You are here

Decision, Risk, and Operations

The Doctoral Program in Decision, Risk, and Operations (DRO) at Columbia Business School is designed to lead a small group of outstanding students to successful research careers in academia and industry. Our recent graduates have accepted appointments at the leading institutions of business education, such as Wharton, MIT, Kellogg, Carnegie Mellon, Cornell, Duke, and NYU, as well as in leading research and development positions in industry.


The Decision, Risk, and Operations Division provides an exceptional research environment for PhD studies. The division’s research focus involves the development and analysis of quantitative models motivated by business problems. These models are used to support decision making, to measure and manage risks, and to enhance understanding of business practices. Such problems are analyzed using tools from mathematical programming, game theory, probability, and statistics. The division has particular expertise and maintains a diverse portfolio of ongoing research projects in the following application areas:

  • Supply Chain Management
  • Revenue Management, Auctions, and Game Theory
  • Financial Engineering and Risk Management
  • Logistics, Production Planning and Scheduling, and Management of Service Systems
  • Stochastic Models, Simulation, Processing, and Queuing Networks

Early student participation in research is strongly encouraged. The division hosts a weekly seminar series, which introduces students to cutting-edge research and provides a forum for faculty-student interactions. Interdepartmental collaborations give students an opportunity to work with their counterparts from the Departments of Industrial Engineering and Operations Research, and Statistics.


Admission to the program is highly competitive. All applicants are required to have a bachelor’s degree or the equivalent, representing a four-year course of study in an accredited college or university. Superior academic performance is expected, and a strong background and ability in mathematics are essential for successful completion of the program. Applicants are strongly encouraged to take the GRE rather than the GMAT. The program is full-time only and is typically completed in five years.


Admitted students are awarded a four-year fellowship that covers their tuition and fees and provides a monthly stipend. During the course of their PhD career, students can receive supplemental support as teaching and/or research assistants. Funding for the fifth year is merit based and determined by the Department.


The Field Exam is administered shortly after the end of the spring semester. It is given in two separate sections one week apart from each other: one covers deterministic optimization, and the other covers stochastic models. Students take both sections at the end of their first year of study. A student who does not earn a sufficiently high score on either section must retake that section at the end of the second year. Passing both sections by the end of the second year is a requirement for continuing in the program. In some cases, a student may be given a Conditional Pass, which requires that the student take an additional course in a specified topic to develop greater proficiency. A required grade in the course is usually specified in such cases. The purpose of the Field Exam is to ensure that students master course material before undertaking research. The faculty members of the division try to ensure that all students are well prepared for the exam. Studying for the exam is important, but a student who does well in course work should not have difficulty passing the exam by the end of the second year.

The following is a list of topics commonly covered in the Field Exam along with indicative references. The specific content of the exam may vary slightly from year to year. Students should talk to the division’s doctoral coordinator in the spring for updated information.

I. Deterministic Optimization

LP duality; sensitivity analysis, parametric programming, and economic interpretation of duality; simplex and interior point algorithms; Dantzig-Wolfe decomposition.
(Reference: Bertsimas and Tsitsiklis, Introduction to Linear Optimization)

Classical optimization and nonlinear programming: unconstrained optimization; Lagrange multipliers; Karush-Kuhn-Tucker theorem. Duality theory. Deterministic continuous-time optimal control: Hamilton-Jacobi-Bellman equation; Pontryagin’s maximum principle.
(References: Sundaram, A First Course in Optimization Theory; Bertsekas, Nonlinear Programming; Sethi and Thompson, Optimal Control Theory)

Shortest paths; maximum flows; minimum cost flows. Assignments. Matchings; minimum spanning trees.
(References: Ahuja, Magnanti and Orlin, Network Flows; and Bertsimas and Tsitsiklis, Introduction to Linear Optimization)

  • Linear Programming
  • Foundations of Optimization
  • Network Flows

II. Stochastic Models

Poisson processes, discrete and continuous-time Markov chains. Renewal processes, semi-Markov processes, regenerative processes. Elementary Markov decision processes. Convergence concepts, SLLN, CLT, martingales, stopping times, optional stopping.
(Reference: Ross, Stochastic Processes)

Markovian queues; M/G/l; priority queues. Stability of queues; random walks associated with G/G/1 queues; Lindley’s recursion; Little’s law, PASTA. GI/GI/1 queue in heavy traffic.
(References: Gross and Harris, Fundamentals of Queuing Theory; and Bertsekas and Gallager, Data Networks)

Stochastic demand, single-item, constant leadtime models
(Reference: Zipkin, Foundations of Inventory Management)

  • Stochastic Processes
  • Queueing Theory
  • Inventory Theory

Additional topics may be included in these exams depending on the specific course offerings that year. Examples include integer programming and combinatorial optimization and simulation.

Course Offerings

During the course of study, students receive rigorous training that includes methodological courses in optimization and stochastic processes; courses in methodology of operations and risk management; and a broad range of courses from the Engineering School and the economics, mathematics, and statistics departments.

For more information, visit the DRO Division.

Sample Decision, Risk, and Operations courses:

Foundations of Optimization
Dynamic Programming
Game Theoretic Models in Operation
Computing for Business Research
Foundations of Stochastic Modeling
Revenue Management

Doctoral Program News

Honigsberg featured in Ideas at Work

The August issue of Ideas at Work features research that doctoral candidate Colleen Honigsberg led in conjunction with Sharon Katz.

Read More about Colleen

Wazlawek featured in Ideas at Work

Abbie Wazlawek's joint research with Professor Daniel Ames is featured in the June 24th, 2014 edition of Ideas at Work

Read More about Abbie

Ethan Rouen featured in Ideas at Work

Ethan Rouen's joint research with Professor Dan Amiram is featured in the May 15th, 2014 edition of Ideas at Work

Read More about Abbie

Rivas Wins Fellowship

The PhD program is proud to congratulate Miguel Duro Rivas, who was awarded the Nasdaq Educational Foundation Doctoral Dissertation Fellowship.

Read More about Miguel

Wong wins Deloitte Fellowship

We are proud to announce that Yu Ting (Forester) Wong is one of the recipients of the 2014 Deloitte Foundation Doctoral Fellowship in Accounting.

Read More About Yu Ting >

The PhD Program Congratulates John Yao

PhD student John Yao was a finalist in the 2013 M&SOM (Manufacturing & Service Operations Management) student paper competition.

Read More About John >

Honigsberg Named Postdoctoral Fellow

The PhD program is proud to congratulate Colleen Honigsberg, who was named the Postdoctoral Fellow in Corporate Governance at the Millstein Center at Columbia Law School in October 2013

Read More about Colleen >


Application Deadlines

Master of Science in Marketing >

For Fall 2015 Entry:
Deadline: January 5th, 2015


Master of Science in Financial Economics

For Fall 2015 Entry:
Deadline: January 5th, 2015


Master of Science in Management Science and Engineering

For Fall 2014 Entry:
Early Decision: Jan 6, 2015
Regular Decision: Feb 15, 2015


Apply Now
Sept 2015

Deadline: 01/05/15

MS Marketing
Deadline: 01/05/15

MS Financial Economics
Deadline: 01/05/15


Check Application Status

Students listening to classroom lecture

Once you've submitted your application, you can login and track your status by using the link below.

Check Status

Top Ten Doctoral Program Questions

Here are the most frequently asked questions about the Doctoral Program.

Expand >

The Program takes a minimum of four years to complete. Most students complete the process in five years.

We do not require a business undergraduate degree or masters to apply or be accepted to our Doctoral Program. We have had several students from degree programs including: Economics, Statistics, Psychology, Sociology, Mathematics, and Engineering, among others.

Unlike an undergraduate or master level program, where individual courses are incorporated with a highly structured learning experience, the doctoral education places an emphasis on self-directed learning and close relationships with a select few faculty in a particular area of specialization. Programs typically involve intense reading of academic journals and writing original research. Doctoral students usually grow close relationships with their faculty mentors. These advisors work closely with the students to define a course of research and help provide guidance in the dissertation process.

You can study in one of our five divisions: Accounting, Decision, Risk and Operations, Finance and Economics, Management, or Marketing. A more nuanced understanding of these fields can be seen in the areas of expertise of the Business School’s faculty research.

Unfortunately our Doctorate is available only as a full time, in residence program.

Apply using our online application. We ask that you do not send any documents directly to the School, all materials can be submitted online. Please comply with the posted application deadlines, being sure to include all required components of the application.

The aim of our Program is to accept 23 students per year (Accounting: 4, DRO: 4, Finance: 6, Management: 5, Marketing: 4).

While we have no prerequisites for application, students with limited quantitative backgrounds may benefit from taking accounting, mathematics, econometrics and statistics before enrolling. We encourage you to explore each Division’s requirements before applying the Analytical thinking and quantitative tools have a significant influence on success in the program.

No, the goal of the Doctoral Program is to place graduates in academic institutions as top researchers and instructors. If you have a different goal in mind we encourage you to investigate our MS Programs which combine the Doctoral level coursework in a masters package.

A full financial aid package is offered to most admitted students, this includes tuition, fees, and stipends. Our living stipend is provided in the form of a fellowship. Students are not required to secure jobs as teaching or research assistants. However, most students do during their careers as a way to supplement their funding package.

< Collapse