OR - Operations Research

OR (ISE) 501Introduction to Operations ResearchUNITS: 3 - Offered in Fall and Spring
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 502Introduction to Systems TheoryUNITS: 3 - Offered in Fall Only
Prerequisite: MA 341, ST 371
Modeling of systems and their dynamics in variety of contexts: systems identification, controllability and observability; operational methods and their use in modeling; analysis and synthesis of systems; optimization.


OR (MA) 504Introduction to Mathematical ProgrammingUNITS: 3 - Offered in Spring Only
Prerequisite: MA 242, MA 405
Basic concepts of linear, nonlinear and dynamic programming theory. Not for majors in OR at Ph.D. level.


OR (ISE) (MA) 505Linear ProgrammingUNITS: 3 - Offered in Fall and Spring
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 506Algorithmic Methods in Nonlinear ProgrammingUNITS: 3 - Offered in Spring Only
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 (CHE) 527Optimization of Engineering ProcessesUNITS: 3 - Offered Alternate Years, Offered in Fall Only
Prerequisite: CHE 451 or OR 501, FORTRAN programming
Formulation and solution of process optimization problems, with emphasis on nonlinear programming techniques. Computer implementation of optimization algorithms and structuring of process models to increase computational efficiency.


OR (E) (MA) 531Dynamic Systems and Multivariable Control IUNITS: 3 - Offered in Fall Only
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 (CSC) (MA) 565Graph TheoryUNITS: 3 - Offered Alternate Even Years, Offered in Fall Only
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 (CSC) (ECE) 579Introduction to Computer Performance ModelingUNITS: 3 - Offered in Fall Only
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 591Special Topics in Operations ResearchUNITS: 1-3 - Offered in Fall Spring Summer
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 601Seminar in Operations ResearchUNITS: 1 - No Course Evaluation, Offered in Fall and Spring
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 610Special Topics in Operations ResearchUNITS: 1-3 - No Course Evaluation, Offered in Fall Spring Summer
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 615Advanced Special Topics in Operations ResearchUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: OR 501, OR(IE,MA) 505
Course allows individual students or small groups of students to take on studies of special areas in OR which fit into their particular program and which may not be covered by other OR courses. The work directed by a qualified faculty member and in some instances by visiting professors. The subject matter in any year dependent on students and faculty members.


OR 652Practicum in Operations ResearchUNITS: 1-3 - No Course Evaluation, Offered in Fall and Spring
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 685Master's Supervised TeachingUNITS: 1-3 - Offered in Fall Spring Summer
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 688Non-Thesis Masters Continuous Registration - Half Time RegistrationUNITS: 1 - No Course Evaluation, Offered in Fall Spring Summer
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 689Non-Thesis Master Continuous Registration - Full Time RegistrationUNITS: 3 - No Course Evaluation, Offered in Fall Spring Summer
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 690Master's ExaminationUNITS: 1-6 - No Course Evaluation, Offered in Fall Spring Summer
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 693Master's Supervised ResearchUNITS: 1-9 - No Course Evaluation, Offered in Fall Spring Summer
Prerequisite: Master's student
Instruction in research and research under the mentorship of a member of the Graduate Faculty.


OR 695Master's Thesis ResearchUNITS: 1-9 - No Course Evaluation, Offered in Fall and Spring
Prerequisite: Master's student
Thesis research.


OR 696Summer Thesis ResearchUNITS: 1 - Offered in Summer
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 699Master's Thesis PreparationUNITS: 1-3 - No Course Evaluation
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 705Large-Scale Linear Programming SystemsUNITS: 3 - Offered Alternate Years, Offered in Spring Only
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 (MA) (ST) 706Nonlinear ProgrammingUNITS: 3 - Offered in Fall and Spring
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 (ISE) (MA) 708Integer ProgrammingUNITS: 3 - Offered Alternate Years, Offered in Spring Only
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 (ISE) 709Dynamic ProgrammingUNITS: 3 - Offered in Spring Only
Prerequisite: MA 405, ST 421
Introduction to theory and computational aspects of dynamic programming and its application to sequential decision problems.


OR 710Advanced Dynamic ProgrammingUNITS: 3 - Offered Alternate Years, Offered in Fall Only
Prerequisite: OR 709, MA 546
Introduction to measure theoretic concepts, review of finite state Markov processes, theory of Markovian programming, discrete decision processes, continuous time dynamic programming, relation to calculus of variation and the Maximum Principle. Emphasis throughout on recent theoretical development in the field.


OR (MA) 719Vector Space Methods in System OptimizationUNITS: 3 - Offered in Fall Only
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 (BMA) (ST) 722Decision Analytic ModelingUNITS: 4 - Offered Alternate Years, Offered in Fall Only
Prerequisite: MA 421 or ST 421 plus ST 511or ST 516
Analysis of decision problems involving risk and uncertainty. Modeling decision process; Bayesian probability analysis, use of information, and subjective probability; utility theory and multiattribute utility assessment; dynamics of interacting with decision makers and subject matter specialists; decision trees, influence diagrams and other tools to assist in modeling decision problems. Laboratory develops skill in implementing methodology.


OR (ISE) 726Theory of Activity NetworksUNITS: 3 - Offered Alternate Years, Offered in Spring Only
Prerequisite: OR 501, OR(IE,MA) 505
Introduction to graph theory and network theory. In-depth discussion of theory underlying (1) deterministic activity networks (CPM): optimal time-cost trade offs; the problem of scarce resources; (2) probabilistic activity networks (PERT): critical evaluation of underlying assumptions; (3) generalized activity networks (GERT, GAN): applications of signal flow graphs and semi-Markov process to probabilistic branching; relation to the theory of scheduling.


OR (E) (MA) 731Dynamic Systems and Multivariable Control IIUNITS: 3 - Offered Alternate Years, Offered in Spring Only
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 (ISE) 760Applied Stochastic Models in Industrial EngineeringUNITS: 3 - Offered in Fall Only
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 (ISE) 761Queues and Stochastic Service SystemsUNITS: 3 - Offered in Fall and Spring
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 (CSC) (ISE) 762Computer Simulation TechniquesUNITS: 3 - Offered in Fall Only
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 (ISE) (MA) 766Network FlowsUNITS: 3 - Offered Alternate Years, Offered in Spring Only
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 (ISE) 772Stochastic Simulation Design and AnalysisUNITS: 3 - Offered in Spring Only
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 (BMA) (MA) (ST) 773Stochastic ModelingUNITS: 3 - Offered Alternate Years, Offered in Spring Only
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 (BMA) (MA) 774Partial Differential Equation Modeling in BiologyUNITS: 3 - Offered in Spring Only
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 (ISE) (MA) 790Advanced Special Topics System OptimizationUNITS: 1-3 - Offered in Fall and Spring
Advanced topics in some phase of system optimization using traditional course format. Identification of various specific topics and prerequisites for each section from term to term.


OR 791Advanced Special TopicsUNITS: 1-3 - Offered in Fall and Spring


OR 801Seminar in Operations ResearchUNITS: 1 - No Course Evaluation, Offered in Fall and Spring
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 810Special Topics in Operations ResearchUNITS: 1-3 - No Course Evaluation, Offered in Fall Spring Summer
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 (ISE) (MA) 812Special Topics in Mathematical ProgrammingUNITS: 1-3 - Offered Alternate Years, Offered in Spring Only
Prerequisite: IE(MA,OR) 505
Study of special advanced topics in area of mathematical programming. Discussion of new techniques and current research in this area. The faculty responsible for this course select areas to be covered during semester according to their preference and interest. This course not necessarily taught by an individual faculty member but can, on occasion, be joint effort of several faculty members from this university as well as visiting faculty from other institutions. To date, a course of Theory of Networks and another on Integer Programming offered under the umbrella of this course. Anticipation that these two topics will be repeated in future together with other topics.


OR 815Special Topics in Operations ResearchUNITS: 3 - Offered in Fall Spring Summer
Prerequisite: OR 501, OR(IE,MA) 505
Course allows individual students or small groups of students to take on studies of special areas in OR which fit into their particular program and which may not be covered by other OR courses. The work directed by a qualified faculty member and in some instances by visiting professors. The subject matter in any year dependent on students and faculty members. Credits Arranged.


OR (ISE) (MA) 816Advanced Special Topics Sys OptUNITS: 1-3 - Offered in Fall and Spring
Advanced topics in some phase of system optimization. Identification of various specific topics and prerequisite for each section from term to term.


OR 852Practicum in Operations ResearchUNITS: 1-3 - Offered in Fall and Spring
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 (ISE) 862Scheduling and RoutingUNITS: 3 - Offered Alternate Years, Offered in Spring Only
Prerequisite: IE 723, OR 501, OR(MA) 504
In-depth study of analytical models of problems arising in the scheduling of single and parallel processors, flow shops and job shops and in routing and scheduling of delivery vehicles. Emphasis on analysis, solution methodologies and underlying theory. Discussion of recent trends and outstanding problems from both theoretical and applied points of view.


OR 885Doctoral Supervised TeachingUNITS: 1-3 - Offered in Fall Spring Summer
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 890Doctoral Preliminary ExaminationUNITS: 1-9 - No Course Evaluation, Offered in Fall Spring Summer
Prerequisite: Doctoral student
For students who are preparing for and taking written and/or oral preliminary exams.


OR 893Doctoral Supervised ResearchUNITS: 1-9 - No Course Evaluation, Offered in Fall Spring Summer
Prerequisite: Doctoral student
Instruction in research and research under the mentorship of a member of the Graduate Faculty.


OR 895Doctoral Dissertation ResearchUNITS: 1-9 - No Course Evaluation, Offered in Fall Spring Summer
Prerequisite: Doctoral student
Dissertation research.


OR 896Summer Dissertation ResearchUNITS: 1 - Offered in Summer
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 899Doctoral Dissertation PreparationUNITS: 1-3 - No Course Evaluation, Offered in Fall Spring Summer
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.