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 management science, operations research, and more general discrete optimization that can be solved routinely.

Please find below some example domains of our research.

Exact algorithms for OR and interdisciplinary applications We develop exact methods for dedicated applications as well as optimization problems that serve as a model of economic, otherwise interdisciplinary, or overarching 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 algorithms (flows, shortest-Paths, matchings, ...).

Methods for quadratic optimization problems Many operations research problems depend (regarding 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 Quadratic Unconstrained Binary Optimization (QUBO), 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 chair's research is concerned with models and problems of overarching relevance with typically many applications in industry as well as dedicated problems from e.g. logistics or other specific business domains.

• (Quadratic) Assignment (and Matching) Problems
• Facility Layout and other Ordering, Layout, and Permutation Problems
• Scheduling and Critical-Path Problems