
  • Nemhauser, Wolsey: Integer and Combinatorial Optimization 1999
  • Papadimitriou, Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Dover 1998
  • Wolsey: Integer Programming, 1998


question Will the tutorials be in English or in German?
info There will be three tutorials, two in English and one in German. However, the exercise sheets will be available in English only.

question Will the exam be in English or in German?
info There will be a written exam with questions in English. We will, however, accept answers in both English and German (provided the answers are correct, of course).

question Whatever happened to exercise sheet 8?
info While work on the multiple choice sheet 9 was started, there were plans for an exercise sheet 8. However, we decided to incorporate the main ideas of the exercises on sheet 8 into sheet 9, as there were no more tutorial sessions were sheet 8 could be discussed. Hence sheet 8 was discarded, but its spirit lives on in sheet 9.

wip ... The FAQs will be extended whenever necessary. If you have any questions about the course, please do not hesitate to ask! ...

Research Unit M9

Department of Mathematics
Boltzmannstraße 3
85748 Garching b. München
phone:+49 89 289-16858
fax:+49 089 289-16859


Prof. Dr. Peter Gritzmann
Applied Geometry and Discrete Mathematics

Prof. Dr. Andreas S. Schulz
Mathematics of Operations Research
(affiliated member of M9)

Prof. Dr. Stefan Weltge
Discrete Mathematics


Jan 25th, 2019
Case Studies 2019: Preliminary Meeting on Wed, Feb 6th, at 16:00 in room MI 03.06.011.