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Our teaching addresses bachelor's and master's students of mathematics, computer science, business administration, economics, and engineering. Below you find descriptions of all courses we offer regularly or irregularly. Previous teaching is listed here, and the current semester schedule is available in CAMPUS.

All courses require basic mathematical skills and the ability to think abstractly and formally. Master's courses require familiarity with fundamental algorithms and linear programming. A general affinity to computers and programming helps. Successful passing of a course requires active and persistant collaboration.

Courses


Name Lecturer Type
  • Lecture Name: Approximation Algorithms
  • Lecturer: Marco Lübbecke
  • Courses of Study: M.Sc. Math, M.Sc. BWL, M.Sc. Wiwi
  • Turnus: irregularly, winter terms
  • Prerequisites:
  • Content:

    .

  • Goals:

    .

  • Literature:
    • D.S. Hochbaum (1995).
      Approximation Algorithms for NP-hard Problems. PWS Publishing Co., Boston [bib]
    • V.V. Vazirani (2001).
      Approximation Algorithms. Springer, Berlin [bib]
    • D.P. Williamson and D.B. Shmoys (2011).
      The Design of Approximation Algorithms. Cambridge University Press, Cambridge [bib]
  • Lecture Name: Column Generation and Branch-and-Price
  • Lecturer: Marco Lübbecke
  • Contact: Michael Bastubbe
  • Courses of Study: M.Sc. Math, M.Sc. Info, M.Sc. BWL, M.Sc. Wiwi
  • Turnus: irregularly, winter term
  • Prerequisites:
  • Content:

    todo

  • Goals:

    todo

  • Literature:
    • J. Desrosiers and M.E. Lübbecke (2011).
      Branch-Price-and-Cut Algorithms. In J.J. Cochran (Ed.) Encyclopedia of Operations Research and Management Science. John Wiley & Sons, Chichester [pdf] [doi] [bib]
    • M.E. Lübbecke (2011).
      Column Generation. In J.J. Cochran (Ed.) Encyclopedia of Operations Research and Management Science. John Wiley & Sons, Chichester [pdf] [doi] [bib]
    • J. Desrosiers and M.E. Lübbecke (2005).
      A Primer in Column Generation. In G. Desaulniers and J. Desrosiers and M.M. Solomon (Eds.) Column Generation. Springer, Berlin [pdf] [doi] [bib]
    • [pdf] [doi] [bib]
  • Lecture Name: Computational Mixed Integer Programming
  • Lecturer: Marco Lübbecke
  • Courses of Study: M.Sc. Math, M.Sc. Inf, M.Sc. BWL, M.Sc. Wiwi
  • Prerequisites:
  • Content:

    todo

  • Goals:

    todo

  • Literature:
    • Lecture Name: OR Praktikum
    • Lecturer: Marco Lübbecke
    • Contact: Annika Thome
    • Courses of Study: M.Sc. Math, M.Sc. Info, M.Sc. BWL, M.Sc. Wiwi
    • Prerequisites:

      Ability to model with integer programs, knowledge of operations research algorithms, as well as solid programming skills and/or mastery of an algebraic modeling language.

    • Content:

      Interdisciplinary teams of 5-6 students from mathematics, computer science, business administration, and engineering work on a real-life problem coming from an industrial partner. They work on the whole OR project, starting with the problem analysis, data gathering and cleaning, modeling, algorithm development, implementation of solution approaches, visualization, validationg, and evaluation of solutions, and presentation of results.


      Previous cooperations were on container terminal logistics (INFORM, Aachen), management of airport baggage handling (Fraport, Frankfurt), and locating stations for electric bicycles (velocity, Aachen).

    • Goals:

      Solution of a real-world optimization problem from an industrial partner. Students develop compentences in interdisciplinary cooperation and communication, the ability to problem solving, and improve their presentation skills.

    • Literature:
      • Lecture Name: Operations Research 1
      • Lecturer: Marco Lübbecke
      • Contact: Jonas Witt
      • Courses of Study: M.Sc. BWL, M.Sc. Info/BWL, M.Sc, Math./BWL
      • Turnus: yearly, winter terms
      • Prerequisites:

        Knowledge of basic graph algorithms and linear optimization, in particular modeling with graphs/networks and linear programs; usually, this is acquired in our B.Sc. lecture quantitative methods, but also in efficient algorithm (computer science), etc.

      • Content:

        We focus on (mixed) integer linear optimization, and in particular on modeling with integer programs. We discuss standard problems in operations research (like network flows, lot sizing, facility location, machine scheduling, cutting and packing, vehicle routing, network design, etc.) and their variants, as well as more abstract, and thus moregenerally applicable concepts like set packing/partitioning/covering problems. Modeling mechanisms and "tricks" when modeling with binary variables are intensively treated. On the algorithmic side, we discuss branch-and-bound and branch-and-cut algorithms, dynamic programming, and meta heuristics.

      • Goals:

        The students learn modeling techniques and methods in integer programming, in particular their applicability and limits. They acquire the ability to identify the abstract mathematical core of an optimization problem, and to successfully exploit its structure when choosing among or developing new models and algorithms. The theoretical knowledge is practically intensified using standard software (CPLEX, GAMS, etc.) applied to practical planning and decision problems. We train the abstract and formal thinking, and basic mathematical skills.

      • Literature:
        • D. Bertsimas and J.N. Tsitsiklis (1997).
          Introduction to Linear Optimization. Athena Scientific, [bib]
        • F.S. Hillier and G.J. Lieberman (2009).
          Introduction to Operations Research. McGraw Hill, Bosten [bib]
      • Lecture Name: Operations Research 2
      • Lecturer: Marco Lübbecke
      • Courses of Study: M.Sc. Math, M.Sc. Inf, M.Sc. BWL, M.Sc. Wiwi
      • Prerequisites:
      • Content:

        todo

      • Goals:

        The goal is to teach everybody everything.

      • Literature:
        • Lecture Name: Praktische Optimierung mit Modellierungssprachen
        • Lecturer: Marco Lübbecke
        • Contact: Michael Bastubbe
        • Courses of Study: M.Sc. maths, M.Sc. computer science, M.Sc. business administration, M.Sc. industrial engineering
        • Turnus: every summer term
        • Prerequisites:

          A first exposure to modeling with linear and integer programs (as tought e.g., in "quantitative methods" and "operations research 1") is helpful.

        • Content:

          At the outset we "only" assume that participants have made first experiences with modeling with linear or integer programs, possibly from different viewpoints, like practice (business administration), theory (mathematics), or implementation tricks and algorithms (computer science). However, almost no textbook mathematical program reflects a realistic optimization problem. In practice, a problem needs to be analyzed and described, data needs to be collected, verified, and cleaned. The subsequent modeling may consume only a small portion of the overall project span.Available algorithms may fail in solving the models. Then we need to apply "tricks" about which a theorist may laugh, but which become essential in practice. Finally, solutions should be visualized and communicated, also validated. Often, solving an optimization problem is not a single shot, but over a rolling time horizon. Notions of robustness and fairness become more and more important. Our companions are scripting languages, data bases, spread sheets, and algebraic modeling languages like GAMS.

        • Goals:

          Students learn the basics of modeling and solving practical optimization problems. They need to overcome obstacles which are not present in a lab environment: imprecise problem descriptions, unknown goals, incomplete data, unsuited algorithms, avoiding infeasible solutions, establishing acceptance by practitioners, etc.

        • Literature:
          • Lecture Name: Programmieren, Algorithmen, Datenstrukturen
          • Lecturer: Marco Lübbecke
          • Contact: Michael Bastubbe
          • Courses of Study: M.Sc. maths, M.Sc. business administration, M.Sc. industrial engineering
          • Turnus: every winter term
          • Prerequisites:
          • Content:

            This is a steep programming course in a higher programming language like Java or python. At the same time, basic algorithms are tought such as sorting and searching or Huffman compression as well as fundamental data structures like arrays, lists, stacks, queues, heaps, hashmaps, and binary search trees. There are homework assignments on the mathematical background and almost every a programming assignment must be successfully completed. The weekly workload is substantial and a careful time management is required.

          • Goals:

            Programming is more than mastering a programming language. Students are enabled to algorithmically structure a given task and implement it in a programming language. They make thoughtful use of suitable data structures and know fundamental algorithmic principles like iteration, recursion, and divide-and-conquer, as well as elements of abstraction like inheritage. They know basic rules of producing clean and easily maintainable code, as well as rules of documentation and style.

          • Literature:
            • T.H. Cormen and C.E. Leiserson and R.L. Rivest and C. Stein (2001).
              Introduction to Algorithms. MIT Press, Cambridge, MA [bib]
          • Lecture Name: Quantitative Methoden
          • Lecturer: Marco Lübbecke
          • Courses of Study: B.Sc. Maths, CS, Business, Industrial Eng.
          • Turnus: every summer term
          • Prerequisites:
          • Content:

            This is most student's first contact with operations research.

          • Goals:

            Students learn about fundamental algorithms of operations research like graph search, shortest path algorithms, and max flow and min cost flow algorithms. The ability to apply these to specific problem instances is acquired. In addition, there are two main goals: 1. to acquire algorithmic thinking; 2. to learn fundamental knowledge and skills for modeling practically motivated optimization problems using graphs and linear programs.

          • Literature:
            • R.K. Ahuja and T.L. Magnanti and J.B. Orlin (1993).
              Network Flows: Theory, Algorithms and Applications. Prentice-Hall, Englewood Cliffs, NJ [bib]
            • D. Bertsimas and J.N. Tsitsiklis (1997).
              Introduction to Linear Optimization. Athena Scientific, [bib]
            • T.H. Cormen and C.E. Leiserson and R.L. Rivest and C. Stein (2001).
              Introduction to Algorithms. MIT Press, Cambridge, MA [bib]
            • F.S. Hillier and G.J. Lieberman (2009).
              Introduction to Operations Research. McGraw Hill, Bosten [bib]