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...
Ross (2015) proposed a recovery theorem which uses prices of contingent claims to recover market’s expectations about underlying asset returns. His work relies on two assumptions. He assumes all uncertainty of the economy follows a finite state irreducible Markov chain and that the pricing kernel is transition independent. We first...
Simulation analytics treats stochastic simulation as data analytics for systems that do not yet exist, and extends traditional performance estimation and system optimization to uncovering underlying patterns and the key drivers and dynamics of system behavior by retaining the sample paths generated throughout simulation runs. My dissertation addresses two research...
It is well documented that an individual’s ability to know who knows whom in their network has positive benefits in various facets of professional life. But people vary in their network acuity - that is, their ability to accurately assess who knows whom in their network. This poster seeks to...
Traditionally, simulation analysis has focused on designing a computationally efficient algorithm assuming a correct simulation model is given. As computation becomes cheaper, we are now able to perform more sophisticated simulation analyses involving extensive computation and consider all sources of errors in the simulation model and their effects to the...
As the title suggests, this dissertation is composed of three major topics. The first two are optimization problems focusing on developing effective solution methodologies, while for the last topic we present a large-scale information retrieval system in the domain of sports. With the algorithms and frameworks developed in this dissertation,...
We introduce and advocate a new paradigm in simulation experiment design and analysis, called ``green simulation,'' for the setting in which experiments are performed repeatedly with the same simulation model but different input parameters. In this dissertation three classes of green simulation estimators are proposed: the likelihood-ratio-based estimators, the metamodeling-based...