VCU Courses

College of Humanities and Sciences :: Operations Research

OPER 327/MATH 327 Mathematical Modeling

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH 200.Fundamental concepts of mathematical modeling. Topics may include differential equation models, optimization models and probabilistic models. Practical problems will be discussed throughout.

OPER 490/STAT 490 Communications in Statistics and Operations Research

Semester course; 3 lecture hours. 3 credits. Prerequisites: ENGL 200 and STAT 314 or OPER 327, or permission of the instructor.Designed to help students attain proficiency in professional and academic communication in the context of statistics and operations research. Focus on the discipline-specific communication skills necessary to excel in careers or graduate studies in these disciplines.

OPER 520/MATH 520 Game Theory and Linear Programming

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH 310.The mathematical basis of game theory and linear programming. Matrix games, linear inequalities and convexity, the mini-max theorems in linear programming, computational methods and applications.

OPER 527 Optimization I

Semester course; 3 lecture hours. 3 credits. Prerequisites: CMSC 245 or 255, MATH 310 or permission of the instructor.Introduction to optimization and mathematical programming. Course addresses fundamental concepts of optimization (such as optimality conditions and duality) as well as the construction, solution, analysis and application of linear programming and network models. Emphasis is placed on using software to solve problems as well as on understanding its underlying methodology. Integer programming models will be introduced.

OPER 528 Stochastic Simulation

Semester course; 3 lecture hours. 3 credits. Prerequisites: CMSC 245 or 255, MATH/STAT 309, and MATH 310 or equivalent.Introduces topics in discrete-event and Monte Carlo simulation. Students will develop skills related to the application of probabilistic models in real-world situations. Random number generation and random variate generation form the basis of simulation modeling and will also be covered.

OPER 591 Topics in Operations Research

Semester course; 1-3 lecture hours. 1-3 credits. May be taken more than once for credit. Prerequisite: Permission of the instructor.A detailed study of selected topics in operations research.

OPER 627 Optimization II

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER 527.Builds on the concepts addressed in OPER 527 by examining integer and nonlinear programming models. Study of interger programming focuses on advanced modeling with binary variables, solution techniques and the relationship to linear programming. Study of nonlinear programming includes discussion of special cases for which optimal solutions can be obtained and verified, as well as appropriate solution techniques for general nonlinear programs. Basic concepts of computational complexity and deterministic dynamic programming are introduced.

OPER 635 Network Models and Graph Theory

Semester course; 3 lecture hours. 3 credits. Prerequisites: CMSC 401 or permission of instructor.This course will focus on optimization models for network problems, as well as on the underlying graph theoretic structure for such models. Emphasis will be on solution procedures and applications with some discussion of related implementation issues. The course will concentrate on the study of polynomial-time algorithms for well-solved problems. May also include treatment of solution techniques for NP-hard network problems. Possible topics for the course include, but are not limited to, maximum flows/minimum cuts in networks, minimum spanning trees, minimum cost flows, matching and assignment, shortest path problems, traveling salesman problems and multicommodity flows.

OPER 636/STAT 636 Machine Learning Algorithms

Semester course; 3 lecture hours. 3 credits. Prerequisite: STAT 541 or equivalent.Includes an in-depth analysis of machine learning algorithms for data mining, equipping students with skills necessary for the design of new algorithms. Analyses will include framing algorithms as optimization problems and a probabilistic analysis of algorithms. Students will be exposed to current areas of research in the construction of data mining algorithms.

OPER 639 Practical Optimization

Semester course; 3 lecture hours. 3 credits. Prerequisites: OPER 527 and CMSC 255.The application of optimization theory toward the solution of practical problems in operations research. The use and analysis of computer programs available to solve such problems. The algorithms used in these programs will be discussed from a practical and theoretical point of view.

OPER 641 Discrete Event System Simulation

Semester course; 3 lecture hours. 3 credits. Prerequisite: STAT 541 or equivalent or permission of instructor.An introduction to the application and theoretical background of system simulation. Topics include systems concepts, modeling systems using discrete events and the modeling of manufacturing and materials handling systems, computer systems and service systems through simulation. Theoretical topics include random variable generation, model verification and validation, statistical analysis of output, variance reduction techniques and optimization via simulation. A high-level simulation language will be utilized. Students will complete and present a simulation project.

OPER 643 Decision and Risk Analysis

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH/STAT 309.This course presents the decision and risk analysis theory and methodology. Decision analysis applies to hard problems involving sequential decisions, major uncertainties, significant outcomes, and complex values. The course includes: decision structuring with influence diagrams and decision trees; modeling uncertainty with subjective probabilities; sensitivity analysis and the value of information; and modeling preferences with utility functions. Decision and risk analysis applications in business and government are considered.

OPER 645 Queuing Theory

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER 528 or STAT 503.This operations research course provides a development of some basic queuing systems. Such systems will include birth-death queues, as well as the M/G/I and GI/M/S queuing systems. Other topics may include the GI/G/I queues, overflow queues, and some basic queuing networks.

OPER 647 Multiobjective Decision Analysis

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER 643 or permission of instructor.Introduction to the mathematical foundations of multiattribute utility theory. Topics covered include: structuring objectives; tradeoffs under certainty; unidimensional utility theory; multiattribute preferences under uncertainty; preferences over time; and aggregation of individual preferences. Real world applications will be discussed throughout.

OPER 648/STAT 648 Systems Reliability Analysis

Semester course; 3 lecture hours. 3 credits. Prerequisite: STAT 541 or equivalent, or permission of instructor.An introduction to engineering reliability and risk analysis, specifically failure data analysis, maintenance problems, system reliability and probabilistic risk assessment. Applications in computer science and engineering will include stochastic characterization of wear in hardware systems and the development of failure models for software systems. Decision problems such as the optimal maintenance of repairable systems and optimal testing policies for hardware and software systems will be examined. The analysis of risk through fault trees, event trees and accident precursor analysis also will be discussed.

OPER 649/STAT 649 Statistical Quality Control

Semester course; 3 lecture hours. 3 credits. Prerequisite: STAT 541 or equivalent, or permission of instructor.Demonstrates how statistics and data analysis can be applied effectively to process control and management. Topics include the definition of quality, its measurement through statistical techniques, variable and attribute control charts, CUSUM charts, multivariate control charts, process capability analysis, design of experiments, and classical and Bayesian acceptance sampling. Statistical software will be used to apply the techniques to real-life case studies from manufacturing and service industries.

OPER 690/STAT 690 Research and Communications Seminar

Semester course; 3 lecture hours. 3 credits. Prerequisites: 9 graduate credits in operations research (OPER) and/or statistics (STAT) and permission of the instructor.Designed to help students attain proficiency in professional and academic communication and research in the context of statistics and operations research. The course focuses on the discipline-specific communication and research skills necessary to excel in careers or graduate studies in these disciplines.

OPER 691 Special Topics in Operations Research

Semester course; 1-3 lecture hours. 1-3 credits. May be taken more than once for credit. Prerequisite: Permission of the instructor.A detailed study of selected topics in operations research.

OPER 696/STAT 696 Applied Project

Semester course; variable hours (to be arranged). 1-3 credits. A total of three credits will be applied to the M.S. in Mathematical Sciences (operations research or statistics concentration). Can be repeated for credit. Prerequisite: STAT/OPER 690 or permission of the faculty adviser.Designed to allow students to apply concepts and theories learned in other courses to a practical situation. Includes the selection, written description, completion and written report of the project and a presentation of the findings. Students may not receive credit for both OPER/STAT 696 and OPER/STAT 698.

OPER 697 Directed Research

Semester course; variable hours. 1-3 credits. May be taken more than once for credit. Prerequisite: Graduate standing.Supervised individual research and study in an area not covered in the present curriculum or in one which significantly extends present coverage. Research culminates with an oral presentation and submission of a written version of this presentation to the supervising faculty member.

OPER 698 Thesis

Hours to be arranged. 1-3 credits. A total of 3 or 6 credits may be applied to the M.S. in Mathematical Sciences/Operations Research. (A total of 3 credits for an expository thesis or a total of 6 credits for a research thesis.) May be taken more than once for credit. Prerequisite: Graduate standing.Independent research culminating in the writing of the required thesis as described in this bulletin. Grade of "S," "U" or "F" may be assigned in this course.

OPER 731 Discrete Optimization

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER 627.Provides the theoretical background necessary to design and evaluate advanced solution techniques for discrete optimization problems. Topics include theory of polyhedra and valid inequalities for integer programming models, matchings, computational complexity, and sufficient conditions for integer programs to be polynomially solvable. Scheduling, packing, covering and routing models will also be examined.

OPER 732 Computational Optimization

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER 627.Offers an exploration of issues concerning the real-world application of operations research models. Topics addressed include computational complexity, advanced modeling techniques and specialized algothrims for mathematical programs. Special attention is paid to the use of callable libraries and manipulation of software features, as well as to the development of special-purpose code, designed to enhance software functionality and performance. Heuristic procedures for large-scale problems are also discussed.

OPER 736/STAT 736 Mathematics of Knowledge and Search Engines

Semester course; 3 lecture hours. 3 credits. Prerequisite: STAT 541 or equivalent.Investigates the mathematics, methods and algorithms for searching for and extracting structures of interest (knowledge) from large and possibly high-dimensional datasets. The motivation is the rapid and phenomenal growth of the search engine (as demonstrated by Google) as a major tool for search on the Internet, which has impacted commerce, education and the study of social, financial and scientific datasets. The development of the mathematical and statistical learning algorithms behind these search engines has led to advances in how large, high-dimensional datasets can be effectively analyzed for the extraction of knowledge.

OPER 741 Discrete Event System Simulation II

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER 641.Introduces the current areas of research in the field of discrete event simulation. Simulation is applied to modeling systems where closed-form mathematical solutions cannot be obtained. Includes current research in modeling input uncertainty, Bayesian simulation, selecting the best simulated system and simulation optimization.

OPER 743 Decision Analysis II

Semester course; 3 lecture hours. 3 credits. Prerequisite: OPER 643.Introduces the current areas of research in the field of decision analysis, which applies to hard problems involving sequential decisions, major uncertainties, significant outcomes and complex values. Includes current research in decision structuring and representation, modeling uncertainty with subjective probabilities, modeling preferences with utility functions and modeling multiattribute preferences.

OPER 791 Special Topics in Operations Research

Semester course; 1-3 lecture hours. 1-3 credits. May be repeated for credit. Prerequisite: permission of instructor.A detailed study of selected advanced topics in operations research.

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