Operations Research and Industrial Engineering
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Graduate Courses
The faculty has approval to offer the following courses in the academic years 20012002 and 20022003; 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.
Unless otherwise stated below, each course meets for three lecture hours a week for one semester.
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.
390Q. Industrial Engineering.
Industrial engineering techniques for quantitative solution of contemporary systems and management problems. May be repeated for credit when the topics vary. Mechanical Engineering 390Q and Operations Research and Industrial Engineering 390Q may not both be counted unless 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, justintime, 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. Mechanical Engineering 392Q (Topic 3: Modeling and Analysis of Manufacturing Systems) and Operations Research and Industrial Engineering 390Q (Topic 4) may not both be counted.
390R. Statistics and Probability.
Concepts of probability and mathematical statistics; application of these analytical methods to planning and evaluation of research and industrial experimentation. May be repeated for credit when the topics vary. Mechanical Engineering 390R and Operations Research and Industrial Engineering 390R may not both be counted unless the topics vary. Prerequisite: Graduate standing, and an undergraduate calculusbased 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: TimeSeries Analysis.
Classical techniques in time domain forecasting BoxJenkins univariate, transfer function, and multivariate timeseries analysis.
Topic 4: Probability and Statistics for Applied Reliability 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 continuoustime 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. Only one of the following may be counted: Mechanical Engineering 390R (Topic 7: Queueing Theory), 391Q (Topic 3: Queueing Theory), Operations Research and Industrial Engineering 390R (Topic 8). Additional prerequisite: Operations Research and Industrial Engineering 390R (Topic 1) or consent of instructor.
Topic 9: Digital Systems Simulation.
Random number generation, simulation experiments, statistical verification, clock routines, simulation language applications, industrial problems. Only one of the following may be counted: Mechanical Engineering 390R (Topic 8: Digital Systems Simulation), 391Q (Topic 5: Digital Systems Simulation), Operations Research and Industrial Engineering 390R (Topic 9).
Topic 10: Statistical Design of Experiments.
Introduction to statistical design of experiments based on both classical analysis of variance and modern heuristic techniques. Mechanical Engineering 390R (Topic 9: Statistical Design of Experiments) and Operations Research and Industrial Engineering 390R (Topic 10) may not both be counted. 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 semiMarkov processes, marked point processes, Martingale theory, Brownian motion, Levy processes, and stochastic calculus. Mechanical Engineering 390R (Topic 10: Advanced Stochastic Processes) and Operations Research and Industrial Engineering 390R (Topic 11) may not both be counted.
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.
391Q. Optimization.
Mathematical optimization techniques with applications to engineering and industrial problems. May be repeated for credit when the topics vary. Mechanical Engineering 391Q and Operations Research and Industrial Engineering 391Q may not both be counted unless the topics vary. Prerequisite: Graduate standing, and Mechanical Engineering 366M or the equivalent.
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 largescale 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 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, minimumcost flows, matching problems; approximation algorithms for NPhard problems.
Topic 9: LargeScale Systems Optimization.
Mathematical programs with special structure, DantzigWolfe decomposition, partitioning and relaxation procedures, duality and decomposition, compact inverse methods, applications in engineering and management. Mechanical Engineering 391Q (Topic 12: LargeScale Systems Optimization) and Operations Research and Industrial Engineering 391Q (Topic 9) may not both be counted.
Topic 10: Stochastic Optimization.
Optimization of mathematical programming models under uncertainty; model formulations; exact, boundingandapproximation, and Monte Carlo samplingbased 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.
197K, 297K, 397K. Graduate Seminar.
One, two, or three lecture hours a week for one semester. May be repeated for credit. Offered on the credit/no credit basis only. Normally required of all students in operations research and industrial engineering. Prerequisite: Graduate standing.
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.
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.
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.
399R, 699R, 999R. Dissertation.
Offered on the credit/no credit basis only. Prerequisite: Admission to candidacy for the doctoral degree.
399W, 699W, 999W. Dissertation.
Offered on the credit/no credit basis only. Prerequisite: Operations Research and Industrial Engineering 399R, 699R, or 999R.
