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Operations Research Courses OPER 498 – RESEARCH METHODS: This course is designed to provide the student with an understanding of the research process and department research expectations. Topics include problem definition, use of secondary sources, research design and communication of results. Students prepare and present a research proposal. Prerequisites: None. Spring Quarter 1 credit hour OPER 500 – OPERATIONAL SCIENCES SEMINAR: This seminar acquaints students with the application of operations research to Air Force and DoD issues and with faculty research interests. This course also provides a forum for lectures by distinguished visitors. Prerequisites: None. Fall, Winter, and Spring Quarters 0.5 credit hour OPER 501 – QUANTITATIVE DECISION MAKING: This is an introductory course in management science applications for the logistics, systems, acquisition and transportation manager. Emphasis is on understanding and applying the techniques to managerial problem solving and decision making. Major topics include linear programming, decision theory, networks, and queueing theory. Prerequisites: None. Fall and Winter Quarters 3 credit hours OPER 503– DETERMINISTIC MODELING: (Non-thesis only.) This course applies the basic theories of optimization to develop standard approaches to deterministic modeling. This course is designed to expose students to deterministic modeling in operational analysis. Topics include fundamentals of linear programming, network-flow problems and interger programming. The emphasis of this course is on model formulation and model buiding. Prerequisites: None. 3 credit hours OPER 504– PROBABILISTIC MODELING: (Non-thesis only.) This course introduces probabilistic models prevalent in the operational sciences. The tools employed include conditioning, elementary counting processes, and Markov chains. These tools shall be applied to analyze queueing, inventory, and reliability models. Prerequisites: STAT 526, OPER 503. 3 credit hours OPER 510 – DETERMINISTIC OPERATIONS RESEARCH: This course develops basic optimization theory, building on mathematical fundamentals introduced in the calculus. The emphasis of this course is on exposure to deterministic methods at an introductory graduate level. Topics include fundamentals of linear programming, integer programming, nonlinear programming, and dynamic programming. The emphasis is on problem solving and examples. Prerequisites: Co-requisite: MATH 501. 4 credit hours OPER 540 – STOCHASTIC MODELING AND ANALYSIS I: This course applies the fundamental probability theory to develop standard approaches to stochastic modeling in operations research. Specific topics include conditional probability and expectation, the Poisson process and exponential distribution, discrete-time Markov chains, and continuous-time Markov chains. The various models are discussed in the context of military applications. Prerequisites: OPER 510, STAT 527. Winter Quarter 4 credit hours OPER 543 – DECISION ANALYSIS: This course is decision 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 analysis applications for USAF and DoD problems are considered. Prerequisites: STAT 527. Winter and Spring Quarters 3 credit hours OPER 561 – DISCRETE-EVENT SIMULATION: This is an introductory course on the use of computer simulation modeling to analyze complex military systems. The focus of the course is on the development of discrete-event simulation models and the analysis of simulation model input and output. A modern simulation language is taught to provide a modeling framework and the means for implementing a computerized model. Basic concepts important to simulation studies such as random number and random variate generation, model verification and validation, and output analysis are discussed. Examples and applications are oriented toward operational systems within the DoD. Prerequisites: STAT 537. Spring Quarter 4 credit hours OPER 595 – ISSUES IN DEFENSE ANALYSIS: This course discusses the role of analysis in defense decisions and examines the historical contributions and limitations of analysis in the decision-making process. Specific topics include the origins of defense analysis, measures of merit, modeling, analytical pitfalls, contemporary topics, and issues of bias, advocacy, and ethics in defense analysis. Prerequisites: OPER 510, OPER 540, OPER 560. Winter Quarter 3 credit hours OPER 596 – APPLYING ANALYSIS TO DEFENSE ISSUES: (Non-thesis only). This capstone course discusses the application of Operations Research (OR) in making defense decisions. In particular, the course examines the application of OR to support senior decision makers in their planning and warfighting efforts. Specific topics include the use of analysis in evaluating Department of Defense and Air Force issues, the use of analysis to make better decisions, and contemporary operational and tactical Air Force topics. Prerequisites: OPER 503, OPER 504, OPER 561 3 credit hours OPER 601 – OPERATIONS RESEARCH SEMINAR: This course is designed to provide students, primarily those enrolled in the doctoral program with information relating to the state-of-the-art within the Operations Research field. Prominent speakers in the field will be invited and used whenever possible. This course may also be used by the faculty to present recent developments in their research and by doctoral candidates to present progress reports on their dissertation research. Prerequisites: None. Offered All Quarters 0 credit hours OPER 610 – LINEAR PROGRAMMING AND NETWORK FLOWS: This course is an in-depth view of linear programming (LP) and network-flow problems. It includes model formulation, theoretical constructs, solution algorithms (simplex and interior-point methods), post optimality analysis, and large-scale considerations. Related areas, such as specialized LP, network models and first-order approximations are presented. Software systems and models used to solve DoD problems are discussed. Prerequisites: OPER 510. Spring Quarter 4 credit hours OPER 612 – NONLINEAR PROGRAMMING: This course is a detailed study of applied nonlinear programming techniques. The differential calculus and Karush-Kuhn-Tucker results for constrained optimization are presented, including convexity, local and global optima, and saddle point conditions. Techniques for solving nonlinear programs are presented. Geometric programming, including signomial programming, is covered, along with applications. Students gain experience with nonlinear programming through applications to real-world problems. Prerequisites: OPER 610. Summer Quarter 3 credit hours OPER 613 – INTEGER PROGRAMMING: Integer programming is the class of mathematical programming models that requires some or all of the variables to assume discrete or integer values. This courses covers modeling, theoretical developments, and the principal solution procedures associated with the subject. At the completion of the course, the student should be able to recognize when integer programming is appropriate, set up a model for solution by an available algorithm, solve the model, interpret the solution, and understand the theoretical basis for the solution procedure. Prerequisites: OPER 610. Summer Quarter 3 credit hours OPER 614– DYNAMIC PROGRAMMING: This is a course on the theory and practice of dynamic programming, i.e. optimal sequential decision making over time. The course will stress intuition, the mathematical foundations being for the most part elementary. Applications will be considered in capital investment, transportation, and production and inventory control. Prerequisites: STAT 527, OPER 510. OPER 615 – LARGE SCALE SYSTEMS OPTIMIZATION: Large scale systems optimization takes advantage of the structure of large problems to develop efficient algorithms for their solution. Many large problems can only be solved by taking advantage of these special structures. The course examines the relationship between special structures and the algorithms which take advantage of them. Topics include interior point methods, Dantzig-Wolfe decomposition, column generation, Bender’s decomposition, generalized upper bounding, and Lagrangian relaxation. Several examples of large problems will be examined, including scheduling a delivery fleet. Prerequisites: OPER 610. Winter Quarter 3 credit hours OPER 616 – GRAPH THEORY: An introduction to the theory and application of graphs. Topics include introductory concepts and definitions, digraphs, connected and disconnected graphs, graph traversals, connection problems, trees, planar and non-planar graphs, eulerian and hamiltonian graphs, coloring problems, graph isomorphisms, multigraphs. Applications of graph theory to problems in network flows and in combinatorial optimization are described. Prerequisites: OPER 610. 4 credit hours OPER 617 – NETWORKS AND COMBINATORIAL OPTIMIZATION: This course is an in-depth study of combinatorial programming and network flow optimization. The emphasis will be placed on discrete optimization and specialized solution techniques which are efficient ways to solve mixed-integer programming problems. These techniques include minimum cost flow, networks with gains, multi-commodity flow networks, networks with side constraints, and Lagrangian relaxation. Computational complexity is also discussed. Prerequisites: OPER 610. Fall Quarter 3 credit hours OPER 621– MULTICRITERIA DECISION ANALYSIS: This course exposes students to a variety of approaches to the modeling and solution of multiple criteria decision making problems. Topics covered will include a discussion of preference structures, dominance, utility and value functions, analytic and interactive MCDM techniques, plus compromise programming and multi-objective optimization formulations. Prerequisites: OPER 510 or OPER 501 or equivalents. Summer Quarter 3 credit hours OPER 623 – HEURISTIC SEARCH METHODS: Introduction and application of modern search methods for solving complex optimization problems. Topics include genetic algorithms, simulated annealing, tabu search, hybrid combinations, and adaptive techniques. Prerequisites: OPER 613. Fall Quarter 3 credit hours OPER 626 – SCHEDULING THEORY: This course will cover the fundamentals of sequencing and scheduling. It will concentrate on the terminology, measures of effectiveness and basic problems found in the literature. Specific applications in vehicle scheduling will be introduced. Prerequisites: OPER 510. Summer Quarter 3 credit hours OPER 628 – ANALYSIS OF ALGORITHMS WITH OR APPLICATIONS: This course is an introduction to the analysis of the computational complexity of algorithms. It will cover basic counting techniques, O(*) notation, and NP-Completeness. General algorithms will be studied in the areas of sorting and graph theory. Classic approaches to such problems as the traveling salesman problem and scheduling will also be covered. Prerequisites: OPER 610. Winter Quarter 3 credit hours OPER 632 – COST ANALYSIS FOR SYSTEMS DESIGN: This course covers the principles of engineering economy, the development of cost estimating relationships, and the employment of the life cycle concept. Attention is paid to the measurement of tangible and intangible benefits. The goal of the course is to provide a complete treatment of cost analysis, originating with the identification of a need and ending with phase-out and disposal. Prerequisites: STAT 527. 3 credit hours OPER 641 – STOCHASTIC MODELING AND ANALYSIS II: This course develops advanced concepts in the modeling and analysis of complex stochastic systems. Specific topics include generalizations of the Poisson process, renewal theory, regenerative processes, Markov-renewal theory, and Markov-regenerative processes. The course also introduces martingale, Brownian motion, and other diffusion processes. Prerequisites: OPER 540. Summer Quarter 3 credit hours OPER 643 – ADVANCED DECISION ANALYSIS: This course presents advanced decision analysis concepts, theory, and methodology. The course covers value-focused thinking; hierarchal value structures; utility, value and scoring functions; multi-attribute utility and value problems; multi-attribute preferences under uncertainty; aggregation of individual preferences; and utilization of group preferences. Real-world applications of the course material to DoD problems are emphasized. Prerequisites: OPER 543. Summer Quarter 3 credit hours OPER 645– RISK MODELING AND ANALYSIS: This is a course on the theory and practice of risk analysis. Specific topics include quantitative risk assessment, multi-objective risk assessment, multi-objective risk analysis, Bayesian networks, game theory, actuarial risk, and fault tree analysis. Military and industrial applications are discussed. OPER 646– DECISION AND RISK ANALYSIS: This course presents multi-attribute decision, risk, value, and utility theory, methodology, and analysis. Decision modeling applies to complex problems involving sequential decisions, major uncertainties, conflicting objectives, and multi-attribute value and utility functions. The course includes value-focused thinking, decision structuring with influence diagrams and decision trees, modeling uncertainty with subjective probabilities, sensitivity analysis and the value of information, and modeling decision maker preferences using value and utility functions. Real-world applications will be discussed throughout. Prerequisites: STAT 526, STAT 536. 4 credit hours OPER 647 – QUEUEING SYSTEM ANALYSIS: This course begins with an overview of stochastic modeling and transform methods. These techniques are then employed in equilibrium analysis of simple Markov and imbedded Markov queueing systems. Results are extended to address more advanced modeling concepts such as priority customers, bulk arrivals or service, generalized distributions of interarrival or service times, and networks of queues. Potential applications are discussed, including performance evaluation and optimization of communication systems, transportation networks, computer systems, and other resource-constrained operations. Prerequisites: OPER 540. Fall Quarter 3 credit hours OPER 660 – STATISTICAL ASPECTS OF SIMULATION: INPUT ANALYSIS: This course provides an in-depth treatment of a number of important issues in the Statistical Aspects of Simulation. The emphasis in this course is on input modeling. Topics include random number generation, random variate modeling and generation, the structure of simulation programs, and model validation. Prerequisites: OPER 560, OPER 561, OPER 680 or STAT 696. Fall Quarter 3 credit hours OPER 662 – ADVANCED TOPICS IN SIMULATION: This is an advanced course focusing on several topics related to simulation. Areas of coverage include, but are not limited to input modeling, verification, and validation, distributed simulation, and simulation optimization. The course requires students to review the literature pertinent to these areas. Students will be given the opportunity to present selected papers from this literature search in the form of lectures. Guidance will be provided in terms of possible areas of topic concentration. Prerequisites: OPER 561. Summer Quarter. 3 credit hours OPER 671 – COMBAT MODELING I: The purpose of this course is to present high resolution combat modeling. High resolution combat modeling provides detailed interactions of individual combatants or weapons systems. Topics include: simulating the battlefield environment, target search, acquisition and selection processes, single round accuracy and lethality models, and multiple round assessment models. Models currently in use for DoD analysis are used as examples throughout the course. Prerequisites: OPER 560 and OPER 561. Summer Quarter 3 credit hours OPER 672 – COMBAT MODELING II: The purpose of this course is to present modeling of large-scale air/ground combat operations using aggregated force on force combat models. Topics include: aggregation and disaggregation, types of models used for large-scale operations, firepower index and Lanchester equation approaches to attrition modeling, movement, rate of advance, air allocation, logistics, and C3I models. Models currently in use for DoD analysis are used as examples throughout the course. Prerequisites: OPER 671. Fall Quarter 3 credit hours OPER 674 – JOINT MOBILITY MODELING: The purpose of this course is to present mobility modeling from an application-oriented, large-scale point of view. Models currently in use for DoD analysis are examined. Particular attention will be given to the air mobility problem and its relation to land and sea mobility. Both strategic and theater mobility are explored. Prerequisites: OPER 560 or 561, OPER 610. Winter Quarter 3 credit hours OPER 676 – INFORMATION OPERATIONS RESEARCH: This course is designed to increase the awareness and integration of the relationship between Information Operations (IO) and Operations Research. The focus will be on the tools, techniques, theories, and models currently in use for IO analysis. Particular attention will be paid to current IO modeling issues. Prerequisites: US Military only, CS 525. Summer Quarter 3 credit hours OPER 677– MODELING AND ANALYSIS OF AIR OPERATIONS: The purpose of this course is to present air operations modeling from an application oriented point of view. Topics include high resolution combat modeling, mobility modeling, aggregated modeling, and the Air Force Standard Analysis Toolkit. Models currently in use for DoD analysis are used as examples throughout the course. Prerequisites: OPER 561. 3 credit hours OPER 679 – EMPIRICAL MODELING: Analysis of experimental and observational data from engineering systems. Focus is on empirical model building using observational data for characterization, estimation, inference and prediction. Prerequisites: STAT 527, STAT 537. 3 credit hours OPER 681 – STATISTICAL PROCESS CONTROL: This course provides an in-depth treatment of the fundamental concepts and methods of modern statistical process control. The primary focus will be on the use of control charts for monitoring the process mean and variance. Other topics include process capability analysis, the modern role of acceptance sampling, and the use of such statistical techniques within the context of total quality management. Prerequisites: STAT 537. Winter Quarter 3 credit hours OPER 683 – RESPONSE SURFACE METHODOLOGY: Emphasis in this course is directed towards understanding the basic concepts and uses of RSM to examine and quantify the effect of a large number of variables which influence a system’s performance. Key topic areas are experimental design and exploration of response surfaces for determining an optimum conditions response model. Emphasis is on the application of RSM to simulation results. Prerequisites: OPER 680 or STAT 696. Summer Quarter 3 credit hours OPER 684 – QUANTITATIVE FORECASTING TECHNIQUES: This is a course in applied techniques to predict discrete time-series phenomena. The emphasis is on understanding and applying forecasting tools in analysis and management settings. Both classical smoothing methods and the Box-Jenkins methodology for model identification, estimation, and prediction are presented. Time series data are modeled and predictions made with interactive computer software. Prerequisites: OPER 679 or STAT 696. Summer Quarter 3 credit hours OPER 685 – APPLIED MULTIVARIATE ANALYSIS I: This course is oriented toward the computer-assisted analysis of multidimensional data. The course will present statistical techniques such as multiple regression, principal components analysis, canonical correlation, factor analysis, cluster analysis, discriminant analysis, and neural networks. Emphasis will be on practical application to data sets using computerized statistical packages. Prerequisites: OPER 679 or STAT 696. Spring Quarter 3 credit hours OPER 688– OPERATIONAL EXPERIMENTATION: Introduction to designing experiments for operational testing and evaluation. This is an applied course intended for operations analysts who perform experiments or serve as advisors to experimentation. A statistical approach to the design and analysis of experiments is provided as a means to efficiently study and comprehend the underlying process or system being evaluated. Insight gained leads to improved system performance and quality. Students must understand basic statistical concepts. Prerequisites: OPER 679 or equivalent. 3 credit hours OPER 710 – ADVANCED LINEAR PROGRAMMING AND EXTENSIONS: This course will explore the theoretical properties of the general linear program (LP), developing results concerning extreme points, the existence of extreme point solutions, interior point methods for LP, computational complexity, fractional programming, and current developments in LP. Prerequisites: OPER 610. Summer Quarter 3 credit hours OPER 712 – ADVANCED MATH PROGRAMMING: This course is intended for students planning advanced study and research in the areas of mathematical programming and optimization. A continuation of material covered in OPER 612, the course covers in more detail the theoretical and topological properties of the general nonlinear programming problem. Other topics are drawn from the current literature. Prerequisites: OPER 612. Spring Quarter 3 credit hours OPER 713– ADVANCED INTEGER PROGRAMMING: Integer programming is the class of mathematical programming models that requires some or all of the variables to assume discrete or integer values. This course covers modeling, theoretical developments, and the principal solution procedures associated with the subject. At the completion of the course, the student should be able to recognize when integer programming is appropriate, set up a model for solution by an available algorithm, solve the model, interpret the solution, and understand the theoretical basis for the solution procedure. Prerequisites: OPER 613. 3 credit hours OPER 741 -- ADVANCED STOCHASTIC MODELING: This doctoral-level course first develops the rudimentary concepts of measure-theoretic probability necessary for advanced stochastic modeling. Subsequently, we shall study discrete- and continuous-time martingale theory followed by Brownian motion processes and stochastic integration. Applications in operations research, finance, and engineering will also be discussed. Prerequisites: MATH 600, OPER 641. Fall Quarter, 3 credit hours. OPER 743 – DECISION ANALYSIS PRACTICE: This course examines the professional practice of decision and risk analysis. The course provides new material on the selection of decision analysis topics, the interface with the decision makers and technical experts, the advanced use of decision analysis software, and the presentation of results to decision makers. Students have the opportunity to apply their knowledge and risk analysis to a real decision for a real decision maker. Prerequisites: OPER 543 (old OPER 645) or OPER 646. Fall Quarter 3 credit hours OPER 746 – ADVANCED TOPICS IN RELIABILITY: This course develops advanced mathematical concepts for application in the reliability and maintainability areas. Topics include censored reliability data analysis, optimal preventive maintenance policies, warranty analysis, burn-in strategies and other topics of current interest. The emphasis is on both analytic development as well as actual application to data analysis. The course will consider the implications of reliability during the system design phase as well as the system operational phase. Simulation software as well as “solver” software will be utilized in class exercises. Prerequisites: STAT 687 or STAT 697. 3 credit hours OPER 747 – QUEUEING NETWORKS: This course applies results from fundamental queueing theory to complex networks of queues. Specific topics of study include the modeling and analysis of product-form networks (open and closed), BCMP networks, and networks with multiple classes of customers. Approximation methods, including diffusion and decomposition, are explored. Applications in telecommunications, transportation, and manufacturing are also discussed. Prerequisites: OPER 647. 3 credit hours OPER 760 – STATISTICAL ASPECTS OF SIMULATION: OUTPUT ANALYSIS: This course provides an in-depth treatment of a number of important issues in the statistical aspects of simulation. The emphasis in this course is on output modeling. Topics include the analysis of terminating and steady state simulation output as well as variance reduction techniques. It is intended to provide a rigorous treatment of current issues within the simulation literature. Prerequisites: OPER 660. Winter Quarter 3 credit hours OPER 785 – APPLIED MULTIVARIATE ANALYSIS II: PATTERN RECOGNITION: This course is a survey course in pattern recognition. The course covers Bayesian Decision Theory, parameter estimation, linear discriminant functions, multilayer neural networks, and other topics. Real- world applications will be emphasized. Prerequisites: OPER 685 or Permission of Instructor. Fall Quarter 3 credit hours OPER 786 -APPLIED MULTIVARIATE ANALYSIS III: ADVANCED TOPICS: This course examines a variety of topics in pattern recognition such as Bayesian networks, hidden Markov models, neural feature selection procedures and sensor fusion. Recent research in these areas is explored. Prerequisites: OPER 785 or Permission of Instructor. Spring Quarter 3 credit hours OPER 791– RESEARCH PROJECT FOR OPERATIONAL SCIENCES: (Non-thesis only.) A research topic is selected from problems of interest to USAF and DoD. This topic is thoroughly investigated by the student, and the findings, recommendations, and conclusions are presented as a graduate research paper under the supervision of an AFIT faculty member. Prerequisites: None. 6 credit hours OPER 799 – THESIS RESEARCH: Prerequisites: None. 1-12 credit hours OPER 999 – DISSERTATION RESEARCH: Prerequisites: Approval of Research Advisor. 1-12 credit hours AFIT Home Graduate School Home Please send questions or comments to ENS webmaster |