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Operations Research (OR)

  • Courses
  • OR - Operations Research Courses

    OR 501 Introduction to Operations Research 3.
    Prerequisite: MA 421 or ST 421 or ST 371 and ST 372.

    OR Approach: modeling, constraints, objective and criterion. Problems of multiple criteria, optimization, model validation and systems design. OR Methodology: mathematical programming; optimum seeking; simulation, gaming; heuristic programming. Examples, OR Applications: theory of inventory; economic ordering under deterministic and stochastic demand. Production smoothing problem; linear and quadratic cost functions. Waiting line problems: single and multiple servers with Poisson input and output. Theory of games for two-person competitive situations. Project management through PERT-CPM.

    OR 504 Introduction to Mathematical Programming 3.
    Prerequisite: MA 242, MA 405.

    Basic concepts of linear, nonlinear and dynamic programming theory. Not for majors in OR at Ph.D. level.

    OR 505 Linear Programming 3.
    Prerequisite: MA 405.

    Introduction including: applications to economics and engineering; the simplex and interior-point methods; parametric programming and post-optimality analysis; duality matrix games, linear systems solvability theory and linear systems duality theory; polyhedral sets and cones, including their convexity and separation properties and dual representations; equilibrium prices, Lagrange multipliers, subgradients and sensitivity analysis.

    OR 506 Algorithmic Methods in Nonlinear Programming 3.
    Prerequisite: MA 301, MA 405, knowledge of computer language, such as FORTRAN or PL1.

    Introduction to methods for obtaining approximate solutions to unconstrained and constrained minimization problems of moderate size. Emphasis on geometrical interpretation and actual coordinate descent, steepest descent, Newton and quasi-Newton methods, conjugate gradient search, gradient projection and penalty function methods for constrained problems. Specialized problems and algorithms treated as time permits.

    OR 531 Dynamic Systems and Multivariable Control I 3.
    Prerequisite: MA 341, MA 405.

    Introduction to modeling, analysis and control of linear discrete-time and continuous-time dynamical systems. State space representations and transfer methods. Controllability and observability. Realization. Applications to biological, chemical, economic, electrical, mechanical and sociological systems.

    OR 537 Computer Methods and Applications 3.
    Prerequisite: CSC 112 and (MA 341 or MA 305).

    Computational approaches to support civil planning, analysis, evaluation and design. Applications to various areas of civil engineering, including construction, structures, transportation and water resources.

    OR 560 Stochastic Models in Industrial Engineering 3.

    ISE/OR 560 will introduce mathematical modeling, analysis, and solution procedures applicable to uncertain (stochastic) production and service systems. Methodologies covered include probability theory and stochastic processes including discrete and continuous Markov processes. Applications relate to design and analysis of problems, capacity planning, inventory control, waiting lines, and service systems.

    OR 565 Graph Theory 3.
    Prerequisite: MA 231 or MA 405.

    Basic concepts of graph theory. Trees and forests. Vector spaces associated with a graph. Representation of graphs by binary matrices and list structures. Traversability. Connectivity. Matchings and assignment problems. Planar graphs. Colorability. Directed graphs. Applications of graph theory with emphasis on organizing problems in a form suitable for computer solution.

    OR 579 Introduction to Computer Performance Modeling 3.
    Prerequisite: CSC 312 and MA 421, Corequisite: CSC 501.

    Workload characterization, collection and analysis of performance data, instrumentation, tuning, analytic models including queuing network models and operational analysis, economic considerations.

    OR 591 Special Topics in Operations Research 1-6.

    Individual or small group studies of special areas of OR which fit into students' programs of study and which may not be covered by other OR courses. Furthermore, course serves as a vehicle for introducing new or specialized topics at introductory graduate level.

    OR 601 Seminar in Operations Research 1.
    Prerequisite: OR Major or OR Minor.

    Seminar discussion of operations research problems. Case analyses and reports. Graduate students with minors or majors in operations research expected to attend throughout period of their residence.

    OR 610 Special Topics in Operations Research 1-6.

    Individual or small group studies of special areas of OR which fit into students' programs of study and which may not be covered by other OR courses. Furthermore, course serves as a vehicle for introducing new or specialized topics at introductory graduate level.

    OR 652 Practicum in Operations Research 1-3.
    Prerequisite: OR 501, OR 505, OR 709 and OR 761.

    Practicum in problem solving in industry applying applicable OR methodologies. Practical experience in diagnosing and solving problems in operational systems at either an industrial site or at NC State.

    OR 685 Master's Supervised Teaching 1-3.
    Prerequisite: Master's student.

    Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.

    OR 688 Non-Thesis Masters Continuous Registration - Half Time Registration 1.
    Prerequisite: Master's student.

    For students in non-thesis master's programs who have completed all credit hour requirements for their degree but need to maintain half-time continuous registration to complete incomplete grades, projects, final master's exam, etc.

    OR 689 Non-Thesis Master Continuous Registration - Full Time Registration 3.
    Prerequisite: Master's student.

    For students in non-thesis master's programs who have completed all credit hour requirements for their degree but need to maintain full-time continuous registration to complete incomplete grades, projects, final master's exam, etc. Students may register for this course a maximum of one semester.

    OR 690 Master's Examination 1-9.
    Prerequisite: Master's student.

    For students in non thesis master's programs who have completed all other requirements of the degree except preparing for and taking the final master's exam.

    OR 693 Master's Supervised Research 1-9.
    Prerequisite: Master's student.

    Instruction in research and research under the mentorship of a member of the Graduate Faculty.

    OR 695 Master's Thesis Research 1-9.
    Prerequisite: Master's student.

    Thesis research.

    OR 696 Summer Thesis Research 1.
    Prerequisite: Master's student.

    For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.

    OR 699 Master's Thesis Preparation 1-9.
    Prerequisite: Master's student.

    For student who have completed all credit hour requirements and full-time enrollment for the master's degree and are writing and defending their theses.

    OR 705 Large-Scale Linear Programming Systems 3.
    Prerequisite: OR 505 and FORTRAN programming experience.

    Specialized algorithms for efficient solution of large-scale LP problems. Parametric programming, bounded variable algorithms, generalized upper bounding, decomposition, matrix factorization and sparse matrix techniques. Emphasis on gaining firsthand practical experience with current computer codes and computational procedures.

    OR 706 Nonlinear Programming 3.
    Prerequisite: OR(IE,MA) 505 and MA 425.

    An advanced mathematical treatment of analytical and algorithmic aspects of finite dimensional nonlinear programming. Including an examination of structure and effectiveness of computational methods for unconstrained and constrained minimization. Special attention directed toward current research and recent developments in the field.

    OR 708 Integer Programming 3.
    Prerequisite: MA 405, OR (MA,IE) 505, Corequisite: Some familiarity with computers (e.g., CSC 112).

    General integer programming problems and principal methods of solving them. Emphasis on intuitive presentation of ideas underlying various algorithms rather than detailed description of computer codes. Students have some "hands on" computing experience that should enable them to adapt ideas presented in course to integer programming problems they may encounter.

    OR 709 Dynamic Programming 3.
    Prerequisite: MA 405, ST 421.

    Introduction to theory and computational aspects of dynamic programming and its application to sequential decision problems.

    OR 719 Vector Space Methods in System Optimization 3.
    Prerequisite: MA 405, 511.

    Introduction to algebraic and function-analytic concepts used in system modeling and optimization: vector space, linear mappings, spectral decomposition, adjoints, orthogonal projection, quality, fixed points and differentials. Emphasis on geometricinsight. Topics include least square optimization of linear systems, minimum norm problems in Banach space, linearization in Hilbert space, iterative solution of system equations and optimization problems. Broad range of applications in operations research and system engineering including control theory, mathematical programming, econometrics, statistical estimation, circuit theory and numerical analysis.

    OR 731 Dynamic Systems and Multivariable Control II 3.
    Prerequisite: OR(E,MA) 531.

    Stability of equilibrium points for nonlinear systems. Liapunov functions. Unconstrained and constrained optimal control problems. Pontryagin's maximum principle and dynamic programming. Computation with gradient methods and Newton methods. Multidisciplinary applications.

    OR 747 Reliability Engineering 3.
    Prerequisite: ST 511.

    Introduction to basic concepts of reliability engineering. Application of probability and statistics to estimate reliability of industrial systems; development of reliability measures; analysis of static and dynamic reliability models; development and analysis of fault trees; analysis of Markovian and non-Markovian models; and optimization of reliability models.

    OR 760 Applied Stochastic Models in Industrial Engineering 3.
    Prerequisite: MA 303, ST 371.

    Formulation and analysis of stochastic models with particular emphasis on applications in industrial engineering; univariate, multivariate and conditional probability distributions; unconditional and conditional expectations; elements of stochastic processes; moment-generating functions; concepts of stochastic convergence; limit theorems; homogeneous, nonhomogeneous and compound Poisson processes; basic renewal theory; transient and steady-state properties of Markov processes in discrete and continuous time.

    OR 761 Queues and Stochastic Service Systems 3.

    Introduction of general concepts of stochastic processes. Poisson processes, Markov processes and renewal theory. Usage of these in analysis of queues, from with a completely memoryless queue to one with general parameters. Applications to many engineering problems.

    OR 762 Computer Simulation Techniques 3.

    Basic discrete event simulation methodology: random number generators, simulation designs, validation, analysis of simulation output. Applications to various areas of scientific modeling. Simulation language such as SLAM and GPSS. Computer assignments and projects.

    OR 766 Network Flows 3.
    Prerequisite: OR(IE,MA) 505.

    Study of problems of flows in networks. These problems include the determination of shortest chain, maximal flow and minimal cost flow in networks. Relationship between network flows and linear programming developed as well as problems with nonlinear cost functions, multi-commodity flows and problem of network synthesis.

    OR 772 Stochastic Simulation Design and Analysis 3.
    Prerequisite: (CSC,ECE,IE,OR) 762 and ST 516.

    Advanced topics in stochastic system simulation, including random variate generation, output estimation for stationary and non-stationary models, performance optimization techniques, variance reduction approaches. Student application of these techniques to actual simulations. A current topic research paper required.

    OR 773 Stochastic Modeling 3.
    Prerequisite: BMA 772 or ST (MA) 746.

    Survey of modeling approaches and analysis methods for data from continuous state random processes. Emphasis on differential and difference equations with noisy input. Doob-Meyer decomposition of process into its signal and noise components. Examples from biological and physical sciences, and engineering. Student project.

    OR 774 Partial Differential Equation Modeling in Biology 3.
    Prerequisite: BMA 771 or MA/OR 731; BMA 772 or MA 401 or MA 501.

    Modeling with and analysis of partial differential equations as applied to real problems in biology. Review of diffusion and conservation laws. Waves and pattern formation. Chemotaxis and other forms of cell and organism movement. Introduction to solid and fluid mechanics/dynamics. Introductory numerical methods. Scaling. Perturbations, Asymptotics, Cartesian, polar and spherical geometries. Case studies.

    OR 791 Advanced Special Topics 1-6.

    OR 801 Seminar in Operations Research 1.
    Prerequisite: OR Major or OR Minor.

    Seminar discussion of operations research problems. Case analyses and reports. Graduate students with minors or majors in operations research expected to attend throughout period of their residence.

    OR 810 Special Topics in Operations Research 1-6.

    Individual or small group studies of special areas of OR which fit into students' programs of study and which may not be covered by other OR courses. Furthermore, course serves as a vehicle for introducing new or specialized topics at introductory graduate level.

    OR 852 Practicum in Operations Research 1-3.
    Prerequisite: OR 501, OR 505, OR 709 and OR 761.

    Practicum in problem solving in industry applying applicable OR methodologies. Practical experience in diagnosing and solving problems in operational systems at either an industrial site or at NC State.

    OR 885 Doctoral Supervised Teaching 1-3.
    Prerequisite: Doctoral student.

    Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.

    OR 890 Doctoral Preliminary Examination 1-9.
    Prerequisite: Doctoral student.

    For students who are preparing for and taking written and/or oral preliminary exams.

    OR 893 Doctoral Supervised Research 1-9.
    Prerequisite: Doctoral student.

    Instruction in research and research under the mentorship of a member of the Graduate Faculty.

    OR 895 Doctoral Dissertation Research 1-9.
    Prerequisite: Doctoral student.

    Dissertation research.

    OR 896 Summer Dissertation Research 1.
    Prerequisite: Doctoral student.

    For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.

    OR 899 Doctoral Dissertation Preparation 1-9.
    Prerequisite: Doctoral student.

    For students who have completed all credit hour, full-time enrollment, preliminary examination, and residency requirements for the doctoral degree, and are writing and defending their dissertations.