Graduate Courses

The faculty has approval to offer the following courses in the academic years 2017–2018 and 2018–2019; however, not all courses are taught each semester or summer session. Students should consult the Course Schedule to determine which courses and topics will be offered during a particular semester or summer session. The Course Schedule may also reflect changes made to the course inventory after the publication of this catalog.

Operations Research and Industrial Engineering: ORI

ORI 180M, 280M, 380M, 680M, 980M. Research.

May be repeated for credit. Offered on the credit/no credit basis only. Prerequisite: Graduate standing in operations research and industrial engineering.

ORI 381. Deterministic Methods for Operations Research.

Theory and algorithms for deterministic operations research methods. Algorithms for solving linear, integer, and nonlinear optimization models. Three lecture hours a week for one semester. May not be counted toward a degree in operations research and industrial engineering. Prerequisite: Graduate standing.

ORI 382. Stochastic Methods for Operations Research.

Theory and algorithms for stochastic operations research methods. Algorithms related to stochastic processes: Markov chain analysis; queueing theory; stochastic inventory theory and decision analysis. Three lecture hours a week for one semester. May not be counted toward a degree in operations research and industrial engineering. Prerequisite: Graduate standing and Mechanical Engineering 335 or the equivalent.

ORI 390Q. Industrial Engineering.

Industrial engineering techniques for quantitative solution of contemporary systems and management problems. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of instructor.

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. 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. Same as Mechanical Engineering 392Q (Topic 10: 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. Additional prerequisite: Knowledge of basic probability and statistics and consent of instructor.

ORI 390R. Statistics and Probability.

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. May be repeated for credit when the topics vary. Prerequisite: Graduate standing, and an undergraduate calculus-based course in probability and statistics or consent of instructor.

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. Same as Mechanical Engineering 384Q (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. 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 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. Same as Mechanical Engineering 388H. 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 391Q. Optimization.

Mathematical optimization techniques with applications to engineering and industrial problems. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and a course in operations research methods.

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.
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: A graduate course in integer programming.
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 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. Prerequisite: Coursework in computer programming, algorithms and optimization, and probability; or consent of instructor.
Topic 15: Convex Optimization. Same as Electrical Engineering 381K (Topic 18). 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 Engineering 381K (Topic 18), 381V (Topic: Large Scale Optimization), Operations Research and Industrial Engineering 391Q (Topic 15).
Topic 16: Optimization in Engineering Systems. Same as Electrical Engineering 380N (Topic 11). Formulation and solution of continuous optimization problems in engineering design and operations. Electrical Engineering 380N (Topic 11) and Operations Research and Industrial Engineering 391Q (Topic 16) may not both be counted.

ORI 397. Current Studies in Operations Research and Industrial Engineering.

The equivalent of three class hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing and consent of the graduate adviser.

ORI 197K, 297K, 397K. Graduate Seminar.

One, two, or three lecture hours a week for one semester. Normally required of all students in operations research and industrial engineering. May be repeated for credit. Offered on the credit/no credit basis only. Prerequisite: Graduate standing.

ORI 397M. Graduate Research Internship.

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. Offered on the credit/no credit basis only. Prerequisite: Graduate standing and consent of the graduate adviser and supervising faculty member.

ORI 197P, 297P, 397P. Projects in Operations Research and Industrial Engineering.

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. May be repeated for credit. Prerequisite: Graduate standing and consent of instructor and the graduate adviser.

ORI 698. Thesis.

The equivalent of three lecture hours a week for two semesters. Offered on the credit/no credit basis only. Prerequisite: For 698A, graduate standing in operations research and industrial engineering and consent of the graduate adviser; for 698B, Operations Research and Industrial Engineering 698A.

ORI 398R. Master's Report.

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. Offered on the credit/no credit basis only. Prerequisite: Graduate standing in operations research and industrial engineering and consent of the graduate adviser.

ORI 399R, 699R, 999R. Dissertation.

Offered on the credit/no credit basis only. Prerequisite: Admission to candidacy for the doctoral degree.

ORI 399W, 699W, 999W. Dissertation.

Offered on the credit/no credit basis only. Prerequisite: Operations Research and Industrial Engineering 399R, 699R, or 999R.