Research - Chair of Management Science
Ultimately, we strive to push frontiers in terms
of the size or share of practically relevant instances of
important problems in operations research and discrete
optimization that can be solved
routinely.
Please find below some example domains of our research.
Exact algorithms for OR applications and difficult optimization problems
We develop exact methods for dedicated applications as well as optimization problems that serve as a model of overarching or interdisciplinary relevance.
- Sophisticated methods based on integer programming and combinatorial algorithms, like enhanced separation procedures and branch-and-cut algorithms
- Modeling and Reformulation towards (a better) practical solvability.
- Linear or Quadratic Programming Relaxations and polynomial-time Combinatorial Optimization (Flows, Shortest-Paths, Matchings, ...)
Methods for quadratic optimization problems
Many operations research problems depend (in terms of the objective or the feasibility of a solution) on simultaneous decisions, and thus on quadratic terms. We address this by different problem-specific methods, such as e.g.:
- Linearization and Convexification Techniques, in particular the Inductive Linearization Technique
- Transformations towards a Quadratic Unconstrained Binary Optimization (QUBO) problem and corresponding resolution techniques.
- Direct Techniques based on Convex and Non-Convex Quadratic Relaxations
Algorithm Engineering
Typically, our developments and publications follow well the Algorithm Engineering paradigm, in particular in terms of a repeated integration and refinement of the following ingredients:
- Theoretical investigations: Polyhedral Theory, Graph Theory, Complexity Theory, Algorithmic Game Theory
- Algorithmic Implementations of High-Performance
- Qualified Experimental Studies
Some example Management Science applications
The chairs research involves (model) problems of overarching relevance with typically many applications in industry as well as dedicated problems from e.g. logistics or other specific business domains.
- Traveling Salesman Problem, Vehicle Routing
- (Quadratic) Assignment Problems
- Facility Layout and other Ordering, Layout, and Permutation Problems
- Scheduling and Critical-Path Problems