George Mason University 1997-98 Catalog Catalog Index
Course Descriptions

Search the 1997-1998 Catalog:


Operations Research Courses (OR)


School of Information Technology and Engineering

435 Computer Simulation Modeling (3:3:0). Prerequisites: A course in probability and statistics and a scientific programming language. An introduction to the basic concepts of simulating complex systems by computer. Topics include Monte-Carlo methods, discrete-event modeling, a specialized simulation language, and the statistics of input and output analysis. f

441/MATH 441 Deterministic Operations Research (3:3:0). Prerequisite: MATH 203 or permission of instructor. A survey of deterministic methods for solving "real-world" decision problems. The linear programming model and simplex method of solution, duality, and sensitivity analysis; transportation and assignment problems; shortest path and maximal flow problems; and an introduction to integer and nonlinear programming are covered. Emphasis is on modeling and problem solving. f,s,su

442/MATH 442 Stochastic Operations Research (3:3:0). Prerequisite: STAT 344, MATH 351, or equivalent. A survey of probabilistic methods for solving decision problems under uncertainty. Probability review, queueing theory, inventory models, Markov decision processes, reliability, decision theory and games, and simulation are covered. Emphasis is on modeling and problem solving. s

451/DESC 451 Optimization Models (3:3:0). Prerequisite: DESC 352 or equivalent. An examination of optimization models as applied to business problems. Both linear and nonlinear models are considered including dynamic, integer, and goal programming. Applications to management, finance, and marketing are presented. f,ay

481/MATH 446 Numerical Methods in Engineering (3:3:0). Prerequisites: MATH 213 or 215, and MATH 203 or 322; or equivalent. Modern numerical methods and software. Emphasis is on problem solving through software and assessing the quality of solutions obtained. Topics include computer arithmetic, linear equations and least squares data fitting, interpolation, nonlinear optimization, and differential equations. The course involves extensive computer use. f,s

498 Independent Study in Operations Research (1-3:0:0). Prerequisite: 60 hours; must be arranged with an instructor and approved by the department chair before registering. Directed self-study of special topics of current interest in operations research. May be repeated for a maximum of six credits if the topics are substantially different. f,s,sum

499 Special Topics in Operations Research (3:3:0). Prerequisite: 60 hours and permission of instructor; specific prerequisites vary with nature of topic. Topics of special interest to undergraduates. May be repeated for a maximum of six credits if the topics are substantially different. f,s,sum

540 Management Science (3:3:0). Prerequisites: MATH 108 and STAT 250 or DESC 200, or equivalent. Operations research techniques and their application to managerial decision making. Mathematical programming, Markov processes, queueing theory, inventory models, PERT, CPM, and computer simulation are covered, as well as use of contemporary computer software for problem solving. A case-study approach to problem solving is used. OR/MS majors do not receive credit. f,s

541 Operations Research: Deterministic Models (3:3:0). Prerequisite: MATH 203 or equivalent. A survey of deterministic methods for solving "real-world" decision problems. The linear programming model and simplex method of solution, duality and sensitivity analysis; transportation and assignment problems; shortest path and maximal flow problems; and an introduction to integer and nonlinear programming are covered. Emphasis is on modeling and problem solving. Students who have taken OR/MATH 441 do not receive credit. f,s

542 Operations Research: Stochastic Models (3:3:0). Prerequisite: STAT 344, MATH 351, or equivalent. A survey of probabilistic methods for solving decision problems under uncertainty. Probability review, project networks including PERT and CPM, queueing theory, inventory theory, Markov decision processes, reliability, decision theory and games, and simulation are covered. Emphasis is on modeling and problem solving. Students who have taken OR/MATH 442 do not receive credit. f,s

635 Discrete System Simulation (3:3:0). Prerequisites: STAT 344 and OR 542, or equivalents, and knowledge of both elementary statistical inference and a scientific programming language. Computer simulation as a scientific methodology in operations analysis, with emphasis on model development, implementation, and analysis of results. Discrete-event models, specialized languages, experimental design and output statistics are covered. Extensive computational work is required. f

641 Linear Programming (3:3:0). Prerequisite: OR 541 or permission of instructor. An in-depth look at the simplex method. Computational enhancements¬the revised simplex method; sparse-matrix techniques; bounded variables and generalized upper bounds; and large-scale decomposition methods¬are also covered. Other topics include computational complexity of the simplex algorithm, and the Khachian and Karmarkar algorithms. f

642 Integer Programming (3:3:0). Prerequisite: OR 541 or permission of instructor. Cutting plane and enumeration algorithms for solution of integer linear programs; bounding strategies and reformulation techniques; knapsack problems, matching problems, set covering and partitioning problems; applications to problems in OR/MS, such as capital budgeting, facility location, political redistricting, engineering design, and scheduling. s

643 Network Modeling (3:3:0). Prerequisites: OR 541 and 542 or permission of instructor. An introduction to network problems in operations research, computer science, electrical engineering, and systems engineering. Solution techniques for various classes of such problems are developed. Topics include minimal-cost network flow, maximal flow, shortest path, and generalized networks; plus stochastic networks, network reliability, and combinatorially based network problems. The complexity of each problem class is also analyzed. f

644 Nonlinear Programming (3:3:0). Prerequisites: MATH 213 or equivalent and knowledge of a scientific programming language. Optimization theory and techniques applicable to problems in engineering, economics, operations research, and management science. The course covers convex sets and functions, optimality criteria and duality; algorithms for unconstrained minimization, including descent methods, conjugate directions, Newton-type and quasi-Newton methods; and algorithms for constrained optimization, including active set methods and penalty and barrier methods. s

645/STAT 645 Stochastic Processes (3:3:0). Prerequisite: OR 542, STAT 544, or permission of instructor. Selected applied probability models including Poisson processes, discrete- and continuous-time Markov chains, renewal and regenerative processes, semi-Markov processes, queueing and inventory systems, reliability theory, and stochastic networks. Emphasis is on applications in practice as well as analytical models.

647 Queueing Theory (3:3:0). Prerequisite: OR 542, STAT 544, or permission of instructor. A unified approach to queueing organized by type of model. Single- and multiple-channel exponential queues; Erlangian models, bulk and priority queues, networks of queues; general arrival and/or service times; and statistical inference and simulation of queues are covered. s

648 Production and Inventory Systems (3:3:0). Prerequisites: OR 541 and 542, or permission of instructor. An analysis of production and inventory systems. The use of mathematical modeling for solutions of production planning and inventory control problems is introduced. Also included are stochastic inventory systems of lot sized-reorder type; periodic review and single-period models; application of dynamic programming theory to deterministic and stochastic cases; and static and dynamic production-planning models.

649 Topics in Operations Research (3:3:0). Prerequisite: Permission of instructor. An advanced topic chosen according to interests of students and the instructor from dynamic programming, inventory theory, queueing theory, Markov and semi-Markov decision processes, reliability theory, decision theory, network flows, large-scale linear programming, nonlinear programming, and combinatorics. May be repeated for a maximum of six credits if the topics are substantially different.

671/SYST 671 Judgment and Choice Processing and Decision Making (3:3:0). Prerequisite: STAT 610 or STAT 554 or equivalent. A study of intuitive nature of human judgment and decision making, and some methods currently being used for improving individual and group decisions. The nature of judgment emphasizing limitations on human information processing abilities, and the use of decision- analytic techniques to improve decision making are covered.

675/STAT 678/SYST 675 Reliability Analysis (3:3:0). Prerequisite: STAT 554 or equivalent. An introduction to component and system reliability, their relationship, and problems of inference. Topics include component lifetime distributions and hazard functions, parameter estimation and hypothesis testing, life testing, accelerated life testing, system structural functions, and system maintainability.

677/STAT 677/SYST 677 Statistical Process Control (3:3:0). Prerequisite: STAT 610, STAT 554, or equivalent. An introduction to the concepts of quality control and reliability. Acceptance sampling, control charts, and economic design of quality control systems are discussed, as are system reliability, fault-tree analysis, life testing, repairable systems, and the role of reliability, quality control and maintainability in life-cycle costing. The role of MIL and ANSI standards in reliability and quality programs is also considered.

680 Applications Seminar (3:3:0). Prerequisites: OR 541 and 542. This course is designed to be the capstone of the master's degree in Operations Research. The focus is on model development and implementation involved in the practice of operations research and management science. A key activity is the completion of a major applied group project. Work includes project proposal, planning, completion, documentation, and presentation.

681/DESC 744 Contemporary Issues in Decision Analysis (3:3:0). Prerequisite: OR 542 or DESC 611. Application of analytic reasoning and skills to practical problems in decision making. Topics include problem structure, and analysis and solution implementation, emphasizing contemporary approaches to decision analytic techniques. f

682/STAT 682 Computational Methods in Engineering and Statistics (3:3:0). Prerequisites: MATH 203 and 213 or equivalent. Numerical methods have been developed to solve mathematical problems that lack explicit closed-form solutions or have solutions that are not amenable to computer calculations. Examples include solving differential equations or computing probabilities. This course discusses numerical methods for such problems as regression, analysis of variance, nonlinear equations, differential and difference equations, and nonlinear optimization. Applications in statistics and engineering are emphasized. The course involves extensive computer use. s

741 Advanced Linear Programming (3:3:0). Prerequisites: OR 541 and 641. Recent developments in linear programming. The course highlights advances in interior point methods and also addresses developments in the simplex method. Projective methods, including Karmarkar's original work, affine methods, and path-following methods, are examined. The relationships between these methods are discussed, as well as their relationships to methods in nonlinear programming. Also discussed are advances in data structures and other implementation issues. Students have the opportunity to test software and solve large-scale linear programs.

745 Optimization in Vector Spaces (3:3:0). Prerequisites: OR 541 and 644; or ECE 521 and 620; or equivalent. An introduction to infinite dimensional optimization. Topics include geometric interpretations; elementary functional analysis¬strong and weak topologies, Banach spaces, Hilbert spaces, and Sobolev spaces; Gateaux and Frechet differentiability; Weierstrass theorem in Banach spaces; variational inequalities as necessary conditions; Kuhn-Tucker conditions for infinite dimensional mathematical programs; systems of functional equations/inequalities; applications to variational calculus and optimal control; and sufficiency in infinite dimensional optimization.

777/SYST 777 The Modeling of Nonlinear Dynamic Systems (3:3:0). Prerequisites: OR 441 or 541; ECE 521; OR/STAT 682; or equivalents. An introduction to the use of nonlinear ordinary differential, difference and integral equations in modeling dynamic phenomena in engineering, the natural sciences, and the social sciences. Emphasis is on the art of constructing and solving very large-scale, complex dynamic models. Examples are drawn from operations research, environmental engineering, mathematical biology, economics, transportation, and other fields.


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