## Program in Engineering and Management Systems

#### Director

Warren B. Powell

#### Executive Committee

Elad Hazan, Computer Science

Ning Lin, Civil and Environmental Engineering

Alain L. Kornhauser, Operations Research and Financial Engineering

Warren B. Powell, Operations Research and Financial Engineering

Daniel A Steingart, Mechanical and Aerospace Engineering

Robert F. Stengel, Mechanical and Aerospace Engineering

The certificate Program in Engineering and Management Systems (EMS) provides students with tools for the complex decision-making problems that arise in engineering, the sciences, and management. It is aimed at three types of students:

1. Engineering students interested in preparing for careers in management or consulting

2. Students in the liberal arts looking to acquire the analytic tools typically used for careers in corporate or government settings

3. Students in the sciences interested in a stronger exposure to analytic methods and, potentially, careers in management or public policy

The program offers a coherent, integrated set of core courses that are based on analytic methods, with applications in the planning and control of complex systems required by a modern technological society. Emphasis is placed on rigorous modeling and analysis, taking advantage of the vast flow of data and ubiquitous computing power available today.

The EMS certificate program complements the certificate programs in applications of computing, applied and computational mathematics, and finance.

#### Admission to the Program

The EMS 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.

To be admitted, interested students should e-mail Professor Warren Powell. The e-mail 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. In some cases, a course can fulfill both a certificate program requirement, with the exception that ORFE concentrators may not double count the course that integrates optimization and uncertainty. The EMS certificate program does not have a GPA requirement, so courses *may *be taken pass/fail, limited only by university regulations on pass/fail courses. The program requirements are as follows:

**Course requirements. **All students must take courses from the following five areas:

1. An introductory statistics course:

- ECO 202 Statistics and Data Analysis for Economics

- ORF 245 Fundamentals of Engineering Statistics

- PHY 301 Thermal Physics and PHY 312 Experimental Physics (both courses must be taken)

- PSY 251 Quantitative Methods

- SOC 301 Sociological Research Methods

- WWS 200 Statistics for Social Sciences

This requirement may be satisfied with a score of 5 on the AP statistics exam or by taking a higher-level statistics course such as ORF 350 or 405, or ECO 302/312.

2. An introductory optimization course:

- CBE 442 Design, Synthesis, and Optimization of Chemical Processes

- ELE 382 Distributed Algorithms and Optimization Methods for Engineering Applications

- MAE 433 Automatic Control Systems

- ORF 307 Optimization

3. Probability:

- ORF 309 Probability and Stochastic Systems

4. A course integrating optimization and uncertainty:

- COS 402 Artificial Intelligence

- ECO 418 Strategy and Information

- ECO 462 Portfolio Theory and Asset Management

- ECO 465 Options, Futures and financial Derivatives

- MAE 345 Robotics and Intelligent Systems

- ORF 311 Optimization under Uncertainty

- ORF 418 Optimal Learning

**Note: ORFE concentrators (beginning with the Class of 2018 and later) may not count the course used in this category as a departmental elective.**

5. An integrative course in management, entrepreneurship, or systems:

- CBE 442 Design, Synthesis and Optimization of Chemical Processes

- EGR/ELE 491 High-Tech Entrepreneurship

- EGR 497 Entrepreneurial Leadership

- ORF 411 Operations and Information Engineering

The program is willing to add courses which satisfy the goal of each area. Students wishing to propose a course should send the syllabus to Professor Powell, 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 statistics, probability 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 EMS certificate program, including statistic, probability 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 the Chinese economy, and hard-science theses (laboratory-based theses) that do not have a significant data-analysis component (for example, collecting observations and taking averages is not sufficient).

#### Certificate of Proficiency

Students who fulfill the requirements of the program receive a certificate of proficiency in engineering and management systems upon graduation.

### Courses

ORF 105 The Science and Technology of Decision Making (also EGR 106) Not offered this year QR

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.
* Staff*

ORF 245 Fundamentals of Statistics (also EGR 245) Fall, Spring QR

A first introduction to probability and statistics. This course will provide the foundations of 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 real-world data sets. Prerequisite MAT 201 Equivalent or concurrent. Three lectures, one preceptorial.
*
R. Vanderbei**,
S. Kpotufe*

ORF 307 Optimization (also EGR 307) Spring

Many real-world problems involve maximizing a linear function subject to linear inequality constraints. Such problems are called Linear Programming (LP) problems. Examples include min-cost network flows, portfolio optimization, options pricing, assignment problems and two-person zero-sum games to name but a few. The theory of linear programming will be developed with a special emphasis on duality theory, which is used to derive algorithms for solving LP problems. These algorithms will be illustrated on real-world examples such as those mentioned. Two 90 minute lectures, one preceptorial. Prerequisite MAT 202.
*
R. Vanderbei*

ORF 309 Probability and Stochastic Systems (also EGR 309/MAT 380) Fall

An introduction to probability and its applications. Random variables, expectation, and independence. Poisson processes, Markov chains, Markov processes, and Brownian motion. Stochastic models of queues, communication systems, random signals, and reliability. Prerequisite: MAT 201, 203, 217, or instructor's permission.
*
R. van Handel*

ORF 311 Optimization Under Uncertainty Not offered this year

A survey of quantitative approaches for making optimal decisions involving uncertainty and complexity including decision trees, Monte Carlo simulation, and stochastic programming. Forecasting and planning systems are integrated with a focus on financial applications. Prerequisites: ORF 307 or MAT 305, and 309. Two 90-minute classes, one preceptorial.
*
J. Mulvey*

ORF 322 Human-Machine Interaction (see PSY 322)

ORF 335 Introduction to Financial Mathematics (also ECO 364) Spring QR

This course introduces the basics of quantitative finance, particularly the use of stochastic models to value and hedge risks from options, futures and other derivative securities. The models studied include binomial trees in discrete time, and the Black-Scholes theory is introduced in continuous-time models. Computational methods are introduced in Matlab. The second half of the class looks at modern topics such as credit risk, stochastic volatility, portfolio optimization, as well as lessons from the financial crisis. Prerequisites: ORF 309, ECO 100, and MAT 104. R. Sircar
*
R. Sircar*

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.
*
J. Mulvey*

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.
*
A. Kornhauser*

ORF 376 Independent Research Project Spring

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.
*
A. Kornhauser*

ORF 401 Electronic Commerce Spring

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.
*
A. Kornhauser*

ORF 405 Regression and Applied Time Series Fall

Statistical Analysis of financial data: Density estimation, heavy tail distributions and dependence. Regression: linear, nonlinear, nonparametric. Time series analysis: classical models (AR, MA, ARMA), state space systems and filtering, and stochastic volatility models (ARCH, GARCH). Prerequsites: ORF 245 and MAT 202.
*
R. Carmona*

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.
* Staff*

ORF 407 Fundamentals of Queueing Theory Spring QR

An introduction to the fundamental results of queuing theory. Topics covered include: the classical traffic, offered load, loss, and delay models for communication systems. The theory of Markov chains, Poisson processes, and renewal theory are discussed through concrete examples and motivations. Fundamental queuing results such as the Erlang blocking and delay formulae, Jackson networks, Little's law and Lindley's equation are presented. Applications are drawn from classical problems in voice and data network performance, to modern issues in healthcare operations. Prerequisite: ORF 309 or equivalent. Two 90-minute lectures.
*
W. Massey*

ORF 409 Introduction to Monte Carlo Simulation Fall

Introduction to the uses of simulation and computation in the analysis of stochastic models and interpreting real phenomena. Topics include generating discrete and continuous random variables, the statistical analysis of simulated data, variance reduction techniques, statistical validation techniques, stochastic ordering, nonstationary Markov chains, and Markov chain Monte Carlo methods. Applications are drawn from problems in finance, insurance, manufacturing, and communication networks. Students will be encouraged to program in Python. Precept offered to help students with the language. Prerequisite: ORF 309. Two 90-minute lectures.
*
W. Massey*

ORF 411 Operations and Information Engineering Fall

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.
*
W. Powell*

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.
* Staff*

ORF 418 Optimal Learning Spring QR

Addresses the problem of collecting information used to estimate statistics or fit a model which is then used to make decisions. Of particular interest are sequential problems where decisions adapt to information as it is learned. The course introduces students to a wide range of applications, demonstrates how to express the problem formally, and describes a variety of practical solution strategies. Prerequisite: ORF 245, ORF 309. Two 90-minute lectures, one preceptorial.
*
W. Powell*

ORF 435 Financial Risk Management Fall

This course covers the basic concepts of modeling, measuring and managing different types of financial risks. Topics include portfolio optimization (mean-variance approach and expected utility), interest rate risk, pricing and hedging in complete and incomplete markets, indifference pricing, risk measures, systemic risk. Prerequisites: ORF 245, ORF 335 or ECO 465 (concurrent enrollment is acceptable) or instructor's permission. Two 90-minute lectures, one preceptorial.
*
P. Cheridito*

ORF 455 Energy and Commodities Markets

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 application of Financial Mathematics to a variety of different products and markets. Topics include: energy prices (including oil and electricity); cap and trade markets; storable vs non-storable commodities; financialization of commodities markets; applications of game theory.
*
R. Sircar*

ORF 467 Transportation Systems Analysis Fall

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.
*
A. Kornhauser*

ORF 473 Special Topics in Operations Research and Financial Engineering Not offered this year

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

ORF 474 Special Topics in Operations Research and Financial Engineering Not offered this year

A course covering one or more advanced topics in operations research and financial engineering. Subjects may vary from year to year.
* 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.
*
A. Kornhauser*

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.
*
A. Kornhauser*