Joint Ph.D. Programs

Our joint Ph.D. programs include:

- Algorithms, Combinatorics, and Optimization (joint with Mathematics and Computer Science)
- Economics and Public Policy (joint with the Heinz School of Public Policy and Management)
- Management of Manufacturing and Automation (joint with the Robotics Institute)

Please read below for more information on each joint Ph.D. program.


  • Algorithms, Combinatorics and Optimization

    Related to the Ph.D. program in operations research, Carnegie Mellon offers an interdisciplinary Ph.D. program in algorithms, combinatorics and optimization. This program is administered jointly by the Tepper School of Business (operations research group), the Computer Science Department (algorithms group) and the Mathematics Department (discrete mathematics group).

    Interdisciplinary Approach

    To a great extent, the mathematics used by computer scientists and operations researchers overlap. The boundaries between operations research and computer science have become blurred. Important new theories and whole fields, like polyhedral combinatorics, have been and are being developed jointly by computer scientists, operations researchers, and applied mathematicians (who consider themselves a little bit of both). Presentations of new results on graphs and matroid theory can be heard at operations research conferences, while papers on linear programming, network flows, and matching in graphs are frequently presented at computer science conferences. The mathematical content of the papers has become greater and more diverse. Yet, in spite of this, few Ph.D. students graduate with an equally solid knowledge of all three areas.

    The Ph.D. program in algorithms, combinatorics, and optimization is intended to fill this gap. It brings together the study of the mathematical structure of discrete objects and the design and analysis of algorithms in areas such as:

    - Graph theory
    - Combinatorial optimization
    - Integer programming
    - Polyhedral theory
    - Computational algebra
    - Geometry
    - Number theory

    Course of Study

    The academic requirements are the same for all students in the program. The coordinating committee has established a challenging core curriculum in analysis, algebra, probability, linear and integer programming, graph theory, dynamic programming, convex analysis, algorithms, and complexity theory. For more information, see the separate brochure for the Algorithms, Combinatorics and Optimization program, or go to the ACO homepage.

  • Economics and Public Policy

    Within Tepper, Ph.D. students are not required to take courses, but they are required to pass qualifying examinations. Tepper students (those in this joint program who matriculate through Tepper) take the following qualifying examinations:

    - Microeconomics
    - Econometrics
    - Macroeconomics
    - Public Economics

    The microeconomics and macroeconomics qualifying exams are the same exams that all Tepper Economics Ph.D. students take. The microeconomics exam covers Microeconomics I, Microeconomics II, Game Theory and Applications, and Economics of Contracts. The macroeconomics exam covers Macroeconomics I, Dynamic Competitive Analysis, and Computational Methods for Economics. Students in the joint program may satisfy the econometrics requirement in two ways. They may satisfy the econometrics requirement in one of two ways. They may take the Tepper qualifying examination in econometrics, or they may take the Heinz quantitative requirements course sequence and take a qualifying examination based on that course sequence.

    Students with appropriate preparation prior to their entry to the program may choose to take the qualifying exams prior to the third semester, however, they must take the entire set of qualifiers as outlined above.

    Commentary on Course Requirements

    In large measure, the course requirements combine those of the separate programs. The changes are as follows:

    Tepper:

    Students will have the flexibility to take either Tepper’s or Heinz’s econometrics sequences.

    Heinz:

    The research seminar requirement is reduced from a two to one course requirement. We anticipate that public Economics will be taught in research seminar format. Further, we wanted to reduce the course work demands in an already demanding curriculum. Note that the research seminar requirement is similarly reduced in the joint statistics Ph.D. program.

  • Management of Manufacturing and Automation

    The Tepper School of Business and the Robotics Institute at Carnegie Mellon University offer a new doctoral program in the Management of Manufacturing and Automation.

    The program gives qualified students a total-system perspective on manufacturing issues. It provides students with an understanding of the management of automated manufacturing systems including robotic systems, flexible manufacturing systems and assembly systems.

    The program is particularly useful for students interested in gaining a perspective which integrates management, engineering and computer science to solve the new challenges of design, planning, operation (including real-time control) and evaluation of modern and automated manufacturing systems and industries.

    The program draws upon a broad base of techniques in operations research, including graph theory and network flows, stochastic models and control and artificial intelligence, that have been used in a diversity of areas such as computer communication networks, computer architecture, process control and robotics. These methods are amalgamated with management areas to generate approaches for solving problems of management and control in modern automated manufacturing complexes.

    Research

    The program in the Management of Manufacturing and Automation draws on the resources of both the Robotics Institute and the Tepper School of Business.

    Carnegie Mellon Robotics Institute

    The highly-acclaimed Robotics Institute is an interdepartmental research institute that conducts research and development in intelligent robots and machine systems. The Institute also facilitates the transfer of the resulting technology to industry.

    One of the major thrusts of the research program of the Institute is automation and computer-integrated manufacturing. Faculty members are conducting projects in areas such as:

    - Industrial robots and manipulators
    - Automated assembly, monitoring, inspection, and packaging of electronic and mechanical components
    - Flexible manufacturing cells
    - Intelligent information systems and integrated factory management systems
    - Robotic welding systems
    - Computer vision
    - Automatic inspection
    - Robotic machining station design

    Tepper School of Business

    The Tepper School, likewise, is highly acclaimed as one of the nation's foremost mathematically-oriented management schools, and it brings its strength in quantitative analysis to the study of management problems. The school also maintains close research interactions with state-of-the-art automated manufacturing facilities, so that students and faculty members continually test their ideas against real-world industrial realities.

    Among the projects that faculty members are now addressing in the area of Management of Manufacturing and Automation are the following:

    - Manufacturability of VLSI circuits
    - Planning, scheduling, and real-time control for electronic/computer assembly
    - Design and operation of flexible manufacturing systems/factories of the future
    - Intelligent systems for production, planning and control
    - Production control in automated automobile manufacturing and assembly

    Interdisciplinary Approach

    Students in the Management of Manufacturing and Automation program work with faculty members both from the Tepper School and from the Robotics Institute, and on projects that involve faculty members from both areas.

    This interdisciplinary focus means that students also work closely on issues in accounting, finance, economics, and marketing, and the ways in which they affect the design and operation of modern manufacturing facilities.

    Students are immediately involved in research activities and in publishing papers, often joint papers with faculty members. Because the program is small, the faculty is able to tailor programs to meet the needs of each student.