Cluster Analysis deals with classifying a sample of multivariate measurements into different categories. In this dissertation we study the effect of the correlation structure of the data on the performance of a clustering method. We begin with the analysis of two-component normal mixture models and then proceed to cluster analysis...
In this thesis, we study routing and resource allocation problems which have probabilistic objective functions. This class of problems has received limited attention in literature despite its promising applications. A probabilistic objective function is capable of incorporating business targets into the problem modeling and representing the risk attitude of a...
Portfolio optimization problems with transaction costs have been widely studied by both financial economists and financial engineers through various approaches. In this paper, we propose the following approach. In analogy to American option pricing, we study the problem through the Finite Element Method (FEM) combined with an optimization method: We...
The classic error bounds for quasi-Monte Carlo approximation follow the Koksma-Hlawka inequality based on the assumption that the integrand has finite variation. Unfortunately, not all functions have this property. In particular, integrands for common applications in finance, such as option pricing, do not typically have bounded variation. In contrast to...
This thesis concerns the development of robust algorithms for large-scale nonlinear programming. Despite recent advancements in high-performance computing power, classes of problems exist that continue to challenge the practical limits of contemporary optimization methods. The focus of this dissertation is the design and analysis of algorithms intended to achieve economy...
This dissertation examines the impact of product returns on effective supply chain management. Within this area of research, known as Closed-Loop Supply Chain Management, we consider both strategic and tactical level reverse logistics and inventory management problems from the perspective of a firm which must efficiently process returned items. More...
At the heart of nonlinear optimization methods lies the solution of linear systems of equations. As the size of the problem increases, it is imperative to use iterative methods, such as the conjugate gradient algorithm, to solve these linear systems. In the context of constrained optimization, it has proved to...
Flexibility can be created in manufacturing and service operations by using multipurpose production sources such as cross-trained labor and flexible machines/factories. We focus on control and design issues in systems with flexible resources. In Chapter 2, we consider optimal scheduling of a fully cross-trained server in a finite-population queueing system...
In financial risk management, coherent risk measures have been proposed as a way to avoid undesirable properties of measures such as value at risk that discourage diversification and do not account for the magnitude of the largest, and therefore most serious, losses. A coherent risk measure equals the maximum expected...
The goal of this thesis is to design practical algorithms for nonlinear optimization in the case when the objective function is stochastic or nonsmooth. The thesis is divided into three chapters. Chapter 1 describes an active-set method for the minimization of an objective function that is structurally nonsmooth, viz., it...