BAE, WI, DTBS

Mathematical maturity and the ability to write down precise and rigorous arguments.
Solid basic knowledge of linear algebra.

2

Domschke und Drexl (2005). Einführung in OR. Springer Science + Business Media: Berlin.
Bertsimas, D., and Tsitsiklis, J. N. (1997). Introduction to Linear Optimization. Athena Scientific: Massachusstets.
Winston, W. (2003). Operations Research: Applications and Algorithms. Brooks/Cole: Belmont.

After successful participation in the module, students will be able to:
Read and interpret optimization models, independently work out models for variations of basic optimization problems
Select a suitable solution approach based on basic problem classifications as well as on considerations on the required solution quality and the acceptable computational complexity
Evaluate computational complexity of algorithms
Understand in-depth foundations of linear programming and duality theory, elaborate on the success and the design components of the simplex method
Evaluate MIP models, discriminate between good and less fortunate modeling decisions, incl. for integer programs
Apply basic versions of the selected exact algorithms (the cutting plane method and the branch-and-bound method) and elaborate on promising variations and extensions of these methods
Understand the concept of total unimodularity and solve selected respective optimization problems heuristically and exactly with state-of-the-art solution approaches
Apply and understand principles of various heuristic and metaheuristic solution approaches
Critically evaluate the potential of the generic heuristic solution approaches (such as metaheuristics, reinforcement learning based heuristics), incl. in the light of the no-free-lunch theorem

Lecture 2 SWS (30 h attendance and 45 h own work)
Exercise 2 SWS (30 h attendance and 45 h own work)
Calculation basis: 15 weeks in a semester, including an examination week; each SWS corresponds to 60 minutes