Field of Operations Research
The following requirements guarantee that Ph.D. students obtain a core of knowledge in Operations Research, yet allow substantial flexibility to pursue specialized interests. Evaluation procedures are designed to provide each student with timely information about her/his progress.
Major Subjects and Areas of Concentration
All Ph.D. students in the Field of Operations Research major in the subject Operations Research with a concentration in one of: Applied Probability and Statistics, Manufacturing Systems, or Mathematical Programming. The concentration is generally determined by the student no later than the second year.
The following requirements apply to the first four semesters of Ph.D.-level work, during which the student’s primary goal should be to obtain broad exposure to the discipline of Operations Research. These requirements are intended to provide such academic breadth.
- Core courses: Each student must know the content of the following courses:
- ORIE 6300 Mathematical Programming I
- ORIE 6500 Applied Stochastic Processes
- ORIE 6700 Statistical Principles
- MATH 4130 Introduction to Analysis
- MATH 4330 Introduction to Algebra (emphasizing proof-based linear algebra)
Depending on background, a student may be allowed to bypass one or more of ORIE 6300, 6500, 6700. In each such instance, however, the student is still required to take the final examination at the end of the first semester of study; these final examinations become a part of the student’s Qualifying Examination (discussed later). On the other hand, if, for any course among these three, a student is not academically prepared to take the course during the first semester of study, it may be delayed until the third semester, with an appropriate preparatory course taken during the first year. Whether a student should take MATH 4130 and/or 4330 is determined by the student in consultation with a designated Field member prior to the beginning of the first semester of study.
- Advanced courses: Students must perform well (A- or better) in three advanced Ph.D. courses (i.e., beyond the core courses ORIE 6300, 6500, 6700), with one course from three of the following four areas: Manufacturing and Simulation, Mathematical Programming, Probability, Statistics. As a general rule, 6000-level ORIE courses, i.e., Ph.D.-level electives, are used to satisfy this requirement. With DGS approval (see (5) below) courses from other departments may also be used to meet this requirement.
- Computer literacy: Each Ph.D. candidate must demonstrate computer literacy by taking an appropriate Ph.D.-level course. This course may simultaneously satisfy another requirement; e.g., the simulation course ORIE 6580 would establish computer literacy, as well as providing partial fulfillment of requirement (2).
- Course load: In each of the first three semesters each student is expected to enroll in at least three appropriately sophisticated, technical courses, each with adequate provision for evaluating student progress, e.g., through regularly scheduled lectures, homework assignments, and/or examinations. Technical means courses in engineering, mathematics, or science, in addition to certain areas of business, such as quantitative finance or operations management. Appropriately sophisticated means either at Ph.D.-level or at a level appropriate to a student’s background. (For example, someone who has taken an undergraduate class very similar to MATH 4130 should not enroll in this course, unless the former class was taken several years earlier.)
- Exceptions: Any deviation from (1) – (4) above requires the written approval of the Field’s Director of Graduate Studies (DGS). For example:
- The computer literacy requirement (3) may be fulfilled by completion of an appropriate project supervised by a Field member. In this case, the supervising Field member must, of course, agree to the arrangement. Prior to undertaking such a project, the student must submit a one- to two-page project proposal to the DGS, who, in consultation with appropriate Field faculty, will decide whether the project meets this requirement; at the completion of the project, the supervising Field member must submit to the DGS written certification that the work accomplished in the project meets the computer literacy requirement.
- DGS approval is required for courses from other departments used to satisfy the advanced breadth requirement (2); for example, several appropriate Ph.D.-level probability courses are offered by the Department of Mathematics.
- Exceptionally well-prepared students beginning serious research investigation under the direction of a Field faculty member may seek DGS approval for using the course ORIE 7900 Special Investigations in satisfying the course load requirement (4). The research project must be documented (at the beginning) by a student proposal approved by the supervising faculty member and (at termination) by a report from the faculty member on the work accomplished.
Minor Subjects and the Special Committee
Each student forms a Special Committee no later than the fourth semester, although the composition of the committee may be changed at a later date. The Special Committee consists of a Chair—who in the final composition of the committee is the student's thesis advisor—and at least one member for each of two minor subjects, the minor advisors. It is entirely the student's choice as to whom to ask to be on her/his committee.
Minors must be taken in engineering, science (including mathematics), or technical areas of business (e.g., finance). (Students may petition for exceptions.) Of a student's two minor subjects, at least one must be from outside the Field of Operations Research. If a minor subject is Operations Research, the student must select for the Special Committee a member of the Field to represent an area of concentration different from that of the student's major concentration.
A minor subject typically involves three Ph.D. courses—sometimes four—determined by the minor advisor in consultation with the student. Required courses can count toward a minor; for example, OR&IE 6300(630) can count towards a minor in Operations Research with concentration in Mathematical Programming. The role of each minor subject is to enhance the student's exposure to the subject, either in breadth or in depth, beyond the courses that would generally be included as part of the student's major program of study. At least one minor should be entirely satisfied by courses different from those used to satisfy the course requirements (1) and (2) (as listed above). No course may be used to count simultaneously toward both minors.
The Qualifying Exam is the only exam that is Field-administered, as opposed to being administered by the Special Committee. The purpose of the Qualifying Exam is to judge whether a student can be expected to perform at an appropriately high level in advanced coursework and research, and to assist the Special Committee in developing a program of study for the student (assuming the student remains in the Ph.D. program).
What constitutes the Qualifying Exam depends in part on the student's performance in courses. Precisely, a student is orally examined on the material of each of the three primary courses—ORIE 6300(630), 6500(650), 6700(670)—for which she/he receives a grade of B+ or less. (If a student is allowed to skip one of these courses, the grade is based only on her/his performance on the mandatory final examination in the course.)
For courses taken during the first year, the oral exam is held at the beginning of the third semester. For courses taken during the third semester, the oral exam is held at the beginning of the fourth semester. Oral exams for separate courses are on separate days.
In addition to the possibility of oral exams on coursework as described above, all Ph.D. students give an oral presentation as part of the Qualifying Exam. Specifically, at the beginning of the third semester, each student presents a research paper selected from a collection submitted by Field members. The presentation is attended by at least three Field members (appointed by the DGS), who may ask questions (related to the paper) of the student.
The DGS determines which paper a student presents based on preference-order rankings provided by all third-semester students. At most one student presents a given paper, so a student can be assigned her/his second or third choice. Once a paper is assigned, a student is informed of the Field member who submitted the paper so that the student can consult with the member if need be, keeping in mind that the student's independence in mastering the paper is being considered.
After a student has completed all of the required oral exams, but in any case no later than the beginning of the fourth semester (and generally at the beginning of the third semester), Field members discuss the student and reach one of two decisions, thus finalizing the Qualifying Exam:
- The student may continue in the Ph.D. program.
- The student is required to leave the Ph.D. program at the end of the second year. (This outcome is relatively uncommon, but when it does occur, the student typically completes a master's thesis and receives a master's degree.)
The decision of the Field takes into account all relevant materials such as performance in all courses and evaluations by Field members who have had an opportunity to assess the student's research promise.
Admission to Candidacy Exam (The A Exam)
This exam is a formal requirement of the Graduate School. It has an oral portion and is administered by the Special Committee of the student. Typically, the exam is taken during the third year. A degree cannot be awarded until at least two units of residence have been earned after passing the exam. At the time of the A exam, the student must submit to the DGS a summary of the courses used to satisfy all program requirements (or to specify intended courses in the rare cases that such coursework has not yet been completed).
Any member of the Field may attend the exam. There are at least three examining members of the Graduate School present at the exam; the DGS ensures this if, say, a Special Committee member is on leave.
The Special Committee often views passing of the Qualifying Exam as a demonstration of the competence of the student in fundamental knowledge in the Field. Thus, the A exam often focuses on assessing the student's mastery of the areas of concentration. Sometimes the A exam is primarily a presentation of proposed research for a thesis and other times the exam is more in the nature of an oral examination; this is at the discretion of the Special Committee. A student consults with the Special Committee members so as to know what to expect in the exam.
Final Exam (The B Exam)
In the B exam, the student presents and defends the Ph.D. thesis. The B exam also must be announced as an ORIE Colloquium.