Operations Research (IN0024)

Prof. Dr. Martin Bichler

Dr. Halil Bayrak · Janik Bürgermeister · Teodora Dobos ·  Matthias Oberlechner ·  Fabian Pieroth 

Description

The lecture introduces optimization methods with a focus on linear and integer linear optimization. In addition, algorithms for network flow problems and nonlinear optimization are covered. The course provides weekly exercises. A solid understanding of linear algebra and analysis is prerequisite.

As in the last year, this course will not be streamed or recorded, but there is a comprehensive set of lecture slides and exercises provided on Moodle.

Plan

• 15.04. Introduction, Tutorials Organization
• 18.04. Modeling with Linear Programming, Graphical Solution
• 22.04. Solving Linear Programs, Convexity
• 25.04. Simplex Algorithm
• 29.04. Simplex Algorithm in Matrix Notation, Goal-Programming
• 02.05. No lecture
• 06.05. Sensitivity Analysis
• 09.05. No lecture
• 13.05. No lecture
• 16.05. Duality Theory, Min-Max Games
• 20.05. No lecture
• 23.05. Modeling Integer Problems
• 27.05. Solving Integer Problems 
• 30.05. No lecture
• 31.05. Midterm Exam (for grade bonus)
• 03.06. Advanced Solution Methods
• 06.06. Polynomial-Time Solvable Integer Problems: Total Unimodularity, Matroids
• 10.06. Network Flow Problems
• 13.06. Traveling Salesperson Problem
• 17.06. Nonlinear Optimization
• 20.06. Convex Optimization I
• 24.06. Convex Optimization II
• 02.08. Endterm Exam 
• 02.10. Retake Exam 

Organization

• Moodle course: https://www.moodle.tum.de
• Teaching materials:
  • The slide deck corresponding to the lecture will be available on Moodle after the lecture. A textbook (see recommendations below) is essential for the course!
• Place and time:
  • Monday and Thursday, 12:15, Interims II, Hörsaal 2; no live streaming
• Registration: Registration for the lecture via TUMonline is required to receive access to the teaching materials on Moodle.
• Exams:
  • Midterm exam (60min) 31.05.2024, 17:00-18:00
    Registration via TUMonline: 03.05.2024 - 24.05.2024
  • Endterm exam (120min) 02.08.2024, 08:30-10:30
    Registration via TUMonline: 03.06.2024 - 30.06.2024
  • Retake exam (120min) 02.10.2024, 16:00-18:00
    Registration via TUMonline: 09.09.2024 - 23.09.2024

Tutorials

Two types of tutorials are offered:

• Central exercise - Thursday 16:15 - 17:45, MI HS 1
  In the central exercise, a teaching assistant discusses solutions to typical problems with students. The central exercise is streamed via TUM-Live.
• Tutor groups - 12 groups, Tuesday - Friday, MI 01.010.011
  An exercise sheet is published weekly on Moodle. Students solve the sheet in the tutor groups. Suggested solutions are discussed together with a student tutor and then published on Moodle.

Exam & Grade Bonus

• There will be two exam opportunities (endterm and retake). Both exams are planned as on-site exams. There will be no online exam option.
• A non-programmable calculator is allowed for the exam.
• In addition to registering for the lecture and tutorials, you must also register for the exam if you wish to take it.
• A midterm exam is also offered, which allows you to earn a grade bonus (0.3 grade points). The grade bonus will be included to the exam grade only if you passed the exam.
• The grade bonus is also valid for the retake exam in the summer semester 2024, but cannot be transferred to future semesters.

Literature

• Winston, A.: Operations Research, Algorithms and Applications, Whiley&Sons, Duxbury Press, 2003. (Physically available in the library.)
• Domschke, W.; Drexl, A.; Klein, R.; Scholl, A.: Einführung in Operations Research, 5. Auflage, Kap. 1-6, Springer, 2015. (in German, electronically accessible via OPAC)
• Koop, A.; Moock, H.: Lineare Optimierung – eine anwendungsorientierte Einführung in Operations Research, Springer, 2018.
• Vanderbei, R.: Linear Programming, 3rd edition, ISOR, 2008.
• Bertsimas, D.; Tsitsiklis, J.: Introduction to Linear Optimization, Athena Scientific, 1997.
• Domschke, W.; Drexl, A.; Klein, R.; Scholl, A.: Einführung in Operations Research, 5. Auflage, Kap. 1-6, Springer, 2015.
• Briskorn, D.: Operations Research, Springer, 2019.
• Nemhauser, G.; Wolsey, L.: Integer and Combinatorial Optimization, Wiley-Interscience, 1999.

• General information at ScienceOfBetter.org