Given a set of circles C = {c₁, ..., cn}on the Euclidean plane with centers {(a₁, b₁), ..., (an, b_n)}and radii {r₁..., r<n},the smallest enclosing circle (of fixed circles) problem is to find the circle of minimum radius that encloses all circles in C. We survey four known approaches for this problem, including a second order cone reformulation, a subgradient approach, a quadratic programming scheme, and a randomized incremental algorithm. For the last algorithm we also give some implementation details. It turns out the quadratic programming scheme outperforms the other three in our computational experiment. / Singapore-MIT Alliance (SMA)

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 85-90). Also available in electronic version.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Large corporations have a significant amount of working capital tied into the acquisition and storage of spare parts. In the industry, spare parts inventory policies and strategies are often developed in isolation from reliability centered maintenance practices – this results in significant wasteful direct and indirect cost attached to spare parts management for the equipment operator. This report will focus on developing a methodology for minimizing lifecycle indirect and direct cost that comes from storing long lead time spares. A combined Monte-Carlo and Genetic Algorithm based optimization approach to finding the optimal spare parts storage strategy is proposed. In this study, the indirect and direct cost of having a spare part in the storage facility will be balanced against the cost of lost opportunity that results from decreased availability - a consequence of not having the required spare part available when an equipment failure event occurs. The results of this study present the benefits of optimizing long lead time spares through a joint Monte-Carlo & Genetic Algorithm based approach. / Engineering Management

Site development in heavy and civil construction need to consider many rules such as ensuring proper drainage, prevention of flood, safety driving, optimizing earthwork, minimizing fleet travel distances, proper fleet matching and achieving high equipment utilization rates. In recent decades, numeral researchers have presented different solutions to improve this process; however they have been either too complicated to be practical or oversimplify the problem definition by ignoring critical facts. This thesis presents three advanced quantitative techniques to enhance current earthwork construction practices including: a modification of least squares method to optimize the earthwork, an application of transportation simplex method to minimize the fleet travel distance, and an earthwork construction process simulation to ensure the accuracy of earthwork operations analysis. The thesis also includes an actual case study to demonstrate the practicality and effectiveness of the proposed methodology. / Construction Engineering and Management

Thesis (Ph.D.)--University of California, Los Angeles, 2002. / Chair: Vasilios I. Manousiouthakis. Includes bibliographical references.

Ph.D. / Computer Science and Engineering / Join-order optimization plays a central role in the processing of relational database queries. This dissertation presents two new algorithms for join-order optimization: a deterministic, exhaustive-search algorithm, and a stochastic algorithm that is based on the deterministic one. The deterministic algorithm achieves new complexity bounds for exhaustive search in join-order optimization; and in timing tests, both algorithms are shown to run many times faster than their predecessors. In addition, these new, fast algorithms search a larger space of join orders than is customary in join-order optimization. Not only do they consider all the so-called bushy join orders, rather than just the left-deep ones, but-what is more unusual-they also consider all join orders that contain Cartesian products. The novel construction of these algorithms enables them to search a space including Cartesian products without paying the performance penalty that is conventionally associated with such a search.

This thesis describes the manufacturing, structural analysis and testing of a composite cylinder for space application. This work includes the design and fabrication of a reusable multicomponent mandrel made of aluminum and steel and the manufacturing of a carbon fiber reinforced tube in an epoxy resin matrix. This structure intends to serve as the optical lens housing onboard a spacecraft. In addition, some future work needs to be done before this component is certified. The objective is to determine if the composite meets the stiffness and strength requirements for lens housing. The structural analysis is made by means of a finite element model simulating the true boundary conditions. The testing includes the design of a fixture to allow the composite cylinder to be mounted in one the testing machines at the Department of Aerospace Engineering at Texas A&M University and the preparation for the actual test. The response to the experimental analysis will be compared to the numerical simulation to verify the results.

This Record of Study contains the details of an optimization model developed for Shell Oil Co. This model will be used during the strategic design process of a supply chain for a new technology commercialization. Unlike traditional supply chain deterministic optimization, this model incorporates different levels of uncertainty at suppliers' nominal capacity. Because of the presence of uncertainty at the supply stage, the objective of this model is to define the best diversification and safety stock level allocated to each supplier, which minimize the total expected supply chain cost. We propose a Monte Carlo approach for scenario generation, a two-stage non-linear formulation and the Sample Average Approximation (SAA) procedure to solve the problem near optimality. We also propose a simple heuristic procedure to avoid the nonlinearity issue. The sampling and heuristic optimization procedures were implemented in a spreadsheet with a user's interface. The main result of this development is the analysis of the impact of diversification in strategic sourcing decisions, in the presence of stochastic supply disruptions.

This Record of Study contains the details of an optimization model developed for Shell Oil Co. This model will be used during the strategic design process of a supply chain for a new technology commercialization. Unlike traditional supply chain deterministic optimization, this model incorporates different levels of uncertainty at suppliers’ nominal capacity. Because of the presence of uncertainty at the supply stage, the objective of this model is to define the best diversification and safety stock level allocated to each supplier, which minimize the total expected supply chain cost. We propose a Monte Carlo approach for scenario generation, a two-stage non-linear formulation and the Sample Average Approximation (SAA) procedure to solve the problem near optimality. We also propose a simple heuristic procedure to avoid the nonlinearity issue. The sampling and heuristic optimization procedures were implemented in a spreadsheet with a user’s interface. The main result of this development is the analysis of the impact of diversification in strategic sourcing decisions, in the presence of stochastic supply disruptions.