Operations Research and Industrial Engineering (ORI)
ORI 119S, 219S, 319S, 419S, 519S, 619S, 719S, 819S, 919S Topics in Operations Research and Industrial Engineering 1-9 Hours
0 Lecture Hours 0 Lab Hours
This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mechanical Engineering. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.
Grading: Student Option
Repeatable for credit: May be repeated for credit when the topics vary.
Academic Level: Lower Division
ORI 129S, 229S, 329S, 429S, 529S, 629S, 729S, 829S, 929S Topics in Operations Research and Industrial Engineering 1-9 Hours
0 Lecture Hours 0 Lab Hours
This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mechanical Engineering. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.
Grading: Student Option
Repeatable for credit: May be repeated for credit when the topics vary.
Academic Level: Upper Division
ORI 365 Data Science for Engineers 3 Hours
3 Lecture Hours 0 Lab Hours
Learn data analysis and programming skills. Explore essential data science techniques, including regression, decision trees, classification, and neural networks. Only one of the following may be counted: Mechanical Engineering 365D, 379M (Topic: Data Science for Engineers), Operations Research and Industrial Engineering 365. Three lecture hours a week for one semester.
Same as: M E 365D
Pre/Corequisites: Upper-division standing; Mechanical Engineering 205 or 318M, and Mechanical Engineering 335
Grading: Student Option
Repeatable for credit: No
Academic Level: Upper Division
ORI 366 Operations Research Models 3 Hours
3 Lecture Hours 0 Lab Hours
Formulation and solution-interpretation for operations research models requiring, for example, optimization, simulation, or analysis of Markov chains or queues. Applications include manufacturing design and control, routing and scheduling, plant location, inventory analysis, and management of queueing systems. Mechanical Engineering 366L and Operations Research and Industrial Engineering 366 may not both be counted. Three lecture hours a week for one semester.
Same as: M E 366L
Pre/Corequisites: For engineering majors, Mathematics 408D or 408M and Mechanical Engineering 318M and 335 with a grade of at least C- in each; for non-engineering majors, upper-division standing and written consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Upper Division
ORI 367 Simulation Modeling 3 Hours
3 Lecture Hours 0 Lab Hours
Basic concepts of discrete-event simulation. Statistical input and output analysis. Application of simulation software. Modeling of systems under uncertainty. Mechanical Engineering 367S and Operations Research and Industrial Engineering 367 may not both be counted. Three lecture hours a week for one semester.
Same as: M E 367S
Pre/Corequisites: For engineering majors, Mechanical Engineering 318M with a grade of at least C-, Mechanical Engineering 335 or the equivalent; for non-engineering majors, upper-division standing and written consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Upper Division
ORI 369 Decision Analysis 3 Hours
3 Lecture Hours 0 Lab Hours
Principles and application of techniques for the logical illumination of complex decision problems within any context. Subjects may include utility theory, probability as a statement of belief, risk preference, value of information and control, probability assessment, influence diagrams, risk sharing and scaling, and life-and-death decision making. Three lecture hours a week for one semester.
Pre/Corequisites: Mechanical Engineering 353 or equivalent with a grade of at least C-.
Grading: Student Option
Repeatable for credit: No
Academic Level: Upper Division
ORI 370 Statistical Methods in Manufacturing 3 Hours
3 Lecture Hours 0 Lab Hours
Contemporary concepts and methods for statistical quality design and control will be presented. These include: descriptive statistics, behavior of process over time, design and interpretation of control charts, process capability studies, measurement system analysis, correlation and regression analysis, design and analysis of two level factorial experiments, design and analysis of two level fractional factorial experiments, response surface methodology, and Taguchi approach to robust design. Mechanical Engineering 379M (Topic: Stat Methods in Manufacturing) and Operations Research and Industrial Engineering 370 may not both be counted. Three lecture hours a week for one semester.
Pre/Corequisites: For engineering majors, Mechanical Engineering 318M with a grade of at least C-, Mechanical Engineering 335 or the equivalent; for others, upper-division standing and written consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Upper Division
ORI 373 Facility Planning and Logistics 3 Hours
3 Lecture Hours 0 Lab Hours
Design and analysis of production systems, including plant layout and location, material flow, and flexible manufacturing. Only one of the following may be counted: Mechanical Engineering 373K, Operations Research and Industrial Engineering 371, 373. Three lecture hours a week for one semester.
Pre/Corequisites: For engineering majors, ME 318M or the equivalent with a grade of at least C, and M E 335 or the equivalent; for non-engineering majors, upper-division standing and written consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Upper Division
ORI 374 Production and Inventory Management 3 Hours
3 Lecture Hours 0 Lab Hours
Introduction to production and inventory models; basic factory dynamics; analysis of variability; push-and-pull production control; sequencing and dispatching. Only one of the following may be counted: Mechanical Engineering 375K, Operations Research and Industrial Engineering 372, 374. Three lecture hours a week for one semester.
Pre/Corequisites: For engineering majors, Mechanical Engineering 318M or the equivalent with a grade of at least C, Mechanical Engineering 335 or the equivalent; for non-engineering majors, upper-division standing and written consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Upper Division
ORI 177K, 277K, 377K Projects in Operations Research and Industrial Engineering 1-3 Hours
1,2,3 Lecture Hours 0.5-1.5 Lab Hours
Independent project carried out under the supervision of a faculty member in operations research & industrial engineering. Student prepares a project proposal and a final report, each of which is evaluated by the faculty committee on individual projects. For each semester hour of credit earned, the equivalent of one lecture hour and half an hour of laboratory a week for one semester.
Pre/Corequisites: A University grade point average of at least 2.50 and a grade point average in the major of at least 2.50; approval of project proposal by the faculty committee on individual projects.
Grading: Student Option
Repeatable for credit: No
Academic Level: Upper Division
ORI 180M, 280M, 380M, 680M, 980M Research 1,2,3,6,9 Hours
1,2,3,6,9 Lecture Hours 0 Lab Hours
Pre/Corequisites: Graduate standing in operations research and industrial engineering.
Grading: Credit No Credit
Repeatable for credit: Yes (Unlimited)
ORI 383 Healthcare Delivery Models 3 Hours
3 Lecture Hours 0 Lab Hours
Study the operations research literature on the use of models and techniques related to healthcare delivery. Discuss decomposition techniques for integer programs, simulation, Markov chains, and stochastic programming. Operations Research and Industrial Engineering 383 and 397 (Topic: Health Care Delivery Models) may not both be counted. Three lecture hours per week for one semester.
Pre/Corequisites: Second year or higher graduate standing; graduate courses in linear programming, integer programming, statistics, stochastic processes.
Grading: Student Option
Repeatable for credit: No
Academic Level: Master's
ORI 384 Emerging Trends in Operations Research and Industrial Engineering 3 Hours
3 Lecture Hours 0 Lab Hours
Explore the development and use of operations research and industrial engineering techniques via weekly presentations and speakers, including faculty and visiting experts. Operations Research and Industrial Engineering 384 and 397 (Topic: Emerging Topics in ORIE) may not both be counted. Three lecture hours a week for one semester.
Pre/Corequisites: Second year or higher graduate standing in Operations Research and Industrial Engineering, or related program.
Grading: Student Option
Repeatable for credit: No
Academic Level: Master's
ORI 390D Topics in Analytics and Decision Making 3 Hours
3 Lecture Hours 0 Lab Hours
Discuss the tools and concepts to enable quantitative analysis and to support decisions under uncertainty. Three lecture hours per week for one semester.
Pre/Corequisites: Graduate standing and an undergraduate calculus-based course in probability and statistics, or consent of instructor.
Grading: Student Option
Repeatable for credit: May be repeated for credit when the topics vary.
Academic Level: Doctoral
Topic 1: Analytics and Data Science. Examine theory and methods to draw inferences from data and apply these insights to support decision making in uncertain environments. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 1).
Topic 2: Decision Analysis. Examine the theory and principles required to make good decisions in the face of uncertainty. Discuss expected utility theory, families of utility functions, Bayesian inference, value of information, probability elicitation, scoring rules, and the verification of probabilistic forecasts. Explore how these apply to areas including engineering, business, public policy, healthcare, and sports. Operations Research and Industrial Engineering 390D (Topic 2) and 390R (Topic 17) may not both be counted. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 1).
Topic 3: Decision Engineering. Examine the tools, methods, and processes required to apply decision analysis to applied problems. Explore creativity, framing, ideation, modeling, approximations, and decision biases that can degrade decision making. Operations Research and Industrial Engineering 390D (Topic 3) and 390R (Topic 18) may not both be counted. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 1) and 390D (Topic 2).
Topic 4: Decision Theory. Explore the fundamental axioms supporting decision analysis and challenges to this approach. Examine behavioral decision making, subjective probability, alternative approaches to decision making, and advanced decision analytic tools. Additional prerequisite: Operations Research and Industrial Engineering 390D (Topic 2).
Topic 5: Markov Decision Processes. Discuss the theory and application of Markov decision processes. Examine finite horizon models, average-cost and discounted-cost infinite horizon problems, discrete-time and continuous-time frameworks. Explore approximate dynamic programming, reinforcement learning, and stochastic bandit problems. Operations Research and Industrial Engineering 390D (Topic 5) and 390R (Topic 16) may not both be counted. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 5) or consent of instructor.
Topic 6: Systems Modeling and Decision Making. Explore the application of operations research, decision analysis, economics, and management science tools and concepts to the modeling of human-designed and natural systems with the goal of improving decisions that involve these systems. Examine models that integrate engineering, economics, natural science, and policy. Only one of the following may be counted: Operations Research and Industrial Engineering 390D (Topic 6), 390Q (Topic 8), 397 (Topic: Systems Modeling). Additional prerequisite: A course in optimization, or consent of instructor. Prior coursework in microeconomics is helpful but not required.
ORI 390D.1 Analytics and Data Science 3 Hours
3 Lecture Hours 0 Lab Hours
Examine theory and methods to draw inferences from data and apply these insights to support decision making in uncertain environments.
Pre/Corequisites: Operations Research and Industrial Engineering 390R (Topic 1).
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390D.2 Decision Analysis 3 Hours
3 Lecture Hours 0 Lab Hours
Examine the theory and principles required to make good decisions in the face of uncertainty. Discuss expected utility theory, families of utility functions, Bayesian inference, value of information, probability elicitation, scoring rules, and the verification of probabilistic forecasts. Explore how these apply to areas including engineering, business, public policy, healthcare, and sports. Operations Research and Industrial Engineering 390D (Topic 2) and 390R (Topic 17) may not both be counted.
Pre/Corequisites: Operations Research and Industrial Engineering 390R (Topic 1).
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390D.3 Decision Engineering 3 Hours
3 Lecture Hours 0 Lab Hours
Examine the tools, methods, and processes required to apply decision analysis to applied problems. Explore creativity, framing, ideation, modeling, approximations, and decision biases that can degrade decision making. Operations Research and Industrial Engineering 390D (Topic 3) and 390R (Topic 18) may not both be counted.
Pre/Corequisites: Operations Research and Industrial Engineering 390R (Topic 1) and 390D (Topic 2).
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390D.4 Decision Theory 3 Hours
3 Lecture Hours 0 Lab Hours
Explore the fundamental axioms supporting decision analysis and challenges to this approach. Examine behavioral decision making, subjective probability, alternative approaches to decision making, and advanced decision analytic tools.
Pre/Corequisites: Operations Research and Industrial Engineering 390D (Topic 2).
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390D.5 Markov Decision Processes 3 Hours
3 Lecture Hours 0 Lab Hours
Discuss the theory and application of Markov decision processes. Examine finite horizon models, average-cost and discounted-cost infinite horizon problems, discrete-time and continuous-time frameworks. Explore approximate dynamic programming, reinforcement learning, and stochastic bandit problems. Operations Research and Industrial Engineering 390D (Topic 5) and 390R (Topic 16) may not both be counted.
Pre/Corequisites: Operations Research and Industrial Engineering 390R (Topic 5) or consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390D.6 Systems Modeling and Decision Making 3 Hours
3 Lecture Hours 0 Lab Hours
Explore the application of operations research, decision analysis, economics, and management science tools and concepts to the modeling of human-designed and natural systems with the goal of improving decisions that involve these systems. Examine models that integrate engineering, economics, natural science, and policy. Only one of the following may be counted: Operations Research and Industrial Engineering 390D (Topic 6), 390Q (Topic 8), 397 (Topic: Systems Modeling).
Pre/Corequisites: A course in optimization, or consent of instructor. Prior coursework in microeconomics is helpful but not required.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390Q Topics in Industrial Engineering 3 Hours
3 Lecture Hours 0 Lab Hours
Industrial engineering techniques for quantitative solution of contemporary systems and management problems. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.
Grading: Student Option
Repeatable for credit: May be repeated for credit when the topics vary.
Academic Level: Doctoral
Topic 1: Project Management. Methods for organizing, coordinating, and controlling resources to minimize risk and conflict and to maintain budgets and schedules. Topics include evaluation of competing alternatives, organization of a project, scheduling of tasks and resources, and the role of management over time.
Topic 2: Production and Inventory Control. Issues in inventory control with known and unknown demand, materials requirement planning, just-in-time, pull control systems, operations scheduling, dispatching and aggregate planning, and the basic dynamics of production and inventory control.
Topic 3: Facility Layout and Location. Layout of operations within a facility, design of the material flow, choice of flexible manufacturing systems and/or cellular manufacturing, location of facilities within a geographic region, and distribution using mathematical models and optimization.
Topic 4: Modeling and Analysis of Manufacturing Systems. Applications of analysis to manufacturing processes, using mathematical models, optimization, and stochastic analysis. Economic evaluation, identification of bottlenecks, estimation of resources requirements, and system design.
Topic 5: Scheduling Theory and Applications. Modeling, analysis, and solution techniques for production and service scheduling problems, machine scheduling in deterministic and stochastic settings, exact and heuristic algorithms, and industrial applications, including semiconductor manufacturing and airlines applications. Additional prerequisite: Operations Research and Industrial Engineering 391Q (Topic 4) or the equivalent.
Topic 6: Multicriteria Decision Making. Techniques for problems involving more than one criterion measured on incommensurate scales, such as dollars, reliability, and quality of life. Topics include methods for generating nondominated solutions, interactive procedures for continuous problems, goal programming, multi-attribute utility theory, and the analytic hierarchy process.
Topic 7: Statistical Methods in Manufacturing. Statistical monitoring of manufacturing processes; methods and applications of various control charts; formal design of experiments (DOE), including the statistical evaluation of main and interaction effects, as well as intelligent experimentation through reduced factorial experimental design; Taguchi's design philosophy as applied to response surface methods and gradient-based search techniques; and advanced issues in quality control and design of manufacturing systems. Same as: M E 392Q.10 Additional prerequisite: Knowledge of basic probability and statistics and consent of instructor.
Topic 8: Systems Modeling. Use approaches from operations research and industrial engineering to construct systems models that permit rigorous analysis of complex, real-world problems. Particular emphasis is devoted to models that integrate concepts from engineering, economics, natural sciences, and policy. Featured modeling challenges are chosen to showcase broad ranges of methodologies and application domains. Operations Research and Industrial Engineering 390Q (Topic 8) and 397 (Topic: Systems Modeling) may not both be counted. Three lecture hours a week for one semester. Additional prerequisite: Graduate standing and a course in optimization, or consent of instructor. Prior coursework in microeconomics is helpful but not required.
Topic 9: Analytics and Control in Semiconductor Manufacturing. Learn key data analytics and process control methods for turning metrology and sensing data into useful information and decisions in semiconductor manufacturing. Explore applications of statistical models for statistical process control, as well as applications of dynamic models for virtual metrology and run-to-run control in semiconductor manufacturing systems. Only one of the following may be counted: Mechanical Engineering 397 (Topic: Analytics/Control Semi Manuf), 392Q (Topic 13), Operations Research and Industrial Engineering 397 (Topic: Analytics/Control Semi Manuf), 390Q (Topic 9). Same as: M E 392Q.13
Topic 10: Logistics Analytics. Discuss strategic, tactical, and operational logistics decision making; exact and heuristic methods for logistics problems; optimization models; deterministic and stochastic logistics modeling; network design and routing; manufacturing, service, and transportation logistics; applications. Explore freight logistics, humanitarian logistics and disaster management. Operations Research and Industrial Engineering 390Q (Topic 10) and 397 (Topic: Logistics Analytics) may not both be counted. Additional prerequisite: Operations Research and Industrial Engineering 391Q (Topic 4).
ORI 390Q.1 Project Management 3 Hours
3 Lecture Hours 0 Lab Hours
Methods for organizing, coordinating, and controlling resources to minimize risk and conflict and to maintain budgets and schedules. Topics include evaluation of competing alternatives, organization of a project, scheduling of tasks and resources, and the role of management over time.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390Q.10 Logistics Analytics 3 Hours
3 Lecture Hours 0 Lab Hours
Discuss strategic, tactical, and operational logistics decision making; exact and heuristic methods for logistics problems; optimization models; deterministic and stochastic logistics modeling; network design and routing; manufacturing, service, and transportation logistics; applications. Explore freight logistics, humanitarian logistics and disaster management. Operations Research and Industrial Engineering 390Q (Topic 10) and 397 (Topic: Logistics Analytics) may not both be counted.
Pre/Corequisites: Operations Research and Industrial Engineering 391Q (Topic 4).
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390Q.2 Production and Inventory Control 3 Hours
3 Lecture Hours 0 Lab Hours
Issues in inventory control with known and unknown demand, materials requirement planning, just-in-time, pull control systems, operations scheduling, dispatching and aggregate planning, and the basic dynamics of production and inventory control.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390Q.4 Modeling and Analysis of Manufacturing Systems 3 Hours
3 Lecture Hours 0 Lab Hours
Applications of analysis to manufacturing processes, using mathematical models, optimization, and stochastic analysis. Economic evaluation, identification of bottlenecks, estimation of resources requirements, and system design.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390Q.5 Scheduling Theory and Applications 3 Hours
3 Lecture Hours 0 Lab Hours
Modeling, analysis, and solution techniques for production and service scheduling problems, machine scheduling in deterministic and stochastic settings, exact and heuristic algorithms, and industrial applications, including semiconductor manufacturing and airlines applications.
Pre/Corequisites: Operations Research and Industrial Engineering 391Q (Topic 4) or the equivalent.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390Q.7 Statistical Methods in Manufacturing 3 Hours
3 Lecture Hours 0 Lab Hours
Statistical monitoring of manufacturing processes; methods and applications of various control charts; formal design of experiments (DOE), including the statistical evaluation of main and interaction effects, as well as intelligent experimentation through reduced factorial experimental design; Taguchi's design philosophy as applied to response surface methods and gradient-based search techniques; and advanced issues in quality control and design of manufacturing systems.
Same as: M E 392Q.10
Pre/Corequisites: Knowledge of basic probability and statistics and consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390Q.9 Analytics and Control in Semiconductor Manufacturing 3 Hours
3 Lecture Hours 0 Lab Hours
Learn key data analytics and process control methods for turning metrology and sensing data into useful information and decisions in semiconductor manufacturing. Explore applications of statistical models for statistical process control, as well as applications of dynamic models for virtual metrology and run-to-run control in semiconductor manufacturing systems. Only one of the following may be counted: Mechanical Engineering 397 (Topic: Analytics/Control Semi Manuf), 392Q (Topic 13), Operations Research and Industrial Engineering 397 (Topic: Analytics/Control Semi Manuf), 390Q (Topic 9).
Same as: M E 392Q.13
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390R Topics in Statistics and Probability 3 Hours
3 Lecture Hours 0 Lab Hours
Concepts of probability and mathematical statistics; application of these analytical methods to planning and evaluation of research and industrial experimentation. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing, and an undergraduate calculus-based course in probability and statistics or consent of instructor.
Grading: Student Option
Repeatable for credit: May be repeated for credit when the topics vary.
Academic Level: Doctoral
Topic 1: Applied Probability. Basic probability theory, combinatorial analysis of random phenomena, conditional probability and independence, parametric families of distributions, expectation, distribution of functions of random variables, limit theorems.
Topic 2: Mathematical Statistics. Sampling distributions, properties of estimators, point and interval estimation, hypothesis testing, introduction to multivariate and nonparametric statistics.
Topic 3: Time-Series Modeling, Analysis, and Control. Methods for analytical modeling, analysis, prediction, and control of linear, stationary time series. Includes examples of advanced research in nonstationary time-series modeling and applications in manufacturing, financial engineering, geosciences, and other areas. Students complete a project on a topic of their choice. Same as: M E 384Q.3 Additional prerequisite: Graduate standing, Mechanical Engineering 364L or the equivalent, an undergraduate calculus-based course in probability and statistics or consent of instructor.
Topic 4: Reliability Theory and Modeling. Theory of probabilistic and statistical models of aging elements, reliability, replacement, and repair maintenance, and their integration in surveillance, quality control, and manufacturing problems.
Topic 5: Applied Stochastic Processes. Poisson process, renewal theory, discrete and continuous-time Markov chains, queueing and reliability applications.
Topic 6: Regression and Analysis of Variance. Fitting equations to data; joint confidence regions; partial correlation analysis; general linear hypotheses; dummy variables; diagnostics and remedial measures; design of experiments; fixed, random, and mixed models; factorial and nested designs. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 2) or consent of instructor.
Topic 7: Statistical Techniques in Image Processing. Statistical techniques for transformation, enhancement, restoration, segmentation, and classification of digital image data.
Topic 8: Queueing Theory. Introduction to the classical and modern theories of queueing systems. Simple Markovian queues; the M/G/1 and G/G/1 queues; Jackson and Kelly networks; multiclass networks; stability, scheduling, and routing in queueing networks; fluid and diffusion approximations. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 1) or consent of instructor.
Topic 9: Systems Simulation. Random number generation, simulation experiments, statistical verification, clock routines, simulation language applications, industrial problems.
Topic 10: Statistical Design of Experiments. Introduction to statistical design of experiments based on both classical analysis of variance and modern heuristic techniques. Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 1) or the equivalent, 390R (Topic 2) or the equivalent, and 390R (Topic 6) or the equivalent.
Topic 11: Advanced Stochastic Processes. Markov renewal processes, generalized semi-Markov processes, marked point processes, Martingale theory, Brownian motion, Levy processes, and stochastic calculus.
Topic 12: Multivariate Statistical Analysis. Theory and applications of multivariate statistics, including multivariate parametric distributions, estimation, hypothesis testing, principal components analysis, canonical correlation, multivariate regression, and classification.
Topic 13: Operations Research: Stochastic Models. Stochastic processes and models in operations research; discrete- and continuous-time Markov chains; queueing and inventory models; simulation. May not be counted toward the Master of Science in Engineering degree with a major in operations research and industrial engineering. Additional prerequisite: Mechanical Engineering 335 or the equivalent.
Topic 14: Special Topics in Probability, Stochastic Processes, and Statistics. Study of specialized topics, such as advanced stochastic processes, Bayesian statistics, simulation, and stochastic optimization, intended to introduce and stimulate further research. Additional prerequisite: Consent of instructor.
Topic 15: Nuclear Safety and Security. Probabilistic risk assessment models and nuclear arms nonproliferation, including failure classifications; failure mode, effects, and criticality analysis (FMECA); fault and event trees; and reliability block diagrams. Discussion of specific areas from the Code of Federal Regulations. Only one of the following may be counted: Mechanical Engineering 337G, 388H, Operations Research and Industrial Engineering 390R (Topic 15).
Topic 16: Markov Decision Processes. The theory of Markov decision processes, also known as stochastic dynamic programming. Includes finite horizon, total discounted cost, and average cost problems; continuous-time and semi-Markokv models; and applications in finance, queueing, and control theory. Additional prerequisite: A course in stochastic processes or consent of instructor.
Topic 17: Decision Analysis. Principles and application of techniques for the logical illumination of complex decision problems within any context. Subjects may include utility theory, probability as a statement of belief, risk preference, value of information and control, probability assessment, influence diagrams, risk sharing and scaling, and life-and-death decision making.
Topic 18: Decision Engineering. Application of decision analysis in practice including framing, decision modeling, sensitivity analysis, discretization, psychological aspects of decision making, probability assessment, and challenges to the decision analysis framework. May include related subjects such as real options, bidding, and portfolio management.
ORI 390R.1 Applied Probability 3 Hours
3 Lecture Hours 0 Lab Hours
Basic probability theory, combinatorial analysis of random phenomena, conditional probability and independence, parametric families of distributions, expectation, distribution of functions of random variables, limit theorems.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390R.14 Special Topics in Probability, Stochastic Processes, and Statistics 3 Hours
3 Lecture Hours 0 Lab Hours
Study of specialized topics, such as advanced stochastic processes, Bayesian statistics, simulation, and stochastic optimization, intended to introduce and stimulate further research.
Pre/Corequisites: Consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390R.2 Mathematical Statistics 3 Hours
3 Lecture Hours 0 Lab Hours
Sampling distributions, properties of estimators, point and interval estimation, hypothesis testing, introduction to multivariate and nonparametric statistics.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390R.3 Time-Series Modeling, Analysis, and Control 3 Hours
3 Lecture Hours 0 Lab Hours
Methods for analytical modeling, analysis, prediction, and control of linear, stationary time series. Includes examples of advanced research in nonstationary time-series modeling and applications in manufacturing, financial engineering, geosciences, and other areas. Students complete a project on a topic of their choice.
Same as: M E 384Q.3
Pre/Corequisites: Graduate standing, Mechanical Engineering 364L or the equivalent, an undergraduate calculus-based course in probability and statistics or consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390R.4 Reliability Theory and Modeling 3 Hours
3 Lecture Hours 0 Lab Hours
Theory of probabilistic and statistical models of aging elements, reliability, replacement, and repair maintenance, and their integration in surveillance, quality control, and manufacturing problems.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390R.5 Applied Stochastic Processes 3 Hours
3 Lecture Hours 0 Lab Hours
Poisson process, renewal theory, discrete and continuous-time Markov chains, queueing and reliability applications.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390R.6 Regression and Analysis of Variance 3 Hours
3 Lecture Hours 0 Lab Hours
Fitting equations to data; joint confidence regions; partial correlation analysis; general linear hypotheses; dummy variables; diagnostics and remedial measures; design of experiments; fixed, random, and mixed models; factorial and nested designs.
Pre/Corequisites: Operations Research and Industrial Engineering 390R (Topic 2) or consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390R.8 Queueing Theory 3 Hours
3 Lecture Hours 0 Lab Hours
Introduction to the classical and modern theories of queueing systems. Simple Markovian queues; the M/G/1 and G/G/1 queues; Jackson and Kelly networks; multiclass networks; stability, scheduling, and routing in queueing networks; fluid and diffusion approximations.
Pre/Corequisites: Operations Research and Industrial Engineering 390R (Topic 1) or consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 390R.9 Systems Simulation 3 Hours
3 Lecture Hours 0 Lab Hours
Random number generation, simulation experiments, statistical verification, clock routines, simulation language applications, industrial problems.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q Topics in Optimization 3 Hours
3 Lecture Hours 0 Lab Hours
Mathematical optimization techniques with applications to engineering and industrial problems. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and a course in operations research methods.
Grading: Student Option
Repeatable for credit: May be repeated for credit when the topics vary.
Academic Level: Doctoral
Topic 1: Nonlinear Programming. Theory and solution techniques for nonlinear, continuous optimization problems. Topological properties of functions, general convexity, optimality conditions, line search methods, unconstrained techniques, and algorithms for constrained formulations. Lagrangian duality theory and bundle methods for nondifferentiable optimization.
Topic 2: Dynamic Programming. Systems that require sequential decisions. Problem modeling and solution algorithms for deterministic and stochastic systems.
Topic 3: Network Flow Programming. Optimization problems related to network flows, shortest path, maximum flow, minimum cost flow, generalized networks, nonlinear costs. Modeling, theory, and computational methods.
Topic 4: Integer Programming. Models, theory, and computational methods for problems with discrete decision alternatives. Greedy algorithms, branch and bound, cutting plane methods, Lagrangian relaxation, and heuristics. Additional prerequisite: Operations Research and Industrial Engineering 391Q (Topic 5).
Topic 5: Linear Programming. Models, algorithms, and theory of linear programming. Linear programming geometry, primal, dual and revised simplex algorithms, duality theory, optimality conditions, sensitivity analyses, interior point methods, and computer implementations.
Topic 6: Algorithms for Mixed Integer Programming. Methods and software for solving large-scale mixed integer programming problems: intelligent heuristics, decomposition, lower bounding schemes, limited enumeration, and simple methods for quickly finding good feasible solutions. Numerous examples taken from industry. Additional prerequisite: Operations Research and Industrial Engineering 391Q (Topic 4).
Topic 7: Multicriteria Decision Making. Techniques for problems involving more than one criterion measured on incommensurate scales, such as dollars, reliability, and quality of life. Topics include methods for generating nondominated solutions, interactive procedures for continuous problems, goal programming, multiattribute utility theory, and the analytic hierarchy process.
Topic 8: Combinatorial Optimization. Optimization of combinatorial structures; computational complexity; stable marriages, shortest paths, maximum flows, minimum-cost flows, matching problems; approximation algorithms for NP-hard problems.
Topic 9: Large-Scale Systems Optimization. Mathematical programs with special structure, Dantzig-Wolfe decomposition, partitioning and relaxation procedures, duality and decomposition, compact inverse methods, applications in engineering and management.
Topic 10: Stochastic Optimization. Optimization of mathematical programming models under uncertainty; model formulations; exact, bounding-and-approximation, and Monte Carlo sampling-based solution techniques that exploit special structures; applications; use of algebraic modeling language.
Topic 11: Advanced Mathematical Programming. Advanced topics in modeling and algorithms for linear, integer, nonlinear, and network programming. Model formulation considerations, decomposition algorithms, interior point and active set methods, duality, modern optimization software. Additional prerequisite: Operations Research and Industrial Engineering 391Q (Topic 5).
Topic 12: Metaheuristics. Reactive and adaptive tabu search methods, simulated annealing, genetic algorithms, and greedy randomized adaptive search methods. Emphasis on theoretical context of methods and on similarities and distinguishing characteristics.
Topic 13: Operations Research: Deterministic Models. Modern optimization techniques. Linear optimization, network optimization models, integer programming, and nonlinear programming. May not be counted toward the Master of Science in Engineering degree with a major in operations research and industrial engineering. Additional prerequisite: Mathematics 408D or the equivalent.
Topic 14: Computational Optimization. Computer programming methods and tools for implementing advanced optimization algorithms, working with data, and visualizing results. Code organization techniques, debugging, and building complex software. Additional prerequisite: Coursework in computer programming, algorithms and optimization, and probability; or consent of instructor.
Topic 15: Convex Optimization. The fundamentals of convex optimization with a focus on modeling, computation and scale: convex sets and functions, unconstrained optimization via first and second-order methods, duality, constrained optimization, SDPs, stochastic and sub-gradient descent methods, ADMMs, and applications. Only one of the following may be counted: Electrical and Computer Engineering 381K (Topic 18), Electrical Engineering 381K (Topic 18), 381V (Topic: Large Scale Optimization), Operations Research and Industrial Engineering 391Q (Topic 15). Same as: ECE 381K.18 Additional prerequisite: Consent of instructor.
Topic 16: Optimization in Engineering Systems. Formulation and solution of continuous optimization problems in engineering design and operations. Only one of the following may be counted: Electrical and Computer Engineering 380N (Topic 11), Electrical Engineering 380N (Topic 11), Operations Research and Industrial Engineering 391Q (Topic 16). Same as: ECE 380N.11
Topic 17: Optimization Under Uncertainty. Introduction to optimization models and methodologies for addressing uncertainty-affected decision problems. Examine fundamental techniques from stochastic programming, robust optimization, and distributionally robust optimization. Explore theory through concrete examples from production planning, supply chain management, project management, portfolio selection, machine learning. Operations Research and Industrial Engineering 391Q (Topic 17) and 397 (Topic: Optimzatn Under Uncertainty) may not both be counted. Three lecture hours per week for one semester. Additional prerequisite: Graduate-level knowledge of linear programming, integer programming, nonlinear programming, probability, and statistics. Knowledge of convex optimization and analysis is beneficial.
Topic 18: Computational and Variational Methods for Inverse Problems. Introduction to the numerical solution of inverse problems that are governed by systems of partial differential equations (PDEs). Explore variational formulations, ill-posedness, regularization, adjoint methods for gradients and Hessians, variational discretization, and efficient large-scale optimization algorithms for inverse problems. Examine the Bayesian framework and draw connections between the classical and the Bayesian interpretations of inverse problems. Additional prerequisite: Courses or background in linear algebra and differential equations.
ORI 391Q.1 Nonlinear Programming 3 Hours
3 Lecture Hours 0 Lab Hours
Theory and solution techniques for nonlinear, continuous optimization problems. Topological properties of functions, general convexity, optimality conditions, line search methods, unconstrained techniques, and algorithms for constrained formulations. Lagrangian duality theory and bundle methods for nondifferentiable optimization.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.10 Stochastic Optimization 3 Hours
3 Lecture Hours 0 Lab Hours
Optimization of mathematical programming models under uncertainty; model formulations; exact, bounding-and-approximation, and Monte Carlo sampling-based solution techniques that exploit special structures; applications; use of algebraic modeling language.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.11 Advanced Mathematical Programming 3 Hours
3 Lecture Hours 0 Lab Hours
Advanced topics in modeling and algorithms for linear, integer, nonlinear, and network programming. Model formulation considerations, decomposition algorithms, interior point and active set methods, duality, modern optimization software.
Pre/Corequisites: Operations Research and Industrial Engineering 391Q (Topic 5).
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.12 Metaheuristics 3 Hours
3 Lecture Hours 0 Lab Hours
Reactive and adaptive tabu search methods, simulated annealing, genetic algorithms, and greedy randomized adaptive search methods. Emphasis on theoretical context of methods and on similarities and distinguishing characteristics.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.14 Computational Optimization 3 Hours
3 Lecture Hours 0 Lab Hours
Computer programming methods and tools for implementing advanced optimization algorithms, working with data, and visualizing results. Code organization techniques, debugging, and building complex software.
Pre/Corequisites: Coursework in computer programming, algorithms and optimization, and probability; or consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.15 Convex Optimization 3 Hours
3 Lecture Hours 0 Lab Hours
The fundamentals of convex optimization with a focus on modeling, computation and scale: convex sets and functions, unconstrained optimization via first and second-order methods, duality, constrained optimization, SDPs, stochastic and sub-gradient descent methods, ADMMs, and applications. Only one of the following may be counted: Electrical and Computer Engineering 381K (Topic 18), Electrical Engineering 381K (Topic 18), 381V (Topic: Large Scale Optimization), Operations Research and Industrial Engineering 391Q (Topic 15).
Same as: ECE 381K.18
Pre/Corequisites: Consent of instructor.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.16 Optimization in Engineering Systems 3 Hours
3 Lecture Hours 0 Lab Hours
Formulation and solution of continuous optimization problems in engineering design and operations. Only one of the following may be counted: Electrical and Computer Engineering 380N (Topic 11), Electrical Engineering 380N (Topic 11), Operations Research and Industrial Engineering 391Q (Topic 16).
Same as: ECE 380N.11
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.17 Optimization Under Uncertainty 3 Hours
3 Lecture Hours 0 Lab Hours
Introduction to optimization models and methodologies for addressing uncertainty-affected decision problems. Examine fundamental techniques from stochastic programming, robust optimization, and distributionally robust optimization. Explore theory through concrete examples from production planning, supply chain management, project management, portfolio selection, machine learning. Operations Research and Industrial Engineering 391Q (Topic 17) and 397 (Topic: Optimzatn Under Uncertainty) may not both be counted. Three lecture hours per week for one semester.
Pre/Corequisites: Graduate-level knowledge of linear programming, integer programming, nonlinear programming, probability, and statistics. Knowledge of convex optimization and analysis is beneficial.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.18 Computational and Variational Methods for Inverse Problems 3 Hours
3 Lecture Hours 0 Lab Hours
Introduction to the numerical solution of inverse problems that are governed by systems of partial differential equations (PDEs). Explore variational formulations, ill-posedness, regularization, adjoint methods for gradients and Hessians, variational discretization, and efficient large-scale optimization algorithms for inverse problems. Examine the Bayesian framework and draw connections between the classical and the Bayesian interpretations of inverse problems.
Pre/Corequisites: Courses or background in linear algebra and differential equations.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.2 Dynamic Programming 3 Hours
3 Lecture Hours 0 Lab Hours
Systems that require sequential decisions. Problem modeling and solution algorithms for deterministic and stochastic systems.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.3 Network Flow Programming 3 Hours
3 Lecture Hours 0 Lab Hours
Optimization problems related to network flows, shortest path, maximum flow, minimum cost flow, generalized networks, nonlinear costs. Modeling, theory, and computational methods.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.4 Integer Programming 3 Hours
3 Lecture Hours 0 Lab Hours
Models, theory, and computational methods for problems with discrete decision alternatives. Greedy algorithms, branch and bound, cutting plane methods, Lagrangian relaxation, and heuristics.
Pre/Corequisites: Operations Research and Industrial Engineering 391Q (Topic 5).
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.5 Linear Programming 3 Hours
3 Lecture Hours 0 Lab Hours
Models, algorithms, and theory of linear programming. Linear programming geometry, primal, dual and revised simplex algorithms, duality theory, optimality conditions, sensitivity analyses, interior point methods, and computer implementations.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.6 Algorithms for Mixed Integer Programming 3 Hours
3 Lecture Hours 0 Lab Hours
Methods and software for solving large-scale mixed integer programming problems: intelligent heuristics, decomposition, lower bounding schemes, limited enumeration, and simple methods for quickly finding good feasible solutions. Numerous examples taken from industry.
Pre/Corequisites: Operations Research and Industrial Engineering 391Q (Topic 4).
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.8 Combinatorial Optimization 3 Hours
3 Lecture Hours 0 Lab Hours
Optimization of combinatorial structures; computational complexity; stable marriages, shortest paths, maximum flows, minimum-cost flows, matching problems; approximation algorithms for NP-hard problems.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 391Q.9 Large-Scale Systems Optimization 3 Hours
3 Lecture Hours 0 Lab Hours
Mathematical programs with special structure, Dantzig-Wolfe decomposition, partitioning and relaxation procedures, duality and decomposition, compact inverse methods, applications in engineering and management.
Grading: Student Option
Repeatable for credit: No
Academic Level: Doctoral
ORI 397 Current Topics in Operations Research and Industrial Engineering 3 Hours
3 Lecture Hours 0 Lab Hours
The equivalent of three class hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of the graduate adviser.
Grading: Student Option
Repeatable for credit: May be repeated for credit when the topics vary.
Academic Level: Doctoral
ORI 197K, 297K, 397K Graduate Seminar 1-3 Hours
1,2,3 Lecture Hours 0 Lab Hours
Normally required of all students in operations research and industrial engineering. One, two, or three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing.
Grading: Credit No Credit
Repeatable for credit: Yes (Unlimited)
ORI 397M Graduate Research Internship 3 Hours
20 Lecture Hours 0 Lab Hours
Students conduct research in an industrial setting to gain practical experience in their area of interest. Twenty to forty hours of fieldwork a week for one semester.
Pre/Corequisites: Graduate standing and consent of the graduate adviser and supervising faculty member.
Grading: Credit No Credit
Repeatable for credit: No
Academic Level: Doctoral
ORI 197P, 297P, 397P Projects in Operations Research and Industrial Engineering 1-3 Hours
0 Lecture Hours 3,6,9 Lab Hours
Independent project carried out under the supervision of a faculty member in operations research and industrial engineering. Three, six, or nine laboratory hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor and the graduate adviser.
Grading: Student Option
Repeatable for credit: Yes (Unlimited)
ORI 698 Thesis 6 Hours
3 Lecture Hours 0 Lab Hours
The equivalent of three lecture hours a week for two semesters.
Pre/Corequisites: For 698A, graduate standing in operations research and industrial engineering and consent of the graduate adviser; for 698B, Operations Research and Industrial Engineering 698A.
Grading: Credit No Credit
Repeatable for credit: No
Academic Level: Master's
ORI 398R Master's Report 3 Hours
3 Lecture Hours 0 Lab Hours
Preparation of a report to fulfill the requirement for the master's degree under the report option. The equivalent of three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing in operations research and industrial engineering and consent of the graduate adviser.
Grading: Credit No Credit
Repeatable for credit: No
Academic Level: Master's
ORI 399W, 699W, 999W Dissertation 3,6,9 Hours
3,6,9 Lecture Hours 0 Lab Hours
Pre/Corequisites: Admission to candidacy for the doctoral degree.
Grading: Credit No Credit
Repeatable for credit: Yes (Unlimited)
Academic Level: Doctoral