Carnegie Mellon University

Requirements for a Ph.D. in Operations Research

The requirements for the Ph.D. in Operations Research include:

  • Course work
  • Third semester qualifying examinations
  • First and second year papers
  • Ph.D. dissertation

A normal course load involves taking 120 units during the first two years, including core Operations Research courses and a minor area of concentration. Courses that run over a mini are worth 6 units.

The purpose of the minor requirement is to broaden the students’ knowledge to make them capable of teaching a wider range of courses and to enhance their research capabilities. The needs and preferences of individuals are recognized; therefore, the courses they take can vary. Examples of areas of concentration for the minor requirement include:

  • Statistics
  • Computer Science
  • Operations Management
  • Finance
  • Marketing
  • Machine Learning

At least 18 units should be taken in the minor area. Students with appropriate preparation prior to their entry to the program may take the qualifying exams prior to the third semester point if they choose, but they must take the entire set of qualifiers in the Operations Research area of study. The qualifying exams consist of eight questions, five of which are mandatory while the other three are chosen from a list of six.

Core Courses

  • Linear Programming
  • Graph Theory
  • Integer Programming
  • Stochastic Processes (e.g. Performance Modeling)
  • Modern Convex Optimization

Plus three from the following list:

  • Advanced Graph Theory
  • Convex Analysis
  • Constraint Programming
  • Advanced Linear Programming
  • Advanced Integer Programming
  • Nonlinear Programming

Additional Electives in Operations Research at the Tepper School

  • Combinatorial Optimization
  • Convex Polytopes
  • Dynamic Programming
  • Open Source Software for Optimization
  • Social, Economic and Information Networks

Students are encouraged to also take electives in other departments on campus, such as Computer Science or Mathematical Sciences.

Example of a Course Sequence

Year 1

M1: Linear Programming, Graph Theory, Performance Modeling

M2: Advanced Graph Theory OR Advanced LP, Constraint Programming OR Convex Analysis, Performance Modeling

M3: Integer Programming, Convex Optimization, course in minor area

M4: Advanced IP, Nonlinear Programming, course in minor area

Year 2

M1: Elective, course in minor area

M2: Advanced Graph Theory OR Advanced LP, Constraint Programming OR Convex Analysis

M3: Elective, course in minor area

M4: Elective, elective