Ph.D. Program in Operations Research
The course of study includes analytics leading to decision-making algorithms and the development of new models for management science applications and controlled experimentation.
The Tepper School's doctoral program in operations research (OR) is designed to encourage students to make contributions toward basic scientific knowledge in the area. This knowledge can take several forms including:
- The derivations of fundamental results of an analytical or mathematical nature that lead to the development of algorithms for aiding decision-making
- The development of new kinds of models appropriate for management science applications
- Controlled experimentation that leads to empirical results that make efficiency comparisons possible among algorithms
Careful attention is also paid to obtaining knowledge of the substantive areas to which operations research can be applied, such as production, finance, marketing or economics. A major goal of the program is to train students to recognize operations research problems in real-world situations, and to give them the opportunity to learn about the implementation of operations research models in one or more of these substantive areas.
Course of Study
The basic operations research courses offered include: linear, nonlinear, integer and dynamic programming; network and graph theory; optimal control; convex analysis; and stochastic models. In most cases, each course is taught by a faculty member who is actively pursuing research in the subject area. Since classes are usually small, students frequently meet informally with their instructors. The third semester competence examination is based on the areas covered in these courses.
The research papers assigned for the first and second summers of graduate study are designed to give students an early introduction to research work. The paper may be done individually or jointly with other students or faculty members. Easy interaction in the Tepper School with researchers in the other areas of business and economics and in such related areas as computer science and statistics encourages the application of operations research in imaginative new directions.
In many cases, work on the summer paper leads to the work on the Ph.D. dissertation, which can begin as soon as the student has passed the third-semester examination.
Almost invariably, by the end of their second year, if not earlier, students have already worked on professional problems with some of the faculty. For this reason, student working papers written in collaboration with a faculty member are common.
Carnegie Mellon has pioneered several important developments in both theoretical and applied operations research. Geometric programming, chance constrained programming, and the applications of linear programming to capital budgeting and cost management were among the accomplishments of the '50s and early '60s. Since 1968, when the doctoral program in operations research was started, the Tepper School has initiated several new developments in integer and nonconvex programming, enumerative methods, cutting plane theory, disjunctive programming, combinatorial programming, networks, scheduling and control theory models. Examples on the Selected Research Topics page illustrate the basic research currently in progress, and examples of new operations research applications can be found elsewhere on the Doctoral Program website.
- Mixed-Integer Programming: Lift-and-Project
- Disjunctive Programming
- Projections Methods in Discrete Optimization
- Branch and Price
- Perfect, Ideal and Balanced Matrices
- The Structure of Scheduling Polyhedra
- Traveling Salesman and Related Problems
- Approximation Algorithms
- Network Design
- Computational Molecular Biology
- Connections with Artificial Intelligence
- Logical Inference
- New Version of the Simplex Method
- Combinatorial Optimization with Parallel Computers
- Cultural Factors
- Ethics of Artificial Intelligence
Many of our students are very active in the Carnegie Mellon INFORMS Student Chapter.