Operations Research (OR)
Systems Engineering and Operations Research
335/SYST 335 Discrete Systems Simulation Modeling (3:3:0) Corequisites: CS 112, STAT 344, SYST 202 or CS 310; or permission of instructor. Introduction to basic concepts of modeling complex discrete systems by computer simulation. Topics include Monte-Carlo methods, discrete-event modeling, specialized simulation software, statistics of input and output analysis. s
441/MATH 441 Deterministic Operations Research (3:3:0) Prerequisite: MATH 203 or permission of instructor. Survey of deterministic methods for solving Òreal-worldÓ decision problems. Covers linear programming model and simplex method of solution, duality, and sensitivity analysis; transportation and assignment problems; shortest path and maximal flow problems; and introduction to integer and nonlinear programming. Emphasizes modeling and problem solving. f,s
442/MATH 442 Stochastic Operations Research (3:3:0) Prerequisite: STAT 344, MATH 351, or equivalent. Survey of probabilistic methods for solving decision problems under uncertainty, probability review, decision theory, queuing theory, inventory models, reliability, Markov chain models, and simulation are covered. Emphasis 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 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. Involves extensive computer use. f,s
498 Independent Study in Operations Research (13:0:0) Prerequisite: 60 credits; must be arranged with instructor and approved by department chair before registering. Directed self-study of special topics of current interest in operations research. May be repeated for maximum 6 credits if topics 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 maximum 6 credits if topics 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. 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 Òreal worldÓ decision problems. Covers 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. 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 theory review, reliability, queuing theory, inventory systems, Markov chain models, and simulation. Emphasis 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 software, input modeling, 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. Introduction to global optimization of 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, multistart 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. 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 described and computational complexity of various algorithms 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. 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. Complexity of each problem class 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. 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 on applications in practice as well as analytical models. f
647 Queuing Theory (3:3:0) Prerequisite: OR 542, STAT 544, or permission of instructor. 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. 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. 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 maximum 6 credits if topics are substantially different.
651 Military Operations Research I: Cost Analysis (3:3:0) Corequisites: OR 541 or 542. While drawing on other disciplines (managerial accounting, econometrics, systems analysis), 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. s
652 Military Operations Research Modeling II: Effectiveness Analysis (3:3:0) Corequisites: OR 541 or 542. Examines 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 presented and solved as case studies. Display of results and presentation techniques for military decision makers emphasized. f
660/SYST 660 Air Transportation Systems Modeling (3:3:0) Prerequisite: SYST 460/560 or permission of instructor. Introduces range of current issues in air transportation, including 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. Students expected to develop broad understanding of contemporary and future issues. Knowledge 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 equivalent, or permission of instructor. How do people make judgments and decisions? Course presents an initial review of scientific literature directed toward answering this question, and emphasizes its importance when performing decision analysis and designing systems to support judgment and decision processes. f
675/STAT 678/SYST 675 Reliability Analysis (3:3:0) Prerequisite: STAT 544 or 554 or permission of instructor. 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. 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. Role of MIL and ANSI standards in reliability and quality programs also considered.
680 Project Course in Operations Research, Systems Engineering and Computational Modeling (3:3:0) Prerequisites: 21 graduate credits in OR or SYST. Capstone course for both the masterÕs program in operations research and certificate in computational modeling. Can also be used in lieu of the project in masterÕs program in systems engineering. Focus is on model development and implementation involved in the practice of operational modeling. Key activity is completion of a major applied group project. Work includes project proposal planning, completion, documentation, and -presentation. To be taken in last spring semester of studies.
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, 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. 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. Involves extensive computer use.
683/SYST 680/ECE 670 Principles of Command, Control, Communications, and Intelligence (C3I) (3:3:0) Prerequisite: ECE 528 or OR 542 or SYST 611 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. f
690 Optimization of Supply Chains (3:3:0) Prerequisites: graduate standing, mathematics through linear algebra, and STAT 344. Focuses on both supply chain optimization from an enterprise-wide perspective, and supply chain optimization from a business-to-business e-commerce concern. Concerned with optimizing the value of goods and services and assuring a reasonable return on such sales. 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. Studies 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 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. 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 KarmarkarÕs original work. Discusses relationships between these methods, and relationships to methods in nonlinear programming. Also discussed are advances in data structures and other implementation issues. Students 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, or recent developments in operations research. 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. 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.