Operations Research and Financial Engineering
The ORFE program places a strong emphasis on mathematical and computational tools. Students in ORFE develop a unique set of skills that build upon a solid foundation in probability, statistics, and optimization.
The theoretical foundations of ORFE are of central importance in many complex problems in engineering and science. Students and faculty in ORFE work in a broad range of application areas, such as finance, energy, health, risk analysis, biostatistics, genomics, machine learning, operations research, stochastic networks, signal and image processing, automated vehicle control systems, optimal design of engineered systems, robotics, astrophysics, and homeland security.
Graduates of the Ph.D. program work in academia, research organizations, and industry. Many ORFE graduates hold faculty positions at top universities.
The department offers two degree programs: the Doctor of Philosophy (Ph.D.) in Operations Research and Financial Engineering, and a Master of Science in Engineering (M.S.E.). These programs provide a great deal of flexibility for students in designing individual plans of study and research according to their needs and interests. The department is a major participant in the Master of Finance (M.Fin.) program offered through the Bendheim Center for Finance.
- All applicants are required to submit a GRE general test. A mathematics subject test is strongly recommended.
- M.S.E. applicants are required to have the endorsement of a faculty member who is willing to supervise them prior to submitting an application.
- M.S.E. applicants are required to submit a Statement of Financial Resources.
The Ph.D. program is formulated to prepare students for research and teaching. The aim of the program is to provide a strong disciplinary background in at least one of the core areas of research in the department. The emphasis is on the theoretical foundations, mathematical models, and computational issues in practical problem-solving. Current teaching and research activities include stochastic analysis, mathematical statistics, machine learning, analysis of big data, linear and nonlinear optimization, stochastic optimization, convex analysis, stochastic networks, queueing theory, mathematical and computational finance, PDE methods, stochastic control, dynamic game theory, and financial econometrics. Application areas of current interest to faculty include finance, energy, health, biostatistics, genomics, robotics, social networks, and astrophysics
The departmental faculty is affiliated with a number of interdisciplinary programs and centers, including the Program in Applied and Computational Mathematics, the Bendheim Center for Finance, the Andlinger Center for Energy and the Environment, the Princeton Environmental Institute, and the Center for Statistics and Machine Learning. Students may combine their departmental work with courses and research opportunities offered by such programs and centers and also by other departments including Computer Science, Economics, and Mathematics.
In the first year of graduate study, students must take all six core courses. By the end of the first year, students are expected to narrow the area of doctoral research and choose an appropriate adviser. Second-year students are required to complete a qualifying examination, undertake advanced coursework, research projects, and prepare for the general examination. The general examination is normally taken at the end of the second year.
Beyond the general examination, the completion of a dissertation usually takes two to three years. Upon acceptance of the dissertation by the department and the Graduate School, candidates for the Ph.D. stand for the final public oral examination, which is primarily a defense of the dissertation.
In consultation with the director of graduate studies, students develop a specific course plan. During the first year, students complete six courses that emphasize the foundations of the program, probability, statistics, and optimization. Students take a total of at least ten courses while enrolled: the six core courses during the first year, and two directed research courses as well as two additional advanced-level courses in the second year.
The following six core courses are required:
- ORF 522 Linear and Nonlinear Optimization
- ORF 523 Convex and Conic Optimization
- ORF 524 Statistical Theory and Methods
- ORF 525 Statistical Foundations of Data Science
- ORF 526 Probability Theory
- ORF 527 Stochastic Calculus
In addition, at least two advanced courses and two semesters of directed research (ORF 509 and ORF 510) are completed under the direction of a faculty adviser in the student's area of interest by the end of the second year in preparation for the general examination.
Students ordinarily match with an adviser by the end of the first year or study in order to begin research in preparation for the general examination. No student may enter the second year without a research adviser of record. Students are expected to identify a faculty adviser in the ORFE department. If a student receives permission to work with a faculty advisor who is not a member of the ORFE department, the student must also be co-advised by an ORFE faculty member, who is seriously involved in co-advising the student.
Each student must satisfy qualifying requirements. Qualifying exams are offered in September of the student’s second year.
A student who obtained a grade of A- or better in four of the six required core classes will be exempt from the September qualifying exams. If this is not the case, the student will meet with the DGS, who will determine which exams need to be taken in September to satisfy the requirements. The optimization exams are based on ORF 522 and ORF 523. The probability exams are based on ORF 526 and ORF 527. The statistics exams are based on ORF 524 and ORF 525.
The results of the qualifying exam are determined by a vote of the faculty. Students who fail must transfer out of the Ph.D. program. There is no option to retake the exam.
By the end of the first year, students are expected to narrow their area of doctoral research and choose an appropriate adviser.
ORFE students take the general exam in April or May of their second year. In order to be considered eligible to stand for the general examination, students must have completed the required core courses, met the qualifying examination requirements, have taken and passed ORF 509, have taken or are currently enrolled in ORF 510, and have received a B+ or higher in two additional advanced courses at the 500 level. The student must also show adequate progress on research and an acceptable level of understanding of his or her area of specialization.
The general examination consists of two parts, a written and oral component, both covering the student's area of specialty. The written component is completed by submitting a written report on the research conducted in ORF 509-510. It is due one week before the exam takes place. The report serves as the basis for the student’s presentation. The oral component is completed by giving a presentation on the research presented in the comprehensive written report. The oral exam may be up to 3 hours in length.
As part of the oral examination, the general examination committee may ask questions related to the research as well as the student’s area of specialization.
For each student, an examining committee is selected by the student and adviser. In addition to the adviser, the committee consists of two ORFE faculty or affiliated faculty and must be approved by the Director of Graduate Studies. The committee will administer the oral exam, evaluate the student’s performance in research and overall knowledge of the student's field, and make a recommendation to the department faculty. A departmental faculty vote determines the final outcome.
The Master of Arts (M.A.) degree is normally an incidental degree on the way to full Ph.D. candidacy and is earned after a student successfully passes the general examination. It may also be awarded to students who, for various reasons, leave the Ph.D. program, provided that these requirements have been met.
Please note, students admitted to the Ph.D. program who do not wish to complete the program may be considered for an M.S.E. degree with approval from the department and the Graduate School. Ph.D. students who have already been awarded the incidental M.A. are not eligible to earn an M.S.E.
Upon completion and acceptance of the dissertation by the department, the candidate will be admitted to the final public oral (FPO) examination.
The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained.
The ORFE department is primarily geared towards educating students pursuing a Ph.D. in the field. As such, the Master of Science in Engineering (M.S.E.) program in ORFE also has a strong research focus, as reflected in the requirement of a thesis and full-time study for two academic years. Students enrolled in this program are eligible for financial support in the form of research or teaching assistantships if such funds are available.
The admission rate for the M.S.E. degree is very low. Admission is based on the qualifications of the applicant and requires support of at least one faculty member who expresses an interest in supervising the applicant. Applicants interested in an M.S.E. degree from ORFE are urged to identify and contact a faculty member in whose area of research they would like to work.
Applicants who are primarily interested in a master's degree in finance should apply for the Master in Finance Program at the Bendheim Center for Finance. The School of Engineering website provides more information regarding the Master of Science in Engineering program.
The course requirements are fulfilled by successfully completing ten one-semester courses approved by the department, two of which are required research courses (ORF 509 and 510).
The M.S.E. program has a strong research focus reflected in the requirement of a thesis. Upon completion and acceptance of the thesis by the department, the candidate will be admitted to the final defense, administered by at least two faculty members.
K. Ronnie Sircar
Director of Graduate Studies
Amir Ali Ahmadi
René A. Carmona
Matias D. Cattaneo
Alain L. Kornhauser
William A. Massey
John M. Mulvey
Warren B. Powell
Halil M. Soner
Robert J. Vanderbei
Ramon van Handel
Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.