Operations Research (OR)
This will focus on the use of optimization in Medicine. The main goal of this course is for you to develop an understanding of the recent methodological literature on optimization methods applied to medical decision making. We will cover a broad range of topics, both from the methodological perspective (study models using integer programming, dynamic programming, simulation, etc.) and from the public policy/public health perspective (who are the stake holders, what are the relevant questions modelers can answer, how is the patient taken into account, etc.).
Typically offered in Spring only
This course intends to provide a comprehensive treatment on the use of quantitative modeling for decision making and best practices in the service industries. The goal of this class is to teach students to able to identify, understand, and analyze services; and acquire the quantitative skills necessary to model key decisions and performance metrics associated with services. Students will be exposed both to classical and contemporary examples of challenges and opportunities that arise when working in the service sector.
Prerequisite: 滨厂贰听361
Typically offered in Spring only
The course aims to introduce the various types of operations research models and techniques. We will address how to formulate a wide range of decision problems using an appropriate mathematical programming model and solve them using an appropriate algorithm or solver. The emphasis will be given to Linear Programming, Network Models, and Integer Programming. Some example applications of mathematical programming to be covered in this class include production planning, network analysis, project scheduling, logistics network design, fixed charge problems, set covering problem, etc.
Prerequisites: An introductory course in linear algebra and calculus.
Typically offered in Fall, Spring, and Summer
Basic concepts of linear, nonlinear and dynamic programming theory. Not for majors in OR at Ph.D. level.
Typically offered in Fall only
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.
Prerequisite: An introductory linear algebra course similar to 惭础听405
Typically offered in Fall only
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.
Prerequisite: Linear algebra or similar coursework (similar to 惭础听303, 惭础听405), and knowledge of a computer language, such as Python, MATLAB, Julia, for example.
Typically offered in Fall only
This will focus on the use of optimization in Medicine. The main goal of this course is for you to develop an understanding of the recent methodological literature on optimization methods applied to medical decision making. We will cover a broad range of topics, both from the methodological perspective (study models using integer programming, dynamic programming, simulation, etc.) and from the public policy/public health perspective (who are the stake holders, what are the relevant questions modelers can answer, how is the patient taken into account, etc.).
Typically offered in Spring only
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.
Typically offered in Fall only
This course intends to provide a comprehensive treatment on the use of quantitative modeling for decision making and best practices in the service industries. The goal of this class is to teach students to able to identify, understand, and analyze services; and acquire the quantitative skills necessary to model key decisions and performance metrics associated with services. Students will be exposed both to classical and contemporary examples of challenges and opportunities that arise when working in the service sector.
Prerequisite: 滨厂贰听361
Typically offered in Spring only
Computational approaches to support civil planning, analysis, evaluation and design. Applications to various areas of civil engineering, including construction, structures, transportation and water resources.
Typically offered in Fall only
Quantitative methods of measuring the reliability of complex engineering systems, including statistical analysis, stochastic process, and optimization theory. Emphasis on solving real-world problems through hands-on experience from class projects.
Typically offered in Fall and Spring
ISE/翱搁听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.
Typically offered in Fall only
This course concentrates on design, construction, and use of discrete/continuous simulation object-based models employing the SIMIO software, with application to manufacturing, service, and healthcare. The focus is on methods for modeling and analyzing complex problems using simulation objects. Analysis includes data-based modeling, process design, input modeling, output analysis, and the use of 3D animation with other graphical displays. Object-oriented modeling is used to extend models and enhance re-usability.
Typically offered in Spring only
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.
Typically offered in Spring only
This course is offered alternate even years
Workload characterization, collection and analysis of performance data, instrumentation, tuning, analytic models including queuing network models and operational analysis, economic considerations.
Prerequisite: CSC 312 or ECE 206 and 惭础听421
Typically offered in Fall and Spring
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.
Typically offered in Fall, Spring, and Summer
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.
Prerequisite: OR Major or OR Minor
Typically offered in Fall and Spring
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.
Typically offered in Fall, Spring, and Summer
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.
Typically offered in Summer only
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.
Prerequisite: Master's student
Typically offered in Spring only
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.
Prerequisite: Master's student
Typically offered in Spring only
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.
Prerequisite: Master's student
Typically offered in Summer only
Instruction in research and research under the mentorship of a member of the Graduate Faculty.
Prerequisite: Master's student
Typically offered in Fall and Spring
Thesis research.
Prerequisite: Master's student
Typically offered in Fall, Spring, and Summer
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.
Prerequisite: Master's student
Typically offered in Summer only
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.
Prerequisite: Master's student
Typically offered in Fall, Spring, and Summer
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.
Prerequisite: 翱搁听505 and FORTRAN programming experience
Typically offered in Spring only
This course is offered alternate years
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.
Prerequisite: OR(IE,MA) 505 and 惭础听425
Typically offered in Spring only
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.
Typically offered in Spring only
This course is offered alternate years
Introduction to theory and computational aspects of dynamic programming and its application to sequential decision problems.
Typically offered in Spring only
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.
Typically offered in Fall only
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.
Prerequisite: OR(E,MA) 531
Typically offered in Spring only
This course is offered alternate years
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.
Prerequisite: 厂罢听511
Typically offered in Fall only
This course is offered alternate years
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.
Typically offered in Spring only
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.
Typically offered in Spring only
Basic discrete event simulation methodology: random number generators, generating random objects, design of discrete event simulation, validation, analysis of simulation output, variance reduction techniques, Markov chain Monte Carlo, simulation optimization. The course has computer assignments and projects. This course is a sequel to ISE/翱搁听760 Stochastic Models which serves as a prerequisite. This is NOT a software based course! Students who are looking for a class on simulation software, such as Arena and Simio, are recommended to take 滨厂贰听562 (master-level simulation class).
Students should have completed a course on stochastic models (similar to 滨厂贰听560 or 滨厂贰听760) and have a working knowledge of a programming language (e.g., Python, Matlab, R, or others).
Typically offered in Fall and Spring
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.
Prerequisite: OR(IE,MA) 505
Typically offered in Spring only
This course is offered alternate years
This course is methodologically focused and a continuation of 滨厂贰听762 in Monte Carlo methods. The topics include, but are not limited to, Quasi-Monte Carlo, importance sampling and other advanced variance reduction approaches, derivative estimation, and advanced simulation optimization in continuous and finite spaces. While the application of these techniques to actual simulations is practiced as assignments, the discussion on simulation software and programming will be minimal. A current topic research presentation/paper required.
Prerequisite: (CSC,ECE,IE,OR) 762 and 厂罢听516
Typically offered in Spring only
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.
Prerequisite: 叠惭础听772 or ST (MA) 746
Typically offered in Spring only
This course is offered alternate years
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.
Typically offered in Spring only
Typically offered in Fall and Spring
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.
Prerequisite: OR Major or OR Minor
Typically offered in Fall and Spring
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.
Typically offered in Fall, Spring, and Summer
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.
Typically offered in Summer only
For students who are preparing for and taking written and/or oral preliminary exams.
Prerequisite: Doctoral student
Typically offered in Summer only
Instruction in research and research under the mentorship of a member of the Graduate Faculty.
Prerequisite: Doctoral student
Typically offered in Fall and Spring
Dissertation research.
Prerequisite: Doctoral student
Typically offered in Fall, Spring, and Summer
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.
Prerequisite: Doctoral student
Typically offered in Summer only
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.
Prerequisite: Doctoral student
Typically offered in Spring and Summer