Algorithms for online buffering problems and applications to the power control of a hybrid electric vehicle

In many situations we have to make repeated decisions in an uncertain environment. Those decisions include to choose a route to drive to work, when to refuel a car or when to purchase and sell shares in the stock market. In each of those settings we decide which actions we take, although we do not possess complete information about the situation. Since part of the missing information might influence the optimal decision, we often make suboptimal choices when examined in hindsight. Furthermore, the actions we take in one time step might influence the options available in the future and can, therefore, avoid optimal choices in the future. In this thesis, we introduce and analyze algorithms for Online Buffering problems, i.e., the problem of making repeated decisions in an uncertain environment to manage a buffer. In Online Buffering, a sequence of demands and prices of a resource is revealed over time. In each time step, we are given the current price and demand, but no information about future prices and demands. Based on this information, we have to decide which amount of the resource we want to purchase. We can store units for a later usage in a buffer of fixed size. The goal is to use the buffer, such that the costs to fulfill the demands are minimized. The costs of a strategy are compared to the costs of purchasing the requested amount in each time step. Since we have no information about future prices and demands, it is impossible to achieve costs which are as low as in the situation where all prices and demands are known beforehand. We study Online Buffering in different settings. First, we show how to use simple threshold algorithms to solve the problem in a stochastic input model. In this model, the prices of the resource are generated by a random walk. The decision which amount the algorithm purchases in a time step, depends on the thresholds of the algorithm and the fact whether the price is above, in between or below the thresholds defined by the algorithm. We show that the threshold algorithm which achieves the lowest expected costs in that setting, is one which fills the buffer if the price equals the lowest price possible, and uses units from the buffer if the price for the resource is above that. We analyze this algorithm quantitatively,