Program in Optimization and Quantitative Decision Science

Faculty

Director

Amir Ali Ahmadi

Executive Committee

Matias D. Cattaneo, Oper Res and Financial Eng
Elad Hazan, Computer Science
Alain L. Kornhauser, Oper Res and Financial Eng
Miklos Z. Racz, Oper Res and Financial Eng
Peter J. Ramadge, Electrical & Comp Engineering
Clarence W. Rowley, Mechanical & Aerospace Eng
Robert J. Vanderbei, Oper Res and Financial Eng

For a full list of faculty members and fellows please visit the department or program website.

Program Information

The certificate Program in Optimization and Quantitative Decision Science and Optimization (OQDS), formerly the certificate Program in Engineering and Management Systems, is focused on developing quantitative skills for optimal decision-making in complex and uncertain environments. These skills are increasingly relevant to problems and decisions that face the leaders, managers, engineers, and scientists of our generation. Through this certificate program, students will learn to quantify risk and uncertainty, and to view any complex decision through the lens of mathematical optimization. This outlook will give them a more structured understanding of the decision itself, as they learn to rigorously formulate their constraints, objective function(s), and the uncertainties involved. It will also lead them to the proper algorithmic tools that are needed to arrive at an optimal decision.

The certificate program can be of interest to students in engineering, the sciences, and the liberal arts who are interested in analytical thinking and quantitative reasoning for the purpose of decision-making under uncertainty. Emphasis is placed on rigorous modeling and analysis, taking advantage of the vast flow of data and ubiquitous computing power available today.

The OQDS certificate program complements the certificate programs in applications of computing, statistics and machine learning, applied and computational mathematics, and finance.

Admission to the Program

The OQDS certificate program is open to both B.S.E. and A.B. students. B.S.E. students are required to take math through Math 201 and 202, which will satisfy the math prerequisites of any of the core courses. However, there is flexibility in the choice of core courses, and the math prerequisites depend on the electives that a student chooses. For A.B. students, it is their responsibility to take the necessary prerequisites for their program of study; students are encouraged to take Math 202 (and preferably Math 201) prior to the certificate program's core course requirements.

To be admitted, interested students should email Professor Amirali Ahmadi. The email should state the student's request to participate in the program, and should include the following information: the student's class year, area of concentration, and whether the student has placed out of any course requirements.

Program of Study

The program for each student is worked out by the student and the departmental adviser. The OQDS certificate program does not have a GPA requirement and students may elect to take one requirement on a pass/fail grading basis. Certificate program students may double-count no more than two courses for both their concentration and the certificate. The program requirements are as follows:

Course Requirements

All students must take five courses from the following three areas:

One core course in optimization
One core course in uncertainty analysis
Three elective courses on applications to quantitative decision-making

1. One core course in optimization*

ORF 307 Optimization
ORF 311 Stochastic Optimization and Machine Learning in Finance
ORF363/COS 323 Computing and Optimization for the Physical and Social Sciences

In special circumstances, the director of the program may approve alternative graduate courses for qualified students. Examples include ORF 522 (Linear and Nonlinear Optimization), ORF 523 (Convex and Conic Optimization), and ECE 522 (Large-Scale Optimization for Data Science).

2. One core course in uncertainty analysis*

ORF 309 Probability and Stochastic Systems
MAT 385 Probability Theory
MAT 486 Random Processes
ORF 409 Introduction to Monte Carlo Simulation
GEO 422 Data, Models and Uncertainty in the Natural Sciences
ECE 382 Probabilistic Systems and Information Processing
PHI 371 Philosophical Foundations of Probability and Decision Theory
CEE 460 Risk Assessment and Management
ORF 245 Fundamentals of Statistics
ECO 202 Statistics and Data Analysis for Economics
POL 345/SOC 305 Introduction to Quantitative Social Science
PSY 251 Quantitative Methods
SOC 301 Statistical Methods in Sociology
WWS 200 Statistics for Social Science

In special circumstances, the director of the program may approve alternative graduate courses for qualified students. An example is ORF 526 (Probability Theory).

3. Three elective courses on applications to quantitative decision-making

MAE 410/ENE 410/CBE 410 Optimization for the Design and Analysis of Energy Systems
ECE 435 Machine Learning and Pattern Recognition
ECE 364 Machine Learning for Predictive Data Analytics
PSY 255/CGS 255 Cognitive Psychology
SPI 340/PSY 321 The Psychology of Decision Making and Judgment
ARC 311 Building Science and Technology: Building Systems
ARC 404 Advanced Design Studio
MUS 314 Computer and Electronic Music through Programming, Performance, and Composition
MUS 316 Computer and Electronic Music Composition
CBE 442 Design, Synthesis and Optimization of Chemical Processes
MAE 345 Introduction to Robotics
MAE 331 Aircraft Flight Dynamics
MAE 433 Automatic Control Systems
MAE 434 Modern Control
ORF 405 Regression and Applied Time Series
ORF 435 Financial Risk Management
ORF 467 Transportation Systems Analysis
ORF 401 Electronic Commerce
ORF 350 Analysis of Big Data
ORF 387 Networks
ORF 407 Fundamentals of Queueing Theory
ORF 542 Stochastic Optimal Control
MAT 490 Mathematical Introduction to Machine Learning
MAT 378 Theory of Games
POL 250 Introduction to Game Theory
POL 341 Experimental Methods in Politics
POL 346 Applied Quantitative Analysis
POL 347/ECO 347 Mathematical Models in the Study of Politics
POL 352 Comparative Political Economy
COS 324 Introduction to Machine Learning
COS 402 Machine Learning and Artificial Intelligence
COS 598D Optimization for Machine Learning
ECO 418 Strategy and Information
ECO 462 Portfolio Theory and Asset Management
ECO 465 Options, Futures and Financial Derivatives
EGR 395 Venture Capital & Finance of Innovation
EGR 494 Leadership Development for Business
EGR 497 Entrepreneurial Leadership
EGR/ECE 491 High-Tech Entrepreneurship

*Students may choose to take more than one course from category (1) or (2) and count the additional course(s) toward category (3) as long as at least one course from category (3) is taken.

In special circumstances, the director of the program may approve alternative graduate courses for qualified students. Examples include ECE 524 (Foundations of Reinforcement Learning), ORF/APC 550 (Probability in High Dimension).

The program is willing to occasionally add courses that clearly satisfy the objective(s) of each area. Students wishing to propose a course should send the syllabus to Professor Ahmadi, with an explanation of which area the course satisfies, and why.

Independent Work

A senior thesis or project must be completed and submitted to the program director that demonstrates a command of some portion of the core disciplines of uncertainty analysis and/or optimization. Students in engineering departments that require a one-semester project can typically use a suitably designed project to satisfy the requirement.

Acceptable theses can be on a wide range of topics, but they must demonstrate a command of the core disciplines of the OQDS certificate program, including stochastics and/or optimization. The thesis must demonstrate, in appropriate mathematics, the ability to model a problem and perform analysis that leads to some conclusion or scientific result. A thesis with minimal or no mathematical modeling is not acceptable.

Theses that are not allowed include "soft" topics such as the history of a nation’s economy, and hard-science theses (laboratory-based theses) that do not have a significant modeling or data-analysis component (for example, collecting observations and computing basic statistics is not sufficient).

Certificate of Proficiency

Students who fulfill the requirements of the program receive a certificate of proficiency in Decision Science and Optimization upon graduation.

Courses

ORF 105 The Science and Technology of Decision Making (also

EGR 106

) Not offered this year QCR

An individual makes decisions every day. In addition, other people are making decisions that have an impact on the individual. In this course we will consider both how these decisions are made and how they should be made. In particular, we will focus on the use of advanced computing and information technology in the decision-making process. Instructed by: Staff

ORF 245 Fundamentals of Statistics (also

EGR 245

) Fall/Spring QCR

A first introduction to probability and statistics. This course will provide background to understand and produce rigorous statistical analysis including estimation, confidence intervals, hypothesis testing and regression and classification. Applicability and limitations of these methods will be illustrated using a variety of modern real world data sets and manipulation of the statistical software R. Prerequisite MAT 201 equivalent or concurrent. Two 90 minute lectures, one preceptorial. Instructed by: Staff

ORF 307 Optimization (also

EGR 307

) Spring

This course focuses on analytical and computational tools for optimization. We will introduce least-squares optimization with multiple objectives and constraints. We will also discuss linear optimization modeling, duality, the simplex method, degeneracy, interior point methods and network flow optimization. Finally, we will cover integer programming and branch-and-bound algorithms. A broad spectrum of real-world applications in engineering, finance and statistics is presented. Two 90 minute lectures, one preceptorial. Prerequisite MAT 202 or 204. Instructed by: Staff

ORF 309 Probability and Stochastic Systems (also

EGR 309

/

MAT 380

) Fall/Spring

An introduction to probability and its applications. Topics include: basic principles of probability; Lifetimes and reliability, Poisson processes; random walks; Brownian motion; branching processes; Markov chains. Three lectures, one precept. Prerequisite: MAT 201 or instructor's permission. Instructed by: M. Shkolnikov, R. van Handel

ORF 311 Stochastic Optimization and Machine Learning in Finance Spring

A survey of quantitative approaches for making optimal decisions under uncertainty, including decision trees, Monte Carlo simulation, and stochastic programs. Forecasting and planning systems are integrated in the context of financial applications. Machine learning methods are linked to the stochastic optimization models.. Prerequisites: ORF 307 or MAT 305, and 309. Two 90-minute classes, one preceptorial. Instructed by: Staff

ORF 322 Human-Machine Interaction (See PSY 322)

ORF 335 Introduction to Financial Mathematics (also

ECO 364

) Spring QCR

Financial Mathematics is concerned with designing and analyzing products that improve the efficiency of markets, and create mechanisms for reducing risk. This course develops quantitative methods for these goals: the notions of arbitrage and risk-neutral pricing in discrete time, specific models such as Black-Scholes and Heston in continuous time, and calibration to market data. Credit derivatives, the term structure of interest rates, and robust techniques in the context of volatility options will be discussed, as well as lessons from the financial crisis. Prerequisites: ORF 309, ECO 100, and MAT 104. Instructed by: M. Soner

ORF 350 Analysis of Big Data Spring QCR

This course is a theoretically oriented introduction to the statistical tools that underpin modern machine learning, whose hallmarks are large datasets and/or complex models. Topics include a rigorous analysis of dimensionality reduction, a survey of models ranging from regression to neural networks, and an analysis of learning algorithms.. Prerequisite: Probability at the level of ORF 309. Statistics at the level of ORF 245. Linear Algebra at the level of MAT 202 or permission of instructor. Lecture and precept. Instructed by: B. Hanin

ORF 360 Decision Modeling in Business Analytics Not offered this year

This is an introductory course to decision methods and modeling in business and operations management. The course will emphasize both mathematical decision-making techniques, as well as popular data-based decision models arising from real applications. Upon completion of this course students will have learned analytical tools for modeling and optimizing business decisions. From a practical perspective, this will be a first course that gives an overview of advanced operations research topics including revenue management, supply chain management, network management, and pricing. Instructed by: Staff

ORF 363 Computing and Optimization for the Physical and Social Sciences (also

COS 323

) Fall/Spring QCR

An introduction to several fundamental and practically-relevant areas of modern optimization and numerical computing. Topics include computational linear algebra, first and second order descent methods, convex sets and functions, basics of linear and semidefinite programming, optimization for statistical regression and classification, and techniques for dealing with uncertainty and intractability in optimization problems. Extensive hands-on experience with high-level optimization software. Applications drawn from operations research, statistics and machine learning, economics, control theory, and engineering. Instructed by: Staff

ORF 374 Special Topics in Operations Research and Financial Engineering Not offered this year

A course covering special topics in operations research or financial engineering. Subjects may vary from year to year. Instructed by: Staff

ORF 375 Independent Research Project Fall

Independent research or investigation resulting in a substantial formal report in the student's area of interest under the supervision of a faculty member. Open to sophomores and juniors. Instructed by: R. Vanderbei

ORF 376 Independent Research Project Spring

ORF 387 Networks Spring

This course showcases how networks are widespread in society, technology, and nature, via a mix of theory and applications. It demonstrates the importance of understanding network effects when making decisions in an increasingly connected world. Topics include an introduction to graph theory, game theory, social networks, information networks, strategic interactions on networks, network models, network dynamics, information diffusion, and more. Instructed by: M. Racz

ORF 401 Electronic Commerce Not offered this year

Electronic commerce, traditionally the buying and selling of goods using electronic technologies, extends to essentially all facets of human interaction when extended to services, particularly information. The course focuses on both the software and the hardware aspects of traditional aspects as well as the broader aspects of the creation, dissemination and human consumption electronic services. Covered will be the physical, financial and social aspects of these technologies. Two 90-minute lectures, one 50-minute preceptorial. Instructed by: A. Kornhauser

ORF 405 Regression and Applied Time Series Fall

An introduction to popular statistical approaches in regression and time series analysis. Topics will include theoretical aspects and practical considerations of linear, nonlinear, and nonparametric modeling (kernels, neural networks, and decision trees). Prerequsites: ORF 245 and ORF 309 or instructor's permission. Instructed by: J. Klusowski

ORF 406 Statistical Design of Experiments Not offered this year

Major methods of statistics as applied to the engineering and physical sciences. The central theme is the construction of empirical models, the design of experiments for elucidating models, and the applications of models for forecasting and decision making under uncertainty. Three lectures. Prerequisite: 245 or equivalent. Instructed by: Staff

ORF 407 Fundamentals of Queueing Theory Spring QCR

This is an introduction to the stochastic models inspired by the dynamics of resource sharing. Topics discussed include: early motivating communication systems (telephone and computer networks); modern applications (call centers, healthcare operations, and urban planning for smart cities); and key formulas (from Erlang blocking and delay to Little's law). We also review supporting stochastic theories like equilibrium Markov chains along with Markov, Poisson and renewal processes. Prerequisite: ORF 309 or equivalent. Instructed by: Staff

ORF 409 Introduction to Monte Carlo Simulation Fall

An introduction to the uses of simulation and computation for analyzing stochastic models and interpreting real phenomena. Topics covered include generating discrete and continuous random variables, stochastic ordering, the statistical analysis of simulated data, variance reduction techniques, statistical validation techniques, nonstationary Markov chains, and Markov chain Monte Carlo methods. Applications are drawn from problems in finance, manufacturing, and communication networks. Students will be encouraged to program in Python. Office hours will be offered for students unfamiliar with the language. Prerequisites: ORF 245 and ORF 309. Instructed by: W. Massey

ORF 411 Sequential Decision Analytics and Modeling (also

ECE 411

) Not offered this year

The management of complex systems through the control of physical, financial and informational resources. The course focuses on developing mathematical models for resource allocation, with an emphasis on capturing the role of information in decisions. The course seeks to integrate skills in statistics, stochastics and optimization using applications drawn from problems in dynamic resource management which tests modeling skills and teamwork. Prerequisites: ORF 245, ORF 307 and ORF 309, or equivalents. Two 90 minute lectures, preceptorial. Instructed by: Staff

ORF 417 Dynamic Programming Not offered this year

An introduction to stochastic dynamic programming and stochastic control. The course deals with discrete and continuous-state dynamic programs, finite and infinite horizons, stationary and nonstationary data. Applications drawn from inventory management, sequential games, stochastic shortest path, dynamic resource allocation problems. Solution algorithms include classical policy and value iteration for smaller problems and stochastic approximation methods for large-scale applications. Prerequisites: 307 and 309. Instructed by: Staff

ORF 418 Optimal Learning Fall QCR

This course develops several methods that are central to modern optimization and learning problems under uncertainty. These include dynamic programming, linear quadratic regulator, Kalman filter, multi-armed bandits and reinforcement learning. Representative applications and numerical methods are emphasized. Prerequisite: ORF 309. Two 90-minute lectures. Instructed by: E. Hubert

ORF 435 Financial Risk and Wealth Management Fall

This course covers the basic concepts of measuring, modeling and managing risks within a financial optimization framework. Topics include single and multi-stage financial planning systems. Implementation from several domains within asset management and goal based investing. Machine learning algorithms are introduced and linked to the stochastic planning models. Python and optimization exercises required. Prerequisites: ORF 245, ORF 309, ORF 335 or ECO 465 (concurrent enrollment is acceptable) or instructor's permission. Two 90-minute lectures, one preceptorial. Instructed by: J. Mulvey

ORF 445 High Frequency Markets: Models and Data Analysis Spring

An introduction to the theory and practice of high frequency trading in modern electronic financial markets. We give an overview of the institutional landscape and basic empirical features of modern equity, futures, and fixed income markets. We discuss theoretical models for market making and price formation. Then we dig into detailed empirical aspects of market microstructure and how these can be used to construct effective trading strategies. Course work will be a mixture of theoretical and data-driven problems. Programming environment will be a mixture of the R statistical environment, with the Kdb database language. Instructed by: R. Almgren

ORF 455 Energy and Commodities Markets (also

ENE 455

) Not offered this year

This course is an introduction to commodities markets (energy, metals, agricultural products) and issues related to renewable energy sources such as solar and wind power, and carbon emissions. Energy and other commodities represent an increasingly important asset class, in addition to significantly impacting the economy and policy decisions. Emphasis will be on the term structure of commodity prices: behavior, models and empirical issues. Prerequisite: ORF 335 or instructor permission. Two 90 minute lectures, one precept. Instructed by: R. Sircar

ORF 467 Transportation Systems Analysis Not offered this year

Studied is the transportation sector of the economy from a technology and policy planning perspective. The focus is on the methodologies and analytical tools that underpin policy formulation, capital and operations planning, and real-time operational decision making within the transportation industry. Case studies of innovative concepts such as dynamic "value pricing", real-time fleet management and control, GPS-based route guidance systems, automated transit networks and the emergence of Smart Driving / Autonomous Cars. Two 90-minute lectures, one preceptorial. Instructed by: A. Kornhauser

ORF 473 Special Topics in Operations Research and Financial Engineering Spring

A course covering one or more advanced topics in operations research and financial engineering. Subjects may vary from year to year. Instructed by: M. Holen

ORF 474 Special Topics in Operations Research and Financial Engineering

A course covering one or more advanced topics in operations research and financial engineering. Subjects may vary from year to year. Instructed by: Staff

ORF 478 Senior Thesis Spring

A formal report on research involving analysis, synthesis, and design, directed toward improved understanding and resolution of a significant problem. The research is conducted under the supervision of a faculty member, and the thesis is defended by the student at a public examination before a faculty committee. The senior thesis is equivalent to a year-long study and is recorded as a double course in the Spring. Instructed by: R. Vanderbei

ORF 479 Senior Project Spring

A one-semester project that fulfills the departmental independent work requirement for concentrators. Topics are chosen by students in consultation with members of the faculty. A written report is required at the end of the term. Instructed by: R. Vanderbei