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<p>In this thesis we study a typical retailer's problem characterized by a slngle item, periodic review of inventory levels in a multi-period setting: and stochastic demands. We consider the case of full backlogging where backorders are penalized via fixed and proportional backorder costs simultaneously. This treatment of backorder costs is a nonstandard aspect of our study. The discussion begins with an introduction in Chapter 1. Next, a review of the relevant literature is provided in Chapter 2. In Chapter 3 we study the infinite horizon case which is of both theoretical and practical interest. From a theoretical point of view tile infinite horizon solution represents the limiting behavior of the finite horizon case. Solving the infinite horizon problem has also its own practical benefits since its solution is easier to compute. Our motivation to study the infinite horizon case in the first place is pragmatic. We prove that a myopic base-stock policy is optimal for the infinite horizon case, and this result provides a basis for our study. We show that the optimal myopic policy can be computed easily for the Erlang demand in Chapter 4; solve a disposal problem which arises under the myopic policy in Chapter 5, and also study in Chapters 6 and 7 the finite horizon problem for which a myopic policy is not optimal. For the finite horizon problem computation of the exact policy may require a substantial effort. From a computational point of view, there is a need for developing a method that overcomes this burden. In Chapter 6 we develop a model for such a method by restricting our attention to the class of myopic base-stock policies, and call the resulting policy the 'best myopic' policy. We discuss analytical and numerical results for the computation of the best myopic policy in Chapter 7. Finally we present a summary of our main findings in Chapter 8.</p> / Doctor of Philosophy (PhD)

<p>We explore two novel applications of stochastic optimization inspired by real-world problems. The first application involves the optimization of appointments-based service systems. The problem here is to determine an optimal schedule of start times for jobs that have random durations, and a range of potential cost structures based on common performance metrics such as customer waiting and server idling . We show that the problem can be formulated as a two-stage stochastic linear program and develop an algorithm that utilizes the problem structure to obtain a near-optimal solution. Various aspects of the problem are considered, including the effects of job sequence, dependence on cost parameters, and job duration distributions. A range of numerical experiments is provided and some resulting insights are summarized. Some simple heuristics are proposed, based on relaxations of the problem, and evidence of their effectiveness is provided. The second application relates to inventory deployment at an integrated steel manufacturer (ISM). The models presented in this case were developed for making inventory design-choice (what to carry) and lot-size (how much to carry) decisions. They were developed by working with managers from several different functional areas at a particular ISM. They are, however, applicable to other ISMs and to other continuous-process industries with similar architectures. We discuss details of the practical implementation of the models, the structure of the problems, and algorithms and heuristics for solving them. Numerical experiments illustrate the accuracy of the heuristics, and examples based on empirical data from an ISM show the advantages of using such models in practice and suggest some managerial insights.</p> / Doctor of Philosophy (PhD)

<p>The effects of pressurization on the properties of metals has long been of interest to scientists. Bridgman found that in general, the ductility (ability of the metal to deform without fracture) increased with superimposed hydrostatic pressure. Pugh et al. confirmed similar findings.</p> <p>The effects of hydrostatistic pressure on the mechanical properties of thin anisotropic zinc, heat treated and non heat treated zinc alloy sheets subjected to biaxial tension (via the circular bulge test) is investigated in this project.</p> <p>A brief look is taken into the generalized conditions for the onset of tensile plastic instability in a thin circular diaphragm bulged under superimposed hydrostatic pressure. The material is assumed to obey Hill's theory of yielding for anisotropic materials. These predictions are verified by conducting bulge tests using back pressures up to 10,000 psi. It is concluded that within the pressure range of investigation there is no detectable changes in the properties of the materials tested.</p> <p>In the appendix section a brief look is taken into the microstructure of the materials tested.</p> / Master of Engineering (ME)

<p>The project described in this thesis was to establish the instrumentation and technique for analysing stability of machine-tools against chatter by harmonic excitation. To test out the technique, two sets of experiments were performed on centre lathes:</p> <p>1) comparison of cutting stability with tour different types of boring bars, and</p> <p>2) comparison of cutting stability of a tool oriented in seven orientations in a single plane perpendicular to the spindle axis.</p> <p>The electro-dynamic exciter was used in 1) while an electro-magnetic exciter was used in 2) Data of the excitation tests were used to compute and plot the cross-receptances which indicate the limit width of cut together with the chatter frequency and the modal shapes which identify the main masses and springs of the structure. The contribution of the individual modes to the resulting degree of stability can also be obtained. Cutting tests were conducted to provide some means of checking the reliability of the excitation test results. In this report also included are the theory of vibration, theory of chatter and specification of various parts of instrumentation.</p> / Master of Engineering (ME)

<p>The Internet provides opportunity for knowledge sharing among people with similar interests (i.e., buddies). Common methods available for people to identify buddies for knowledge sharing include emails, mailing lists, chat rooms, electronic bulletin boards, and newsgroups. However, these manual buddy finding methods are time consuming and inefficient. In this thesis, we propose an agent-based buddy finding methodology based on a combination of case-based reasoning methodology and fuzzy logic technique. We performed two experiments to assess the effectiveness of our proposed methodology. The first experiment was comprised of a stock market portfolio knowledge sharing environment in which a conventional cluster analysis was used as a benchmark to assess the technical goodness of the proposed methodology in identifying the clusters of buddies. Statistical analysis showed that there was no significant ranking difference between conventional cluster analysis and the proposed buddy-finding methodology in identifying buddies. Cluster analysis requires centralized database to form buddies (clusters) with similar properties. The unique advantage of our proposed agent-based buddy finding methodology is that it can identify similar buddies in distributed as well as centralized database environments. A second experiment, in the context of sharing musical-knowledge among human subjects, was used to find out whether selection of the buddies by the proposed methodology is as good as those done by human subjects. The findings from this latter empirical test showed that the buddies found by agents are as good as the buddies found manually by humans.</p> / Doctor of Philosophy (PhD)

There still is a practical need for improved closure models for the Reynolds-averaged Navier-Stokes (RANS) equations. This dissertation explores two different approaches for using experimental data to provide improved closure for the Reynolds stress tensor field. The first approach uses machine learning to learn a general closure model from data. A novel framework is developed to train deep neural networks using experimental velocity and pressure measurements. The sensitivity of the RANS equations to the Reynolds stress, required for gradient-based training, is obtained by means of both variational and ensemble methods. The second approach is to infer the Reynolds stress field for a flow of interest from limited velocity or pressure measurements of the same flow. Here, this field inversion is done using a Monte Carlo Bayesian procedure and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. The two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions. / Doctor of Philosophy / The Reynolds-averaged Navier-Stokes (RANS) equations are widely used to simulate fluid flows in engineering applications despite their known inaccuracy in many flows of practical interest. The uncertainty in the RANS equations is known to stem from the Reynolds stress tensor for which no universally applicable turbulence model exists. The computational cost of more accurate methods for fluid flow simulation, however, means RANS simulations will likely continue to be a major tool in engineering applications and there is still a need for improved RANS turbulence modeling. This dissertation explores two different approaches to use available experimental data to improve RANS predictions by improving the uncertain Reynolds stress tensor field. The first approach is using machine learning to learn a data-driven turbulence model from a set of training data. This model can then be applied to predict new flows in place of traditional turbulence models. To this end, this dissertation presents a novel framework for training deep neural networks using experimental measurements of velocity and pressure. When using velocity and pressure data, gradient-based training of the neural network requires the sensitivity of the RANS equations to the learned Reynolds stress. Two different methods, the continuous adjoint and ensemble approximation, are used to obtain the required sensitivity. The second approach explored in this dissertation is field inversion, whereby available data for a flow of interest is used to infer a Reynolds stress field that leads to improved RANS solutions for that same flow. Here, the field inversion is done via the ensemble Kalman inversion (EKI), a Monte Carlo Bayesian procedure, and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. While further development is needed, the two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions.

Numerous scientific applications have seen the rise of massive inverse problems, where there are too much data to implement an all-at-once strategy to compute a solution. Additionally, tools for regularizing ill-posed inverse problems are infeasible when the problem is too large. This thesis focuses on the development of row-action methods, which can be used to iteratively solve inverse problems when it is not possible to access the entire data-set or forward model simultaneously. We investigate these techniques for linear inverse problems and for separable, nonlinear inverse problems where the objective function is nonlinear in one set of parameters and linear in another set of parameters. For the linear problem, we perform a convergence analysis of these methods, which shows favorable asymptotic and initial convergence properties, as well as a trade-off between convergence rate and precision of iterates that is based on the step-size. These row-action methods can be interpreted as stochastic Newton and stochastic quasi-Newton approaches on a reformulation of the least squares problem, and they can be analyzed as limited memory variants of the recursive least squares algorithm. For ill-posed problems, we introduce sampled regularization parameter selection techniques, which include sampled variants of the discrepancy principle, the unbiased predictive risk estimator, and the generalized cross-validation. We demonstrate the effectiveness of these methods using examples from super-resolution imaging, tomography reconstruction, and image classification. / Doctor of Philosophy / Numerous scientific problems have seen the rise of massive data sets. An example of this is super-resolution, where many low-resolution images are used to construct a high-resolution image, or 3-D medical imaging where a 3-D image of an object of interest with hundreds of millions voxels is reconstructed from x-rays moving through that object. This work focuses on row-action methods that numerically solve these problems by repeatedly using smaller samples of the data to avoid the computational burden of using the entire data set at once. When data sets contain measurement errors, this can cause the solution to get contaminated with noise. While there are methods to handle this issue, when the data set becomes massive, these methods are no longer feasible. This dissertation develops techniques to avoid getting the solution contaminated with noise, even when the data set is immense. The methods developed in this work are applied to numerous scientific applications including super-resolution imaging, tomography, and image classification.

This thesis investigates the numerical treatment of nonlinear eigenvalue problems. These problems are defined by the condition $T(lambda) v = boldsymbol{0}$, with $T: C to C^{n times n}$, where we seek to compute the scalar-vector pairs, $lambda in C$ and nonzero $ v in C^{n}$. The first contribution of this work connects recent contour integration methods to the theory and practice of system identification. This observation leads us to explore rational interpolation for system realization, producing a Loewner matrix contour integration technique. The second development of this work studies the application of rational interpolation to the function $T(z)^{-1}$, where we use the poles of this interpolant to approximate the eigenvalues of $T$. We then expand this idea to several iterative methods, where at each step the approximate eigenvalues are taken as new interpolation points. We show that the case where one interpolation point is used is theoretically equivalent to Newton's method for a particular scalar function. / Master of Science / This thesis investigates the numerical treatment of nonlinear eigenvalue problems. The solutions to these problems often reveal characteristics of an underlying physical system. One popular methodology for handling these problems uses contour integrals to compute a set of the solutions. The first contribution of this work connects these contour integration methods to the theory and practice of system identification. This leads us to explore other techniques for system identification, resulting in a new method. Another common methodology approximates the nonlinear problem directly. The second development of this work studies the application of rational interpolation for this purpose. We then use this idea to form several iterative methods, where at each step the approximate solutions are taken to be new interpolation points. We show that the case where one interpolation point is used is theoretically equivalent to Newton’s method for a particular scalar function.