In this dissertation, we aim to develop a theoretical understanding of foundation models and reinforcement learning. We delve into a comprehensive analysis of specific aspects within these domains. The focal points of our study are as follows: • Generative Adversarial Imitation Learning (GAIL) with Neural Networks: GAIL is poised to...
Derivative-free optimization (DFO) has received growing attention due to important problems arising in practice. Various research communities, ranging from machine learning to engineering design, have adopted distinct DFO methods. In this thesis, we present extensive studies as a meaningful step towards a comprehensive understanding of DFO methods. We study the...
Submodularity is a well-known concept in integer programming and combinatorial optimization. Submodular set functions capture the diminishing returns phenomenon, which has wide-ranging applications in various domains. Typically, a submodular set function models the utility of homogenous items selected from a single ground set. Selecting an item or not is naturally...
This dissertation presents novel advancements in the field of continuous nonlinear optimization, focusing on the development of efficient second-order methods for second-order conic programs (SOCPs) and continuous nonlinear two-stage optimization problems. The primary focus is on the theory and computations of Sequential Quadratic Programming (SQP) methods, which are widely used...
Volunteers play an essential role in humanitarian and non-profit organizations that strive to improve society. 30% of the population in the United States volunteered in 2019, and this percentage has been stable for the past two decades. This dissertation is motivated by the scheduling decision process in nonprofit organizations. These...
This dissertation studies the integration of analytical modeling and optimization, machine learning, and Bayesian learning to optimize cost, access, and quality of healthcare delivery. Chapter 1 models computer-aided triage (patient prioritization) as feature-based priority queuing where types (diseases) are not perfectly observed but are inferred from observed features using a...
For stochastic simulation optimization in a modern computing era, we introduce a new parallel framework for solving very large-scale problems using a ranking & selection (R&S) approach that simulates all systems or feasible solutions to provide a global statistical guarantee. We propose a parallel adaptive survivor selection (PASS) framework that...
This dissertation contains three essays that study the operational challenges in healthcare-related fields. We strive to integrate analytical modeling and empirical methods to study decision-making under uncertainty for practice- and data-driven problems. We use large-scale datasets (millions) gathered from years of data collection. To gain access to these proprietary data,...
Market growth is an important goal for consumer businesses, often leading to lower marginal cost, higher operational efficiency, and larger assortment size - all of which help achieve dominance over competition. Yet, retailers and manufacturers alike should carefully manage their supply chains to sustain growth in customer base and extract...
Travel time is a key aspect of capturing and evaluating the operational performance and service quality of transportation systems, and travel time improvement is a common objective for travelers, service providers, transportation practitioners and agencies. However, the reliability of travel times, including the probability of unexpected delays, is an important...
Recently, machine learning and deep learning, which have made many theoretical and empir- ical breakthroughs and is widely applied in various fields, attract a great number of researchers and practitioners. They have become one of the most popular research directions and plays a sig- nificant role in many fields, such...
Existing nonlinear optimization methods have proven reliable over the past few decades for a wide range of applications but have critically relied on accurate function and gradient evaluations. Modern nonlinear optimization problems arising from machine learning and scientific computing applications are increasingly complex and large scale, which make accurate evaluations...
In this dissertation we consider how simple operational levers affect a firm's revenue and consumer surplus. In particular, we focus on information disclosure as an useful control for omnichannel services.In the first chapter we consider a revenue-maximizing service firm that caters to price and delay-sensitive customers. The firm offers a...
This dissertation focuses on applications of statistical methods in nancial markets and isdivided into three parts. The rst part proposes an accurate variable-order cumulant approximation
method for Black-style shadow interest rate models respecting the zero lower
bound and estimates the interest rates models on historical bond yield data using the...
This dissertation is motivated by the decision process of the supply chain team of a major furniture retailer that delivers its products at the customer's home. In retail supply chains for companies offering home delivery services, demand surges are observed at the store level, which translate to a high volume...
The overall theme in this thesis is about eliciting and leveraging information to improve algorithms in Operations Management, with an emphasis on tractable and integrated approach of estimation and optimization. The main tool that I will be using is Robust Optimization, and the applications in my work vary from online...
This dissertation investigates a number of models and algorithms in the context of optimization under uncertainty. The focus is on risk-averse optimization, where risk aversion is modeled via stochastic dominance, utility theory, and distributionally robust optimization. We first investigate an investment model with fixed contribution rates, optimize asset-allocation decisions in...
We consider the statistical study of partially observed queueing systems arising in application areas such as hospital networks, data centers and cloud computing systems. Since these services operate under strict performance requirements, a statistical understanding of their performance is of great practical interest. A key challenge in these settings is...
This dissertation contains three essays that study the operational challenges and business innovations in service industries. We investigate how service providers could use wisely designed business models and service systems to induce preferable customer behaviors, and therefore manage demand and optimize revenue. Using a stylized model, we study how customers...
Multistage optimization is a prominent modeling tool to solve a broad range of dynamic decision-making problems in the presence of uncertainty. However, computing optimal policies is intractable, since they are obtained by considering all possible realizations of uncertainties and subsequent future decisions over time. To overcome these challenges, we present...
Simulation studies are virtually all motivated by decision making. Because simulation output is stochastic and input models are never perfect, all decisions should include an accounting for risks. Input model risk refers to the exposure due to imperfect simulation input models that are estimated from real-world data, involving both the...
The thesis is concerned with the design and control of large-scaled queueing systems that are operated under heavy traffic, focusing on the following two research questions: For a given queueing system, how to find a proper heavy-traffic limit that accurately approximates various performance metrics? For multi-class queueing systems, how to...
Optimization via simulation (OvS) is the practice of minimizing or maximizing the expected value of the output of a stochastic simulation model with respect to controllable decision variables. Stochastic simulation is a standard tool within operations research and is often required to model complex systems subject to uncertainty where it...
While optimization has received much attention in the machine learning community, most of them consider unconstrained supervised learning models such as neural networks and support vector machine. In this dissertation, we introduce a new class of optimization problems called scale invariant problems that include interesting unsupervised learning models such as...
Across the United States, public school districts are facing critical budget crises. To keep cuts away from the classroom, bus transportation is a common area to look for cost reductions. This thesis studies two fundamental problems that arise in public school transportation: the bus route design problem and the school...
In this dissertation, we study models and methods to address uncertainties that can vary in optimization problems. Robust optimization is a popular approach for optimization under uncertainty, especially if limited information is available about the distribution of the uncertainty. It models the uncertainty through sets and finds a robust optimal...
Demand Response (DR) is an approach that allows electricity users to actively participate in keeping supply-demand balance in power systems, or its future version, smart grid, in order to increase the system efficiency, lower consumers' electricity bills, and thus improve social welfare. To encourage users' participation in DR, a time-varying...
The dissertation consists of three self-contained papers. In Chapter 1, we study the inventory management problem in a dual sourcing system, where there are two supply sources or modes with different sourcing costs and lead times. We provide closed-form solutions to a robust optimization model for inventory management in a...
The goal of this thesis is to design practical algorithms for nonlinear optimization in the case where the objective function is deterministic or stochastic. Problems of this nature arise in many applications including machine learning and image processing. The thesis is divided into four main chapters. Chapters \ref{chap:Inexact}, \ref{chap:Adasample} and...
Cancer radiation therapy relies on optimized treatment plans whose quality assessment is judged by dosimetric planning aims. It is computationally prohibitive to incorporate the planning aims into the optimization models. Therefore, there exists a disconnect between the two steps of (1) optimizing a plan and (2) evaluating the optimized plan,...
Owing to policy action as well as continued cost declines, solar and wind resources are projected to play a central role in many future electricity systems. Since the technological characteristics and cost structures of these resources differ significantly from traditional thermal technologies, many have questioned how market designs will need...
The vast majority of interactions between customers and service providers are experiences that extend over time. Service systems that deliver excellent customer experience achieve greater customer satisfaction and therefore customer loyalty, and eventually raise revenue. The temporal aspects of service delivery have not yet been analyzed as carefully as its...
Two recent developments in the transportation industry – shared-use mobility services and fully-autonomous vehicles (AVs) – have the potential to fundamentally transform urban mobility. Shared-use mobility services (e.g. Uber, Lyft, Via, Chariot, ZipCar, and Car2go) are already beginning to bridge the gap between personal vehicles and fixed-route transit service in...
This dissertation studies topics in health care operations management related to value-based care, where {\em value} can be thought of as the ratio of quality to cost. The objective in value-based care is to increase, or maximize, value by reducing costs and improving quality health outcomes. In Chapter 1 we...
This thesis consists of three projects, centered around the aim to better model real-world systems under uncertainty, specifically, under stochastic disruptions, using optimization. A stochastic disruption is a type of infrequent event in which the timing and the magnitude are random. We introduce the concept of stochastic disruptions and a...