This research addresses several quality control problems which arise in a variety of manufacturing, healthcare, service, finance, and other industries given the existence of human and automated attribute detection error. Several mathematical and economic models are developed for various types of single and multiple inspection screening policies in order first to examine inherent tradeoffs between type I errors, type II errors, and all associated inspection, false-rejection, and false-acceptance costs and then, ultimately, to help identify the minimum expected total cost policy and the optimal amount of inspection for any particular scenario. While originally motivated by industrial problems, these models also have been adapted to various non-manufacturing concerns, including service processes and laboratory cancer screening policies. In particular, similar methods are developed and used to analyze the policy for screening Pap smears for early indications of cervical cancer currently required by the Congressional Laboratory Improvements Amendments Act of 1988 (CLIA'88), to compare this policy with possible alternatives, and to develop an algorithm that identifies the optimal policy in any given scenario. Results show that the mandated CLIA policy never is optimal and always increases total costs, that overall sensitivity of CLIA never can be improved beyond a certain mathematical bound, that CLIA's 10% minimum requirement nor any other amount of partial resampling ever is optimal, that multiple readings in some realistic cases can result in very significant benefits, and that the proposed use of automated rescreening technology recently approved by the FDA may not result in improvements over CLIA nor the optimal policy derived here. Sensitivity analyses indicate that the improvement possible by switching to this optimal policy ranges from 90,000 to 165,000 fewer false-negatives and $250 million to \$1 billion savings annually nationwide. Similar results and savings are demonstrated in several industrial and service applications, with Deming's $k\sb1/k\sb2$ minimum cost criterion in some cases now resulting in the maximum expected cost policy and with multiple inspections often being economically optimal. Several directions for further work are suggested, including extending results to mammography and other cancer screening tests, and an extensive bibliography is provided.

In this dissertation, I developed a unified framework for the modeling, analysis, and computation of solutions to both international financial problems with intermediation as well as to global supply chains through the medium of networks. The framework that I developed can handle as many decision-makers within each country as needed (be they sources of funds, financial intermediaries, or, as in the case of global supply chains: manufacturers, retailers, and/or distributors, as well as consumers), and enables the prediction of the flows (financial and product) between tiers of the networks as well as the prices at the tiers. In addition, I considered not only physical transactions between decision-makers but also virtual ones in the form of electronic transactions. I utilized tools from both management science and finance to identify the commonality in the structures of international financial networks and global supply chains. I modeled the behavior of the various decision-makers, which allows for multiple criteria such as profit maximization as well as risk minimization, and study the dynamics of the various interactions. The analysis was both qualitative in nature as well as computational. The effectiveness of the proposed methodologies was demonstrated through numerous examples. The research in this dissertation was motivated not only by the practical importance of the topic but also by the need to develop rigorous theoretical frameworks for complex decision-making on networks with an international focus. To-date, there have been many innovative models developed for multi-tiered networks. For example, Nagurney and Ke (2001, 2003) focused on financial multitiered networks with intermediation (with and without electronic transactions). Moreover, Nagurney, Dong, and Zhang (2002), Nagurney, Loo, Dong, and Zhang (2002), and Nagurney, Ke, Cruz, Hancock, and Southworth (2002) developed models for multitiered supply chains. All the above research has been centered on a single country. In this thesis, I captured such decisionmaking but in a multiple country, multiple currency context with enhanced risk management.

Sustainable development problems are a genre of multi-objective ill-defined problems. The scarcity of resources in developing countries adds to the convolution of these problems, which is rooted within many disciplines. Focusing on the energy sector development and its sustainability, the main contribution of this research is of two folds: (i) The use of conventional energy sources has many negative implications on the economies of developing countries. A review of the global efforts to enhance economic growth through the deployment of renewable energy technologies is presented. Noting the failure of these efforts to accomplish their objective in due time, the appropriate strategic management tools were identified and integrated in the problem solving process to aid steer the decision process towards more effectual solutions. (ii) On the micro level, energy development projects are capital-intensive and hence prohibitive for most of the developing countries. The essence of a successful strategy is then to find the dynamic strategic fit (DSF) between these systems' external factors (opportunities and challenges) and their internal factors (resources and capabilities). We present an algorithm that utilizes the DSF concept to improve on sub-optimal solutions represented by economically feasible developmental projects. We present two real-world applications that illustrate the algorithm's ability to reduce the behavioral makeup of decision-makers and politics effects, which are discerned with MADM models.

In this dissertation, we discuss various general financial equilibrium problems, for which we present formulations and computational methods. In particular, we introduce financial equilibrium models with quadratic utility functions and general utility functions, with policy interventions in the form of taxes and price controls, and also with transaction costs. Equilibrium conditions are derived for each model, and qualitative analysis of each model, as well as the computational procedures and the convergence results, are studied using the theory of variational inequalities. A variety of numerical results to illustrate the performance of the algorithms is also provided. This dissertation relaxes several conventional assumptions used in deriving the capital asset pricing model. For example, it relaxes the assumption of homogeneous expectations, the assumption of the existence of a riskfree asset, and the assumption of perfect markets which assumes that there are no transaction costs and taxes, etc. We consider an economy in which there are multiple sectors, each of which can hold the multiple financial instruments as assets and/or liabilities. Each sector has his own utility function and his own beliefs about the future. The framework in this dissertation is one of competitive financial equilibrium, in which portfolio optimization is the behavioral assumption underlying each sector in the economy. The instrument prices serve as the market signals reflecting the economic market condition. The solution of the models yields the equilibrium instrument asset and liability volumes, as well as the equilibrium prices. Such problems are inherently complex and large-scale and, hence, present challenges from both modeling and mathematical programming perspectives. The framework which we introduce here is theoretical, although the foundations are empirical and based on the flow of funds accounts that provide a financial snapshot of an economy, and, in the case of the United States, are maintained by the Federal Reserve Board. In this dissertation, hence, we also balance the flow of funds data from the Federal Reserve Board for 1982 to 1991 and create the base-line for the general equilibrium models. We conclude this dissertation with possible extensions of the framework developed here and provide suggestions for future research.

This thesis contains three works in both continuous-time and distributionally robust mean-variance Markowitz models. In the first work, we study naive strategies in the continuous-time mean-variance model. We propose a new type of agent to approximate the dynamic of the naive agent by partitioning the time line into numerous small equal length time intervals. Then, we prove that, the wealth process of the proposed agent converges to that of the naive agent and derive the explicit formula for the limiting wealth process and its corresponding portfolio process. In the end, we compare the naive strategies with two equilibrium strategies in the Black-Scholes market. The second work contributes to the mean-variance model by considering its distributionally robust counterpart, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem to an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive backtesting results on the S&P 500 that compares the performance of our model with those of several well-known models, including the Fama--French model and the Black--Litterman model. In the last part, we develop a distributionally robust model based on the Sharpe ratio optimization problem. We transform the problem into an equivalent convex optimization problem that can be solved numerically. In this model, we do not need to choose the target return parameter, which has to be decided by subjective judgement in previous distributionally robust mean-variance models. As a result, the distributionally robust Sharpe ratio model is completely data-driven. We also provide guidance on the choice of ambiguity set size by using a much simpler scheme than that employed in the second work. In the end, we compare the performance of this model to that of the second work and some other well-known models on S&P500.

Bibliography: pages 311-318. / In this study the distributional properties of certain multivariate complex quadratic forms and their characteristic roots are investigated. Multivariate complex distribution theory was originally introduced by Wooding (1956), Turin (1960) and Goodman (1963a) when they derived and studied the multivariate complex normal distribution. The multivariate complex normal distribution is the basis of complex distribution theory and plays an important role in various areas. In the area of multiple time-series the complex distribution theory is found very useful.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering; and, (S.M.)--Massachusetts Institute of Technology, Operations Research Center, 1997. / Includes bibliographical references (leaves 56-57). / by Te-San Liao. / S.M.

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This dissertation addresses the crucial problem of how environmental policy uncertainty influences investments in energy technological change. The rising level of carbon emissions due to increasing global energy consumption calls for policy shift. In order to stem the negative consequences on the climate, policymakers are concerned with carving an optimal regulation that will encourage technology investments. However, decision makers are facing uncertainties surrounding future environmental policy. The first part considers the treatment of technological change in theoretical models. This part has two purposes: (1) to show–through illustrative examples–that technological change can lead to quite different, and surprising, impacts on the marginal costs of pollution abatement. We demonstrate an intriguing and uncommon result that technological change can increase the marginal costs of pollution abatement over some range of abatement; (2) to show the impact, on policy, of this uncommon observation. We find that under the assumption of technical change that can increase the marginal cost of pollution abatement over some range, the ranking of policy instruments is affected. The second part builds on the first by considering the impact of uncertainty in the carbon tax on investments in a portfolio of technologies. We determine the response of energy R&D investments as the carbon tax increases both in terms of overall and technology-specific investments. We determine the impact of risk in the carbon tax on the portfolio. We find that the response of the optimal investment in a portfolio of technologies to an increasing carbon tax depends on the relative costs of the programs and the elasticity of substitution between fossil and non-fossil energy inputs. In the third part, we zoom-in on the portfolio model above to consider how uncertainty in the magnitude and timing of a carbon tax influences investments. Under a two-stage continuous-time optimal control model, we consider the impact of these uncertainties on R&D spending that aims to lower the cost of non-fossil energy technology. We find that our results tally with the classical results because it discourages near-term investment. However, timing uncertainty increases near-term investment.