Thesis (M. Sc.)--University of Canterbury, 2006. / Typescript (photocopy). Includes bibliographical references (p. 77-79). Also available via the World Wide Web.

Thesis (M.S.)--Ohio University, November, 2006. / Title from PDF t.p. Includes bibliographical references.

In this thesis, we study large-scale dynamic optimization problems in the context of inventory management. We analyze inventory problems with constraints coupling the items or facility locations in the inventory systems, and we propose efficient solutions that are asymptotically optimal or empirically near-optimal. In Chapter 1, we analyze multi-item, single-location inventory systems with storage capacity limits which are formulated as both unconditional expected value constraints and unconditional probability constraints. We first show that problems with unconditional expected value constraints only can be solved to optimality through Lagrangian relaxation. Then, under an assumption on the correlation structure of the demands that is valid under most practical setting, we show that the original problem can be sandwiched between two other problems with expected value constraints only. One of these problems yields a feasible solution to the original problem that is asymptotically optimal as the number of items grows. In Chapter 2, we consider the same problem but with conditional probability constraints, that impose limits on overflow frequency for every possible state in each period. We construct an efficient feasible solution in two steps. First, we solve an unconditional expected value constrained problem with reduced capacity. Second, in each period, given the state information, we solve a single-period convex optimization problem with a conditional expected value constraint. We further show that the heuristic is asymptotically optimal as number of items I grows. In addition, we design another efficient method for moderate values of I, which works empirically well in an extensive numerical study. Moreover, we extract key managerial insights from the numerical study which are critical to decision making in real business problems. In Chapter 3, we analyze single-item, multi-location systems on inventory networks that can be described by directed acyclic graphs (DAG). We propose an innovative reformulation of the problem so that Lagrangian relaxation can still be applied, which, instead of decomposing the problem by facility location, aggregates the state information, leading to a tractable lower bound approximation for the problem. The Lagrange multiplier, which provides information on the value function from the lower bound dynamic program, is used in designing a feasible heuristic. An extensive numerical study is conducted which suggests that both the lower bound approximation and upper bound heuristic perform very well.

Invasive alien plants have widespread ecological and socioeconomic impacts throughout many parts of the world, including Swaziland where the government declared them a national disaster. Control of these species requires knowledge on the invasion ecology of each species including how they interact with the invaded environment. Species distribution models are vital for providing solutions to such problems including the prediction of their niche and distribution. Various modelling approaches are used for species distribution modelling albeit with limitations resulting from statistical assumptions, implementation and interpretation of outputs. This study explores the usefulness of Bayesian networks (BNs) due their ability to model stochastic, nonlinear inter-causal relationships and uncertainty. Data-driven BNs were used to explore patterns and processes influencing the spatial distribution of 16 priority invasive alien plants in Swaziland. Various BN structure learning algorithms were applied within the Weka software to build models from a set of 170 variables incorporating climatic, anthropogenic, topo-edaphic and landscape factors. While all the BN models produced accurate predictions of alien plant invasion, the globally scored networks, particularly the hill climbing algorithms, performed relatively well. However, when considering the probabilistic outputs, the constraint-based Inferred Causation algorithm which attempts to generate a causal BN structure, performed relatively better. The learned BNs reveal that the main pathways of alien plants into new areas are ruderal areas such as road verges and riverbanks whilst humans and human activity are key driving factors and the main dispersal mechanism. However, the distribution of most of the species is constrained by climate particularly tolerance to very low temperatures and precipitation seasonality. Biotic interactions and/or associations among the species are also prevalent. The findings suggest that most of the species will proliferate by extending their range resulting in the whole country being at risk of further invasion. The ability of BNs to express uncertain, rather complex conditional and probabilistic dependencies and to combine multisource data makes them an attractive technique for species distribution modeling, especially as joint invasive species distribution models (JiSDM). Suggestions for further research are provided including the need for rigorous invasive species monitoring, data stewardship and testing more BN learning algorithms. / Environmental Sciences / D. Phil. (Environmental Science)