Operations Research (OR)

School of Information Technology and Engineering

335/SYST 335 Discrete Systems Simulation Modeling (3:3:0). Corequisites: CS 112, STAT 344, SYST 202. An introduction to the basic concepts of modeling complex discrete systems by computer simulation. 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 instruc tor. 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,sum

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, queuing theory, inventory models, reliability, decision theory and games, and simulation are covered. Emphasis is on modeling and problem solving. s

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 (13:0:0). Prerequisite: 60 credits; 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 6 credits if the topics are substantially different. f,s,sum

499 Special Topics in Operations Research (3:3:0). Prerequisite: 60 credits and permission of instructor; specific prerequisites vary with nature of topic. Topics of special interest to undergraduates. May be repeated for a maximum of 6 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, queuing 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 and SE/MS majors do not receive credit. f,s

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

542 Operations Research: Stochastic Models (3:3:0). Prerequisite: STAT 344 or MATH 351, or equivalent. A survey of probabilistic methods for solving decision problems under uncertainty. Probability review, reliability, queuing theory, inventory systems, Markov chain models and Markov decision processes, and discrete-event simulation are covered. Emphasis is on modeling and problem solving. Students who have taken OR 442/MATH 442 do not receive credit.

635 Discrete System Simulation (3:3:0). Prerequisite: OR 542 or STAT 354 or 344, or equivalent, and knowledge of 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.

640 Global Optimization and Computational Intelligence (3:3:0). Prerequisite: MATH 203 or equivalent and knowledge of a scientific programming language. An introduction to global optimization in the context of large-scale, nonconvex mathematical programs and numerical methods for the solution of such problems. Topics covered include: high-level survey of traditional mathematical programming algorithms; critical comparison of metaheuristics and artificial intelligence (AI) algorithms to traditional mathematical programming algorithms; probabilistic search, multi-start methods, statistical tests of performance and confidence, simulated annealing, genetic algorithms, neural networks, Tabu search, homotopies and tunneling; the traveling salesman problem, the Steiner problem, Stackelberg-Cournot-Nash mathematical games and other classical nonconvex optimization problems

641 Linear Programming (3:3:0). Prerequisite: OR 541 or permission of instructor. An in-depth look at the theory and methodology of linear programming: Computational enhancements of the revised simplex method; sparse-matrix techniques, bounded variables and the dual simplex method. Alternative interior point methods are described and the computational complexity of various algorithms is analyzed.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; heuristic approaches to the solution of complex problems; 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 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 OR 541 or permission of instructor. Nonlinear 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, queuing and inventory systems, reliability theory, and stochastic networks. Emphasis is on applications in practice as well as analytical models.

647 Queuing Theory (3:3:0). Prerequisite: OR 542, STAT 544, or permission of instructor. A unified approach to queuing 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. Extensive use of computational software.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, queuing 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 6 credits if the topics are substantially different.

651 Military Operations Research I: Cost Analysis (3:3:0). Corequisites: OR 541 or 542. While drawing on other disciplines (e.g., managerial accounting, econometrics, systems analysis, etc.), cost analysis uses operations research to assist decision makers in choosing preferred future courses of action by evaluating selected alternatives on the basis of their costs, benefits, and risks. Cost analysis is distinctly different from cost estimating in that projecting future courses of action almost always requires mathematical modeling. Topics include analysis overview, economic analysis, estimating relationships (factors, simple and complex models), acquiring and verifying cost data, cost progress curves, life cycle costing, scheduling estimating, effectiveness and risk estimation, relationship of effectiveness models and measures to cost analysis.

652 Military Operations Research Modeling II: Effectiveness Analysis (3:3:0). Corequisites: OR 541 or 542. Examines the issues and modeling underlying military decisions at the Military Service, Joint Staff, and Department of Defense level. Analytical methods with applications to theater campaign analysis, equipment and weapon system modernization, force structure development, strategic mobility and deployment, small scale contingency operations, logistics, and requirements determination are considered. Optimization, simulation, and statistical techniques are stressed. Realistic problems are presented and solved by the students as case studies. Display of results and presentation techniques for military decision makers are emphasized.

660/SYST 660 Air Transportation Systems Modeling (3:3:0). Prerequisite: SYST 460/560 or permission of instructor. The student will be introduced to a wide range of current issues in air transportation. The issues include: public policy toward the industry, industry economics, system capacity, current system modeling capability, human factors considerations, safety analysis and surveillance systems, and new technological developments. The student is expected to develop a broad understanding of the contemporary and future issues. The student's knowledge will be evaluated through class discussions, a take-home midterm exam and a term project to be completed by the end of the semester. s

671/SYST 671 Judgment and Choice Processing and Decision Making (3:3:0). Prerequisite: STAT 510 or 554 or permission of instructor. A study of the 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 544 or 554 or permission of instructor. 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 544 or 554, or permission of instructor. 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 Project Course in Operations Research, Systems Engineering and Computational Modeling (3:3:0). Prerequisites: 21 graduate credits in OR or SYST. This course is designed to be the capstone course for both the master's program in operations research and the capstone course for the certificate in computational modeling. It can also be used in lieu of an individual research project in the master's program in systems engineering. The focus is on model development and implementation involved in the practice of operational modeling. A key activity is the completion of a major applied group project. Work includes project proposal planning, completion, documentation, and presentation.

681/SYST 573 Decision and Risk Analysis (3:3:0). Prerequisite: OR 542 or MBA 638. 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/CSI 700 Computational Methods in Engineering and Statistics (3:3:0). Prerequisites: MATH 203 and 213 or equivalent, modern numerical methods and software. 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 computation probabilities. This course discusses numeri cal 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.

683 Principles of Command, Control, Communications, and Intelligence (C³I) (3:3:0). Prerequisite: ECE 528 or OR 542 or equivalent. Fundamental principles of C³I are developed from a descriptive, theoretical, and quantitative perspective. The principles and techniques are applicable to a wide range of civilian and military situations. Topics include C² process; modeling and simulation for combat operations; detection, sensing, and tracking; data fusion and situation assessment; optimal decision making; methodologies and tools of C³I architectures; tools for modeling and evaluations of C³ systems such as queuing theory are also included. f

690 Optimization of Supply Chains (3:3:0). Prerequisites: graduate standing, mathematics through linear algebra, and STAT 344. This course focuses on both supply chain optimization from an enterprise-wide perspective, and supply chain optimization from a business-to-business e-commerce concern. Thus the course is concerned with optimizing the value of goods and services and assuring a reasonable return on such sales. The course describes both heuristic and exact algorithms for scheduling, production, inventory management, logistics, and distribution. New software that enables such optimization is presented, as are manufacturing and service examples from the public and private sectors. New techniques to handle risk, quality of data, and robustness of solutions are presented. Students perform case studies using state-of-the-art software.

719/STAT 719/CSI 775 Computational Models of Probabilistic Reasoning (3:3:0). Prerequisites: STAT 652 or 664, or permission of instructor. Introduction to theory and methods for building computationally efficient software agents that reason, act, and learn environments characterized by noisy and uncertain information. Covers methods based on graphical probability and decision models. Students study approaches to representing knowledge about uncertain phenomena, and planning and acting under uncertainty. Topics include knowledge engineering, exact and approximate inference in graphical models, learning in graphical models, temporal reasoning, planning, and decision-making. Practical model building experience is provided. Students apply what they learn to a semester-long project of their own choosing.

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, affine methods, and path-following methods are examined, including Karmarkar's original work. 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.

750 Advanced Topics in Operations Research (3:3:0). Prerequisites: OR 541 or 542 and a 600-level course that will vary with the content of the course. Special topics, applications, and/or recent developments in operations re search. Contents vary and may include topics in optimization, stochastic methods, or decision support that are not covered in the standard OR curriculum. May be repeated for credit when topics are distinctly different.

751 Advanced Topics in Operations Research for Planning, Scheduling, and Network Design (3:3:0). Prerequisite: OR 642 or 643 or 690. An introduction to network and combinatorial optimization problems in logistics, computer science, electrical engineering, and systems engineering. Solution techniques for various classes of such problems are developed. Topics include scheduling algorithms, capital budgeting, minimal cost network flow, optimal routings, and generalized networks. Scheduling algorithms, network reliability, stochastic networks and combinatorially-based network problems are discussed.

Organizational LearningSee LRNG

Parks, Recreation, and Leisure Studies (PRLS)

Graduate School of Education

110 Exploring Outdoor Adventure (2:2:0).

115 Introduction to Fly Fishing (1:1:0).

117 Rock Climbing (2:2:0).

119 Trap and Skeet Shooting (2:2:0).

120 Hiking, Orienteering, and Cooking (2:2:0).

170 Introduction to Whitewater Kayaking (1:1:0).

173 Basic Coastal Kayaking (2:2:0).

175 Introduction to Rowing (1:1:0).

180 Whitewater Canoeing (2:2:0).

181 Whitewater Canoeing II (2:2:0).

190 Downhill and Cross-Country Skiing (1:1:0).

195 Introduction to Hot Air Ballooning (2:2:0).

210 Introduction to Recreation and Leisure (3:3:0). Open to nonmajors. Traces the development of current concepts of recreation and leisure and their implications and consequences. Covers the influences of philosophy, religion, science, economics, sociology, and politics on discretionary time and its uses.

220 Experiential Education Theory (3:3:0).

221 Challenge Course Facilitator Field Work (2:2:0).

241 Practicum (3:3:0). Open to majors and minors only. Prerequisites: PRLS 210, 310, 316, 327; Corequisite: PRLS 410. Paid or voluntary work experience in a park and recreation agency. Minimum period of 10­12 weeks of part-time employment or experience. Course serves as a capstone for the minor allowing for integration and application of coursework, theories, and research to a work setting. Worksites are chosen among four approved sites. Includes meetings and assignments prior to and during the practicum.

250 Wilderness Travel and Outdoor Leadership (2:2:0).

253 Florida Everglades Canoe Expedition (3:2:1).

300 People with Nature (3:3:0). Traces the philosophical evolution of perceptions of and attitudes toward nature. Examines the role of philosophers, scientists, nature-writ ers, and artists in the shaping of environmental thought. Includes extensive reading of Emerson, Thoreau, Muir, Leopold, Carson, Wilson, and others.

302 Park Management and Operations (3:3:0). Prerequisite: PRLS 300. Focuses on management and operations of park resources, including the management of visitors and recreation development. Emphasizes understanding of contemporary threats to park integrity and preservation of resources. Also covers maintenance management systems.

310 Program Planning and Design (3:3:0). Corequisite: PRLS 210. Presents fundamental principles and techniques of the planning process for health, fitness, and recreation programs. Covers specifying an area of need; goals, objectives, and a mission statement; generating solutions; and selecting a program design for implementation.

316 Outdoor Education and Leadership (3:3:0). Focuses on promotion of lifelong health and fitness via noncompetitive and informal outdoor activities. Introduces safety, skills, and leadership techniques. Covers sustainable use, conservation, and stewardship of natural resources.

317 Social Psychology of Play and Recreation (3:3:0). Prerequisite: PRLS 210 or permission of instructor. Applies social psychological theories and research to the study of leisure, play, and recreation behavior, including correlates, antecedents, and consequences of and constraints to these concepts.

327 Foundations of Therapeutic Recreation (3:3:0). Covers the nature and perceptions of disability and their consequences; the problems of stigma, stereotype, and labeling; and principles of normalization and inclusion. Introduces the therapeutic recreation model and activity assessment.

402 Human Behavior in Natural Environments (3:3:0). Prerequisites: PRLS 210, 300, or permission of instructor and 60 credits. Applies social and behavioral theories to management for recreational users of land and water resources. Examines deterioration and pollution of land and water, noise, crowding, and conflicts among users. Discusses strategies for mitigation of deleterious impacts and depreciative behaviors, as well as attitudes toward resource conservation, preservation, and use.

405 Planning, Design, and Maintenance of HFRR Facilities (3:3:0). Prerequisites: PRLS 310 or POI and 60 credits. Covers quantity, location, and design standards for facilities. Includes safety, functionality, durability, and maintenance demand criteria in planning and design; programmatic and operational objectives to be met, including user comfort and convenience, crowd management, and traffic flow; and space relationships. Includes field study of local facilities.

410 Administration of HFRR Organizations I (3:3:0). Prerequisite: 60 hours. Focuses on the operation and management of health, fitness, and recreation services organizations. Covers management and leadership theories and techniques, problem solving and decision making, organizational communications, design of organizational structures, and budgeting.

411 Administration of HFRR Organizations II (3:3:0). Prerequisites: PRLS 410 and 60 hours. Focuses on planning techniques for health, fitness, and recreation organizations. Covers program and organizational marketing principles and strategies; service quality assessment and organizational evaluation techniques; and organizational financing.

416 Issues and Trends in Therapeutic Recreation (3:3:0). Prerequisite: PRLS 325. Explores the role of leisure in human development with a specific focus on the leisure needs, demands, and services for people with disabilities in community settings. Presents basic concepts associated with leisure, aging, physical challenge, targeting leisure services, research, and public policy. Field experience is required.

418 Assessment in Therapeutic Recreation (3:3:0). Prerequisite: PRLS 327. Covers methods of assessment, development of treatment program plans, and evaluation of all components. The course extends program design by developing competencies in the planning approaches, individual and group assessment techniques, program evaluation, and documentation strategies for people with disabilities in community settings. Field experience required.

450 Research Methods (3:3:0). Prerequisites: STAT 250 or permission of instructor and 60 credits. Covers the development of empirical research designs for both practical and theoretical problems in health, fitness, and recreation resources management. Includes literature review of hypothesized relationships and formulation of research proposals.

460 Sport and Recreation Law (3:3:0). Prerequisite: 60 hours. Emphasizes safety, liability, and risk. Covers current law and liability issues for administrators of HFRR facilities and programs.

480 Special Topics in Parks, Recreation, and Leisure Studies (3:3:0). Covers selected topics reflecting interest in specialized areas of parks and outdoor recreation or therapeutic recreation.

490 Internship (12:0:0). Prerequisites: 90 hours; HEAL 205, 323, and 350; PHED 200; PRLS 210, 310, 316, 317, and 410 (pass/fail basis). Provides paid or voluntary work experience in a park and recreation agency for a minimum period of 10­12 weeks of full-time employment. Applies course work, theories, and research to work settings. Work sites are chosen by students after approval of faculty supervisors. Includes meetings and assignments before as well as during the internship.

499 Independent Study (1-3:0:0). Provides individual study of topic area in leisure research, theory, or practice under the direction of faculty.

501 Introduction to Natural Resources Law (3:3:0). Prerequisite: PRLS 460 or graduate status or permission of instructor. Examines selected legal issues involving conflicting use and preservation demands on our nation's limited natural resource base, particularly those involving public lands, open space, and recreation resources. Uses case studies of recent court decisions.

503 Disability Rights Law in Sport and Recreation (3:3:0). Prerequisite: PRLS 460 or graduate status or permission of instructor. Provides an overview of several major law and policy issues related to the provision of community recreation services to special populations. The primary focus is the Americans with Disabilities Act and related federal legislation.

526 Environmental Education and Resource Interpretation (3:3:0). Prerequisites: PRLS 402 or permission of instructor and 90 credits. Covers methods for communi cating and disseminating information pertaining to the use of natural recreation resources. Covers the design and implementation of educational materials and programs to enhance understanding and appreciation of cultural, historical, and natural resources.

531 Natural Resources Recreation Planning (3 credits). Covers the origins and evolution of recreation use philosophy, policies, and service of public estate management. Covers planning for a spectrum of opportunities, from wilderness to developed sites, with attention to financial consideration and to sustainable use of cultural and visual resources.

533 Visitor Services (3 credits). Covers the motivation of resource-based recreation participants. Covers visitors' expectations and perceptions, with emphasis on implication for service quality, staff training, and other management responsibilities. Also covers use and user conflicts and placement, information and interpretive service, and human and other interpretive service resources.

535 Evaluating Recreation Outcomes (3:3:0). This web-based technology course applies quantitative and qualitative research methods to the evaluation of programs provided to visitors and users of public lands for outdoor recreation. Covers needs assessment; application of meaningful measures for formative and summative evaluations; and requirements of the Government Performance and Results Act.

560 Liability and Risk Management (3 credits). Covers liability and risk; federal jurisdiction, legal apparatus, and decision making; and analysis of resource-based recreation case law.

598 Special Topics (1-6:0:0). Prerequisite: 90 hours. Focuses on projects related to areas of parks, recreation, and leisure studies. May be repeated for a total of 6 credits.

599 Independent Study (1-3:0:0). Prerequisite: 90 hours. Provides study of a problem area in parks, recreation, and leisure studies research; theory or practice under the direction of faculty member. May be repeated. No more than 3 credits may be earned.

National Forest Land Management Courses

542 Foundations of Federal Land Management (1credit). Covers the history of national land policy and the nature of management activities on federal lands. Examines policies, trends, and management needs. Covers intra- and interagency integration of land management programs. This course is available on the Internet (http://dlp.gmu.edu) without charge. Registration and payment is required for academic or agency credit.

635 Recreation Special Uses and Appeals (3 credits). Covers the management of extensive and varied commercial and noncommercial demands on federal lands. Covers policies and procedures used by federal land managers; implementation, effects, and problems of permit systems; and appeal provisions.

643 Special Uses Management on Federal Lands (4 credits). Covers special use authority and authorizations, and policies, regulations, and directives in processing applications. Covers coordination and administration of special uses and integration with land and resource management plans. Includes agriculture, industry, community, aviation, water, treasure trove, and cultural uses.

644 Linear Uses and FERC Licenses on Federal Lands (3 credits). Covers legislation, regulation policies, and directives governing linear uses. Covers FERC licensing of hydroelectric power generation and distribution; rights-of-way for oil, gas, and electric transmission and railroads, communication, trams, conveyors, roads, and trails; and FERC consultation, exemption, and licensing.

645 Valuation and Land Ownership Adjustment (5 credits). Covers land ownership authority, coordination, and adjustment processes; land valuation and rules; and processes of appraisal, title exchange, purchase, donation, transfer, sale, and condemnation of properties.

646 Right-of-Way Acquisition (3 credits). Covers authorities and procedures for right-of-way acquisition from public agencies and private landowners. Covers planning coordination and project scheduling requirements, steps in the acquisition process, and cooperative development and use of roads.

647 Land Status, Boundaries, Claims, and Withdrawals (3 credits). Covers land survey and status records systems; programs for maintaining and managing boundaries; the handling of claims and encroachments; and the land status record system and Bureau of Land Management master title plat system.

648 American Indian Rights and Claims (3 credits). Covers American Indian sovereignty, Alaska Native corporations, and colonization; treaties, rights, and claims; cultural resources and Indian laws; and consultation with tribal governments. This course is available on the Internet at http://dlp.gmu.edu.