Abstract
In this thesis, we consider several problems related to online resource management. In online optimization, an algorithm has to make decisions based on a sequence of incoming bits of information without knowledge of future inputs. We apply the well-established concept of competitive analysis in order to measure the quality of an online algorithm. First, we analyze an online knapsack problem with incremental capacity which extends the basic online knapsack problem by introducing a dynamic instead of a static knapsack capacity. This setting is applicable to classic problems such as resource allocation or one-way trading. Secondly, we expand the concept of competitive analysis to multi-objective online problems and achieve a novel and consistent framework for the analysis of multi-objective online problems. Finally, we present a real-world optimization problem, namely a cutting problem arising in the veneer industry, featuring uncertainty in the input data and solve this problem by means of deterministic and robust optimization.
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