Methods
Mathematical programming
The basis of our research is the formulation of mixed-integer programs for the given problem settings. This helps to clearly define the considered problem, including constraints and objective functions.
Decomposition
Mixed-integer programs can become difficult to solve, particularly if large real datasets are used. By applying decomposition techniques, such as Benders decomposition, the problem is decomposed into easier solvable subproblems. Nevertheless, these methods still guarantee to find the global optimal solution.
Heuristics and approximations
If decomposition techniques are not efficient enough, we develop heuristics or metaheuristics. In contrast to the optimal procedures, those methods try to efficiently explore the solution space in a smart way. Good implementation and operators specifically tailored towards the problem are necessary to guarantee good solution quality in efficient time.
Machine Learning data-driven approaches
The basis for all described methods is the existence of data, which is assumed to be available. In practice, however, many parameters vary or change over time. To find more robust solutions, we combine existing approaches and Machine Learning or data-driven approaches.
Bilevel Programming
In many real-world applications, several decision makers are involved in the decision process. That means that one person is deciding and influencing the decision space of a second person. This second person is then reacting and influencing again the outcome of the first person. These game-theoretical principals are addressed using principle-agent theory or bilevel programming.