The DRO division consists of roughly 20 faculty members and 20 PhD students in total (with 4-5 students in each year), and as a result, our students benefit from close mentorship by the faculty advisor(s) they choose. Moreover, our weekly internal Brown Bag seminar gives students the opportunity to regularly present their research to the entire division and receive feedback. Our students’ work has been consistently recognized as finalists and winners of society awards such as M&SOM Student Paper Competition, George Nicholson Student Paper Competition, George B. Dantzig Dissertation Award, and the Pierskalla Best paper competition.
The program consists of six core classes, three offered from the Business School’s Decision, Risk and Operations division (DRO) and three offered from the Department of Industrial Engineering and Operations Research (IEOR) from the Engineering School. Electives often come from these two divisions and other Schools at Columbia University: Electrical Engineering, Computer Science, Statistics, Economics, Mathematics, and so on.
Core Classes (First Year):
- Foundations of Optimization (DROM B9118)
- Optimization I/Linear Programming (IEOR 6613)
- Stochastic Modeling I (IEOR 6711)
- Foundations of Stochastic Modeling (DROM B9119)
- Econometrics and Statistical Inference II (DROM B9324)
- Topics Seminar (DROM B9137)
In addition, students must demonstrate proficiency in the area of real analysis at the level of Rudin, “Principles of Mathematical Analysis”, on the basis of prior coursework, an exemption exam, or by taking the “Introduction into Modern Analysis I” at Columbia
By End of Year 3:
- Graduate-level course on game theory (e.g. Micro II offered by the Department of Economics or an equivalent course)
- Graduate-level IEOR course on advanced deterministic optimization (Optimization II/Network Flows, Integer Programming, or Combinatorial Optimization)
- Graduate-level course on dynamic programming
- The DRO qualifying exam consists of two parts: the “stochastic modeling" and the “deterministic optimization” exam. These take place 1 week apart, typically the last two Fridays of May of a student’s 1st year.
- Students that fail one or two of the exams may be given a second chance at the end of their second year in the program to pass the respective exam(s) that they did not pass.
The first year in the program is primarily coursework-focused. At the end of the first year, students take their qualifying exams. In the summer of the first year and during the second year, students start focusing more on research while also taking elective courses.
First-Year Summer project
- Students are required to do a research project under the supervision of a faculty advisor over the Summer of the first year of the program. Such a project could be a literature survey, the beginning of a research paper, a computational study, etc.
- The expectation is not that this project will necessarily lead to a publishable paper, but rather that the student gets actively engaged in research. The faculty advisor for that summer project need not end up being the dissertation advisor of the student.
- In the month of September starting the second year of study, students should:
- Submit a 5-10 page report on their research project to their summer project advisor and the division’s PhD coordinator.
- Present a 20 min summary of their project in the PhD brown bag seminar.
For the next two years, students develop their thesis proposals, which are then formally presented at the end of June in year three. In years four and five, students take courses sparingly while primarily working on research, with the goal of completing a dissertation defense by the end of year five.
Your thesis proposal must take place by June 30 of your 3rd year. Note: The following requirements are meant to serve as a divisional benchmark. Students should discuss with their primary research advisor the precise format which will be most productive for the student in question. In some cases, the research advisor may ask for more (or less) than what is outlined here.
- Schedule a 2-3 hour slot.
- Provide your committee with a 10-15 page document summarizing your thesis proposal at least 1-2 weeks before the proposal.
- The day of the proposal, you will present for roughly one hour your research achievements to date and plans going forward. The presentation will be followed by questions.
- Following the proposal, you should think about how the feedback can help you execute your research plan.