Thesis (Ph. D.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains xi, 158 p. : ill. (some col.), col. map. Vita. Includes abstract. Includes bibliographical references (p. 126-132).

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 98-102). Available also in a digital version from Dissertation Abstracts.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 201-205). Also available in electronic version. Access restricted to campus users.

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Timely provision of quality products at the lowest prices possible has become the utmost competitive edge being pursued by virtually all manufacturing firms. They endeavour to speed up their production and deliveries of goods to end customers in order to make more money and even survive in the fierce competition arena. Although much progress has been made in operations management and a series of production planning approaches have been proposed to achieve various manufacturing operations goals, optimisation results are often rendered unrealistic and even misleading, for few studies have considered the overall corporate goal of shareholder wealth maximisation and the specific economic environments where manufacturing firms operate. Some critical factors closely related to interests of corporate owners, such as working capital management and capital structure, are rarely involved in an overwhelming majority of production planning problems. Moreover, the overlook of the effects of production planning results on the environment makes them more impractical and even unavailable in real-world manufacturing environments. To this end, the dissertation proposes a stochastic production planning model for the uncertain make-to-order production environment, with the focus mainly on the lot sizing decision-making policy. The primary goal of the optimization problem is to maximise the sustainable full interests of corporate owners, namely, the shareholder wealth, rather than to optimise some traditional local or short-term objective functions, such as work flow times, accounting costs, accounting profits and the like. To improve the generality and exactness of the proposed model, all involved uncertain random events are characterized by their own inherent statistical merits without any impractical assumptions on their distributions. The improvement of production planning is not the only one single source of the wealth-based business performance. There are also some other critical factors which can impose direct influences on shareholder wealth. Among these potential shareholder wealth drivers, we choose to examine the effective management of working capital and capital structure, for they are closely pertinent to a firm’s financial position and its cash flow status. In addition, environmental protection has in recent decades aroused extensively global attention because of its far-reaching impingements on the social and economic developments of the world. The carbon emission in production, especially its main component—carbon dioxide, is generally recognized as the most important emission source. To mitigate their diverse interference with the climate and the environment, a wide range of emission reduction measures, laws, and legislations has been enacted and implemented, making production planning optimisations more complicated. To better reflect the emerging production planning environment facing manufacturing firms, the emission trading system for carbon management, which has thus far become the most popular market-based carbon reduction mechanism, is incorporated into the proposed production planning model. To theoretically and analytically validate the proposed approach, the probability and convex theories are adopted to prove the convexity or concavity of the optimisation objectives and the relevant global optimal characteristics. Numerical experiments are further conducted to demonstrate the important implications of the proposed optimisation model to production planning in industrial practices. / published_or_final_version / Industrial and Manufacturing Systems Engineering / Doctoral / Doctor of Philosophy

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In both physical and social sciences, we usually use controlled differential equation to model various continuous evolving system; describing how a response y relates to another process x called control. For regular controls x, the unique existence of the response y is guaranteed while it would never be the case for non-smooth controls via the classical approach. Besides, uniform closeness of controls may not imply closeness of their corresponding responses. Theory of rough paths provides a solution to both concerns. Since the creation of rough path theory, it enjoys a fruitful development and finds wide applications in stochastic analysis. In particular, rough path theory provides an effective method to study irregularity of curves and its geometric consequences in relation to integration of differential forms. In the chapter 2, we demonstrate the power of rough path theory in classical complex analysis by showing the rough path nature of the boundaries of a class of Holder's domains; as an immediate application, we extend the classical Gauss-Green's theorem. Until recently, there has been only limited research on applications of theory of rough paths to high dimensional geometry. It is clear to us that many geometric objects, in some senses appearing as solids, are actually comprised of filaments. In the chapter 3, two basic results in the theory of rough paths which will motivate later development of my thesis has been included. In the chapters 4 and 5, we identify a sensible way to do geometric calculus via those filaments (more precisely, space-filling rough paths) in dimension 3. In a recent joint work of Hambly and Lyons, they have shown that every rectifiable path can be completely characterized, up to tree-like deformation, by an algebraic object called the signature, tensor of all iterated integrals, of the path. It is clear that all tree-like deformation of the path would not change its topological features. For instance, the number of times a planar loop of finite length winds around a point (not lying on the path) is unaltered if one deforms the path in tree-like ways. Therefore, it should be plausible to extract this topological information out from the signature of the loop since the signature is a complete algebraic invariant. In the chapter 6, we express the winding number of a nice loop (respectively linking number of a pair of nice loops) as a linear functional of the signature of the loop (respectively signatures of the pair of loops).

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published_or_final_version / Statistics / Master / Master of Philosophy