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In this thesis we investigate important issues in the area of dynamic pricing for revenue management. Studying the effect of competition and strategic consumer behavior, we characterize the dynamic pricing policies for retailers who sell homogeneous goods in multi-period, discrete time, finite horizon settings. In the first essay an impatient consumer visits only one of two competing retailers in each period. If he does not purchase the good, he visits the competing retailer in the ensuing period. Compared to the corresponding single store monopoly, when the consumer’s valuation is uniformly distributed, prices decline exponentially rather than linearly, with a dramatically lower initial price, and a substantially lower system profit. The model is extended to accommodate many consumers, who may be either identical or similar, a more general valuation distribution, and situations wherein capacities are limited. The base case of a centralized two-store monopoly is also examined. In the second essay the consumer may return to the same retailer with some certain probability. This probability is either affected by market structure characteristics, or it may depend on the consumer’s experience at the last store visited. The robustness of the exponential decline of prices is reinforced. It occurs even when a strong retailer faces competition from a relatively much weaker retailer. We investigate the impact of the return probabilities on prices, profits, and consumer surplus. The model is extended to an oligopoly, and to situations with many similar consumers. The effect of strategic consumer behavior on prices and profits is revealed in the third essay. Characterizing the pricing policies arising in a two-period monopoly and duopoly settings, we find that strategic consumer behavior inflicts larger losses to a duopoly than to a monopoly. A lower strategic consumers’ discounting factor, which is beneficial to a monopoly, may be harmful to a duopoly. Ignoring strategic consumer behaviour is costly to a monopoly, but may, on the other hand, be beneficial to a duopoly. An extension to three periods is studied, and with longer horizons the model is analyzed for the case when all the consumers are strategic.

In recent years there has been increased interest in the development of sensorless switched reluctance machine drives. The proper operation of a switched reluctance machine (SRM) requires knowledge of the position of the rotor of the machine. The inclusion of a physical position sensor compromises the inherent robustness of this type of machine. Thus, there has been a need to develop techniques to estimate the position of the rotor in SRM drives. Switched reluctance machines are able to operate over a large range in speed. A fully loaded SRM is typically designed to saturate the ferromagnetic material that comprises the stator and rotor of the machine whereas a lightly loaded machine does not. Therefore, the model of the machine should be able to handle both a large range in frequency and input excitation levels of the magnetic material in the machine. The development of a new dynamic circuit-based ferromagnetic model is described in this thesis. The investigation of the behaviour of 24 gauge M19 silicon steel led to the conclusion that, for this material, a circuit model that has static parameters is unable to accurately reproduce the behaviour of the actual material over a large range of input frequencies and excitation levels without resorting to retuning the parameters of the model. This thesis provides two new mechanisms that dynamically adjust the resistance values of the flux tubes of the model. Comparisons using a normalized vertical least-squares metric between the newly proposed dynamic model and a model that has static resistance values clearly show the improvement that is gained by using these mechanisms. A practical implementation of the new model is also given. Timing using a general purpose CPU shows that this implementation of the model will most likely be able to be used as part of a multi-phase lumped parameter model for a SRM in realtime.

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