## Program in Engineering and Management Systems

#### Director

Warren B. Powell

#### Executive Committee

Christodoulos A. Floudas, Chemical and Biological Engineering

Alain L. Kornhauser, Operations Research and Financial Engineering

Sanjeev Kulkarni, Electrical Engineering

Robert E. Schapire, Computer Science

James A. Smith, Civil and Environmental Engineering

Robert F. Stengel, Mechanical and Aerospace Engineering

The certificate Program in Engineering and Management Systems provides students with tools for the complex decision-making problems that arise in engineering 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 analytical tools typically used for careers in corporate or government settings.

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

It offers a coherent, integrated set of core courses that are based on analytical 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 both the Program in Finance certificate and the certificate Program in Applied and Computational Mathematics. Our emphasis is on developing analysis skills that are useful in engineering and management.

#### Admission to the Program

The EMS certificate program is open to both B.S.E. and A.B. majors.

B.S.E. students are eligible for admission to the program once they have completed the engineering school core program (or its equivalent):

1. Mathematics through MAT 202

2. PHY 103 and 104

3. CHM 201

4. One course in computing at the level of COS 126

The certificate is available to A.B. students who have completed:

1. The required two science and technology courses (with laboratory)

2. Mathematics through MAT 202, and

3. One course in computing (typically COS 126)

These requirements are satisfied if a student (A.B. or B.S.E.) has received AP credit in the course.

To be admitted, interested students should e-mail the director of the program, stating that you would like to participate in the program. Please include your class and major, and let the director know if you have placed out of any course requirements. Send your request to Professor Powell.

#### Program of Study

The program for each student is worked out by the student and his or her departmental adviser. In some cases, a course can fulfill both a certificate program requirement and a regular departmental requirement. The program requirements are as follows:

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

1. ECO 100 Introduction to Microeconomics

2. An introductory statistics course:

ORF 245 Fundamentals of Engineering Statistics

ECO 202 Statistics and Data Analysis for Economics

PSY 251 Quantitative Methods

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

3. An introductory optimization course:

ORF 307 Optimization

ELE 382 Distributed Algorithms and Optimization Methods for Engineering Applications

CBE 442 Design, Synthesis, and Optimization of Chemical Processes

MAE 433 Automatic Control Systems

4. A course in probability:

ORF 309 Probability and Stochastic Systems

MAT 390 Probability Theory

5. A course integrating optimization and uncertainty:

ORF 311 Optimization under Uncertainty

ORF 417 Dynamic Programming

ORF 418 Optimal Learning

ORF 547 Dynamic Programming (graduate level)

ECO 317 Economics of Uncertainty

ECO 418 Strategy and Information

WWS 312/PSY 321 Psychology of Decision Making and Judgment

6. ORF 411 Operations and Information Engineering

AP credit is allowed for ECO 100 (requires a 5 on the AP exam). AP credit is not allowed for statistics.

#### Independent Work

Acceptable theses can be on a wide range of topics, as long as a significant portion of the thesis uses tools from some part of the core program (statistics, probability and stochastic processes, optimization). Topics do not have to be drawn from business or finance.

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.

#### 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 Engineering Statistics (also EGR 245) Fall, Spring QR

A study of fundamentals of statistical methods and their applications in engineering. Basic concepts of probability, discrete and continuous distributions, sampling and quality control, statistical inference, empirical models, and least squares. Three lectures. Open to freshmen.
*
P. Rigollet*

ORF 307 Optimization (also EGR 307) Spring

Model formulation, analysis, and optimization of deterministic systems. Introduction to quantitative methods: linear programming, duality theory, large-scale mathematical programs, and network analysis. Emphasis will be on applications to problem areas such as allocation of resources, transportation systems, scheduling, capital budgeting, and network problems. Two 90-minute lectures. Prerequisite: MAT 202.
*
A. d'Aspremont*

ORF 309 Probability and Stochastic Systems (also EGR 309/MAT 309) 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.
*
E. Çinlar*

ORF 311 Optimization under Uncertainty Fall

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. Applications in financial planning. Prerequisites: 307 or MAT 305, and 309. Two 90-minute classes.
*
J. Mulvey*

ORF 322 Human-Machine Interaction (see PSY 322)

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

Financial engineers design and analyze products that improve the efficiency of markets and create mechanisms for reducing risk. This course introduces the basics of financial mathematics: the notions of arbitrage and risk-neutral probability measure are developed in the case of discrete models; Black-Scholes theory is introduced in continuous-time models, and interest rate derivatives and the term structure of interest rates are discussed. Prerequisites: 309, ECO 100, and MAT 104.
*
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.
* Staff*

ORF 375 Independent Research Project Fall

Independent research or investigation resulting in a 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 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 is broadly defined as the buying and selling of goods using electronic transaction processing technologies. This course considers the technologies themselves, as well as various economic and financial issues associated with their use. Two 90-minute lectures.
*
A. Kornhauser*

ORF 405 Regression and Applied Time Series Fall

Regression analysis: least squares and robust alternatives, nonparametric techniques (splines, projection pursuit, and neural network). Time-series: trends, seasonal effects, clinical models, state space models. Includes a final project in the form of a realistic forecasting game involving portfolio management and economic time-series data. Prerequisites: 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 queueing theory. Topics covered include: the classical traffic; offered load; and loss and delay stochastic models for communication systems. Through concrete examples and motivations, the theory of Markov chains, Poisson processes, and Monte Carlo simulation are discussed. Fundamental queueing results such as the Erlang blocking and delay formulae, Little's law and Lindley's equation are presented. Applications are drawn from communication network systems, inventory management, and optimal staffing. Prerequisite: 309 or equivalent. Two 90-minute lectures.
*
W. Massey*

ORF 409 Introduction to Monte Carlo Simulation Fall

An introduction to the uses of simulation and direct computation in analyzing stochastic models and interpreting real phenomena. Deals with 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. Prerequisite: 309. Two 90-minute classes.
*
W. Massey*

ORF 411 Operations and Information Engineering Fall

The modeling of complex systems under uncertainty through the control of physical, financial, and informational resources. Students learn how to model stochastic, dynamic systems, using the contextual domain of resource allocation arising in settings such as energy, finance, health, and human resource management. Policy optimization is introduced as a mechanism for controlling systems, along with information exchange and efficient collection of new information. Prerequisites: 245, 307 and 309, or equivalents. Two 90 minute lectures.
*
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 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.
*
W. Powell*

ORF 435 Financial Risk Management Fall

This course covers the basic concepts of modeling, measuring and managing financial risks. Topics include mean-variance portfolio theory, fixed-income securities, options pricing, Greeks, risk measures, and utility functions. Prerequisites: 245, 335 or ECO 465 (concurrent enrollment is acceptable) or instructor's permission. Two 90-minute lectures.
*
B. Rudloff*

ORF 467 Transportation Systems Analysis Fall

Operations research in transportation and logistics. Vehicle routing and scheduling, warehouse location, network flow models in transportation, set partitioning solutions to vehicle and crew assignment problems, fixed-charge problems and network equilibrium models. Emphasis placed on the theory and implementation of algorithms for large, specially structured problems. Two 90-minute lectures. Prerequisites: linear programming and network algorithms.
*
A. Kornhauser*

ORF 474 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. Three classes
* Staff*

ORF 478 Senior Thesis Spring

A year-long, independent study of a significant problem in operations research or financial engineering. Topic proposals must be submitted during the spring of junior year and must be accepted by the ORFE departmental representative. A written report is required at the end of each term, though enrollment is only in the spring term when a double-credit grade is awarded. Students give an oral presentation at the end of the spring term. Students must make acceptable progress in the fall term in order to continue in the spring. Fulfills the departmental independent work requirement for seniors.
*
A. Kornhauser*

ORF 479 Senior Project

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*

ORF 491 High-Tech Entrepreneurship (see ELE 491)