Operations Research and Industrial Engineering

The course material in both operations research and industrial engineering is approached from a highly analytical point of view; theories and techniques from all of the quantitative disciplines are developed and used. Consideration is given to the construction of appropriate mathematical models to represent real-life operational systems and to the development of techniques for investigating the models' performance. Each student pursues a course of study tailored to his or her specific interests.

The faculty has approval to offer the following courses in the academic years 1999-2000 and 2000-2001; 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 that have been made to the courses listed here since this catalog was published.

Unless otherwise stated below, each course meets for three lecture hours a week for one semester.

Operations Research and Industrial Engineering: 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.

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, 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. 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 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 Analysis.
Classical techniques in time domain forecasting Box-Jenkins univariate, transfer function, and multivariate time-series 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 continuous-time Markov chains, queueing and reliability applications.

Topic 6: Regression and Analysis of Variance.

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 theory of waiting lines; occupation process, waiting time process, traffic processes, busy periods; M/M/k small site systems; the M/G/1 queue; queueing networks. 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 5) (or Mechanical Engineering 390R [Topic 4: Applied Stochastic Processes]) 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. Only one of the following may be counted: Mechanical Engineering 390R (Topic 9: Statistical Design of Experiments), 397 (Topic 35: Statistical Design of Experiments), Operations Research and Industrial Engineering 390R (Topic 10). 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. Only one of the following may be counted: Mechanical Engineering 390R (Topic 10: Advanced Stochastic Processes), 397 (Topic 36: Advanced Stochastic Processes), Operations Research and Industrial Engineering 390R (Topic 11).

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.

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 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 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. Only one of the following may be counted: Mechanical Engineering 391Q (Topic 12: Large-Scale Systems Optimization), 397 (Topic 13: Large-Scale Systems Optimization), Operations Research and Industrial Engineering 391Q (Topic 9).

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.

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 letter-grade 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 letter-grade basis only. Prerequisite: Graduate standing in operations research and industrial engineering and consent of the graduate adviser.

399R, 699R, 999R. Dissertation.
Offered on the letter-grade basis only. Prerequisite: Admission to candidacy for the doctoral degree.

399W, 699W, 999W. Dissertation.
Offered on the letter-grade basis only. Prerequisite: Operations Research and Industrial Engineering 399R, 699R, or 999R.

About the Program: Operations Research and Industrial Engineering

Contents |  Chapter 1 |  Chapter 2 |  Chapter 3
Chapter 4 |  Chapter 5 |  Appendix

Related information

Catalogs | Course Schedules |  Academic Calendars
Office of Admissions