Department of Operations Research and Financial Engineering
Chair
Robert J. Vanderbei
Departmental Representative
Alain L. Kornhauser
Professor
René A. Carmona
Erhan Çinlar
Jianqing Fan
Alain L. Kornhauser
William A. Massey
John M. Mulvey
Warren B. Powell
K. Ronnie Sircar
Robert J. Vanderbei
Visiting Professor
Andrezej Ruszczynski
Assistant Professor
Patrick Cheridito
Alexandre W. d’Aspremont
Savas Dayanik
Philippe Rigollet
Birgit Rudloff
Associated Faculty
Yacine Aït-Sahalia, Economics
Ingrid C. Daubechies, Mathematics
Avinash K. Dixit, Economics
Weinan E, Mathematics
Christodoulos A. Floudas, Chemical Engineering
Sanjeev R. Kulkarni, Electrical Engineering
H. Vincent Poor, Electrical Engineering
José A. Scheinkman, Economics
Stuart C. Schwartz, Electrical Engineering
Paul D. Seymour, Mathematics
Yakov G. Sinai, Mathematics
Elias M. Stein, Mathematics
Information and Departmental Plan of Study
Operations research and financial engineering may be considered as the modern form of a liberal education: modern because it is based on science and technology, and liberal in the sense that it provides for broad intellectual development and can lead to many different types of careers. By choosing judiciously from courses in engineering, economics, public policy, and liberal arts, each student may design a program adapted to his or her particular interests.
All students start from a common academic core consisting of statistics, probability and stochastic processes, and optimization. Related courses focus on developing computer skills and exposing students to applications in areas such as finance, operations, transportation, and logistics. Students augment the core program with a coherent sequence of departmental electives. Students may also design specialized programs, which must be reviewed and approved by their academic adviser and the departmental representative. Students often draw on courses from economics, computer science, applied mathematics, civil and environmental engineering, mechanical engineering, and the Woodrow Wilson School. Requirements for study in the department follow the general requirements for the School of Engineering and Applied Science and the University. See page 455.
Program of Study
The student’s program is planned in consultation with the departmental representative and the student’s adviser and requires a year-long thesis or a one-semester senior project. With departmental approval, the exceptional student who wishes to go beyond the science and engineering requirements may select other courses to replace some of the required courses in order to add emphasis in another field of engineering or science or to choose more courses in the area of study. Suggested plans of study and areas of concentration are available from the departmental representative.
In addition to the engineering school requirements (see page 455), there are three components to the curriculum:
1. The core requirements (six courses). These form the intellectual foundation of the field and cover statistics, probability, stochastic processes, and optimization, along with more advanced courses in mathematical modeling.
2. Departmental electives (eight or nine courses). These are courses that either extend and broaden the core, or expose the student to a significant problem area or application closely related to the core program.
3. Senior independent work. A one-semester project or a full-year thesis involving an application of the techniques in the program applied to a topic that the student chooses in consultation with a faculty adviser.
Core requirements (six courses):
ORF 245 Fundamentals of Engineering Statistics
ORF 307 Optimization
ORF 309 Probability and Stochastic Systems
ORF 335 Introduction to Financial Engineering
ORF 405 Regression and Applied Time Series
ORF 411 Operations and Information Engineering
Departmental electives (eight or nine courses, if a senior project is selected):
The departmental electives represent courses that further develop a student’s skills in mathematical modeling either by a more in-depth investigation of core disciplines, applying these skills in specific areas of application, or learning about closely related technologies. Students must choose eight courses from the following list, with the following constraints:
There must be at least one 300-level math course (see list below).
There must be at least two courses from Operations Research and Financial Engineering (ORF).
There can be no more than three courses from any one department (excluding ORF).
There can be no more than two 200-level courses.
Courses that may be used to satisfy the MAT 300-level requirement:
APC 350 Introduction to Differential Equations
MAE 305 Mathematics in Engineering I
MAE 306 Mathematics in Engineering II
MAT 303 Ordinary Differential Equations
MAT 304 Introduction to Partial Differential Equations
MAT 306 Introduction to Graph Theory
MAT 307 Combinatorial Mathematics
MAT 308 Theory of Games
MAT 314 Introduction to Real Analysis
MAT 390 Probability Theory
MAT 391 Random Processes
All other departmental electives:
ORF 301 Elements of Interactive Computer Graphics
ORF 311 Optimization under Uncertainty
ORF 335 Introduction to Financial Engineering
ORF 375, 376 Independent Research Project
ORF 401 Electronic Commerce
ORF 406 Statistical Design of Experiments
ORF 409 Introduction to Monte Carlo Simulation
ORF 417 Dynamic Programming
ORF 435 Financial Risk Management
ORF 467 Transportation
ORF 474 Special Topics in Operations Research and Financial Engineering
ECO 310 Microeconomic Theory: A Mathematical Approach
ECO 317 The Economics of Uncertainty
ECO 341 Public Finance
ECO 342 Money and Banking
ECO 361 Financial Accounting
ECO 362 Financial Investments
ECO 363 Corporate Finance and Financial Institutions
ECO 414 Introduction to Economic Dynamics
ECO 418 Strategy and Information
ECO 462 Portfolio Theory and Asset Management
ECO 464 Corporate Restructuring
ECO 465 Options, Futures, and Financial Derivatives
*ECO 467 Institutional Finance
PSY 322 Human-Machine Interaction (although cross-listed with ORF, this course may not count as one of the two ORF requirements)
COS 217 Introduction to Programming Systems
COS 226 Algorithms and Data Structures
COS 323 Computing for the Physical and Social Sciences
COS 402 Artificial Intelligence
COS 423 Theory of Algorithms
COS 425 Database and Information Management Systems
ELE 485 Signal Analysis and Communication Systems
ELE 486 Digital Communication and Networks
MAE 433 Automatic Control Systems
CEE 303 Introduction to Environmental Engineering
CEE 460 Risk Assessment and Management
Students in the department often participate in the following certificate programs:
Certificate in Finance. The department cooperates with the Bendheim Center in Finance, which offers a certificate program in finance. Interested students can find details of this program on page 211.
Certificate Program in Engineering and Management Systems. The department sponsors a certificate program for students majoring in other departments who complete a significant part of the core of the undergraduate program. The details of this certificate program can be found on page 510.
Certificate in Applied and Computational Mathematics. Students seeking a strong mathematical foundation can combine courses from the department with supporting courses which develop more fundamental mathematical skills.
The department maintains several research laboratories which may be used as part of undergraduate research projects.
Computational and Stochastic Transportation and Logistics Engineering Laboratory. The CASTLE Laboratory works on problems in dynamic resource management with ongoing projects in chemical distribution, railroads, trucking, and the airlift mobility command. Through this lab, students gain access to data and specialized tools to aid them in their research into transportation and logistics.
Financial Engineering Laboratory. This facility provides students with access to specialized software packages and to financial data and news services. Research in the laboratory is concerned with the analysis of the various forms of financial risk and the development of new financial instruments intended to control the risk exposure of insurance and reinsurance companies.
Transportation Information and Decision Engineering Center. The TIDE Center conducts research on information and decision engineering technologies and on how these technologies can be used to improve transportation-related decision making. It is a cooperative effort involving Princeton University, the New Jersey Institute of Technology, and Rutgers University. It is sponsored by the New Jersey Commission on Science and Technology under its Research and Development Excellence Program.
Optimization Tools and Models Library. The OPTOMO Library is an Internet-based library that provides students with access to a large collection of important real-world optimization models, together with state-of-the-art tools for solving them.
Courses
ORF 105 The Science and Technology of Decision Making
(also EGR 106) — Fall 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 201 Computer Methods for Problem Solving — Not offered this year QR
An introduction to problem solving on digital computers, geared toward engineering applications. Examples drawn from statistics, calculus, image processing, graphics, simulation, operations research, and other engineering disciplines. Fundamental programming concepts for problem solving, using the Internet-inspired JAVA programming language. Computer programs developed in the course can be run from any Internet browser. No prior experience with computer programming required. Two lectures, one two-hour laboratory. Prerequisite: calculus (MAT 103 or equivalent). Open to freshmen. R. Vanderbei, H. Simão
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. J. Fan, H. Simão
ORF 301 Elements of Interactive Computer Graphics — Fall
Methods of interactive computer graphics as general-purpose tools for computer-aided design and analysis, visualization of functional and spatial relationships, three-dimensional color rendering and data visualization, graphical and numerical description of networks and their attributes. Two 90-minute lectures, one laboratory. Prerequisites: MAT 201 and ORF 201, or COS 126. A. Kornhauser
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. R. Vanderbei, 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 Engineering (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 engineering: 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 — Spring
A course covering special topics in operations research or financial engineering. Subjects may vary from year to year. Staff
ORF 375, 376 Independent Research Project — Fall, 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. S. Dayanik
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 Mathematics 202. A. Petters
ORF 406 Statistical Design of Experiments — Spring
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 ORF 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 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. Students are organized into teams for a competitive game in resource management that tests modeling skills and teamwork. Prerequisites: 245, 307 and 309, or equivalents. Two 90-minute lectures. W. Powell
ORF 417 Dynamic Programming — Spring
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. S. Dayanik
ORF 435 Financial Risk Management — Fall
This course is about measuring, modeling, and managing financial risks. It introduces the variety of instruments that are used to this effect and the methods of designing and evaluating such instruments. Topics covered include risk diversification, planning models, market and nonmarket risks, and portfolio effects. Prerequisites: 245 or ECO 202; 335 or ECO 465 (concurrent enrollment is acceptable) or instructor’s permission. Two 90-minute lectures. B. Rudloff
ORF 467 Transportation — 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. Staff
ORF 474 Special Topics in Operations Research and Financial Engineering — Fall
A course covering one or more advanced topics in operations research and financial engineering. Subjects may vary from year to year. Three classes. A. Petters
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. S. Dayanik
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. S. Dayanik
ORF 491 High-Tech Entrepreneurship (see ELE 491)
*One-time-only course