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,...