Sequential Decision Making under System-inherent Uncertainty: Mathematical Optimization Methods for Time-dynamic Applications

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In mathematical optimization it is often assumed that a problem's data is known entirely. In practice however this assumption is often not met because data is made known over the course of time requiring iterative decision making under uncertainty. Applications for time-dynamic optimization problems arise on different levels: For instance, in strategic supply chain planning data is made available quarterly, whereas in operational machine scheduling new orders have to be accounted for on a minute-basis. The unifying element are uncertainties in the course of time. There is no systematic, interdisciplinary approach.Several approaches are pursued in research problem-dependently: In online optimization there is no knowledge on future events and decision are made such that even in the worst case the solution is not too far away from the optimal solution that can be computed in retrospective. In stochastic programming one assumes a set of future scenarios along with probabilities and one decides in the sense of the expected outcome. In robust optimization feasibility is guaranteed for all scenarios which is why the degrees of freedom for optimization are restricted. The main deficiency of current research comprises the inconsistent handling of the factors time and uncertainty. Online optimization suffers from the worst case orientation, stochastic programming results are based on unknown stochastic assumptions, robust optimization is not specifically designed to multi-stage problems. General extensions, such as an analysis of the value of future data, is just in the beginning of its scientific evolution. Flexible implementations within planning and control tools in supply chain management do not exist.Therefore, our goal consists in the consolidation of the different approaches dealing with uncertainty in a unified framework facilitating a context-dependent selection of a suitable solution methodology (algorithm from online optimization, stochastic programming, orrobust optimization). This comprises distributional methods of analysis which allow to assess and compare the quality of algorithms and the value of data. Sensitivity analysis is used then in order to check the behavior of different methods under varying circumstances, i.e., under different types of uncertainty. Based on exemplary Problems from production and logistics, we check the applicability of the methods in practice. Furthermore, we intend to lead planning and control tools towards an adaptive functional logic. The increasing amounts of data available in practice, e.g., from GPS or RFID chips, indicate that a comprehensive methological understanding is necessary in order to be able to decide on the value of information and to apply suitable optimization methods. This fact is supported by on-going industrial initiatives such as Industry 4.0 in Germany or the Industrial Internet in the US.