Doctor of Philosophy (Ph.D.) in Operations Research

Doctoral students majoring in operations research concentrate in one of three areas: Applied probability and statistics stresses the techniques and associated underlying theory of probability and statistics, particularly as applied to problems in science, finance, and engineering. The techniques emphasized are those associated with applied stochastic processes (for example, mathematical finance, queuing theory, traffic theory, and inventory theory) and statistics (including statistical decision theory, reliability theory, analysis of life data, and the statistical aspects of the design, analysis, and interpretation of experiments and of ranking and selection theory). Manufacturing systems engineering is concerned with the analysis and design of complex manufacturing and distribution systems. Problems studied include the establishment of inventory-control policies in multistage production and distribution systems; design of manufacturing plants with optimal amounts of equipment and optimal materials-handling systems; planning and scheduling of production in large-scale, multi-item, multi location systems; and economic analysis of engineering processes. Students use modern analytic and computer techniques in the design and analysis of such systems. Students are expected to understand the manufacturing processes associated with some type of industry. Research, which may involve development of new mathematical methodology, is often conducted directly with a cooperating company, for example, in automotive or semiconductor manufacturing. Mathematical programming concentrates on optimization, including linear, nonlinear, integer, and combinatorial programming; network flows; problems of scheduling and sequencing; and discrete and computational geometry. Research ranges from the development and applications of computational algorithms (exact and approximate) to the associated studies of duality theory, convex and variational analysis, polyhedra, combinatorics, and graph theory. Doctoral students also select two minor subjects for the Ph.D. degree, one of which must be outside the field. A minor may be in operations research or in a subject offered in another field, such as computer science, econometrics and economic statistics, environmental systems engineering, managerial economics, mathematics, or planning theory and systems analysis. In addition to the examinations required by the Graduate School, the field requires a qualifying examination for Ph.D. degree candidates, normally taken in the third term of graduate study at Cornell.