Advanced Courses in Operations Research
525 Production Planning and Scheduling Theory and Practice
Production planning, including MRP, linear programming, and related concepts. Scheduling and sequencing work in manufacturing systems. Job release strategies and control of work in process inventories. Focus on setup time as a determinant of plans and schedules
528-529 Selected Topics in Applied Operations Research
Current topics dealing with applications of operations research.
533 Heuristic Methods for Optimization
Teaches heuristic search methods including simulated annealing, tabu search, genetic algorithms, de-randomized evolution strategy, and random walk developed for optimization of combinatorial- and continuous-variable problems. Application project options include wireless networks, protein folding, job shop scheduling, partial differential equations, satisfiability, or independent projects. Statistical methods are presented for comparing algorithm results. Advantages and disadvantages of heuristic, search methods for both serial and parallel computation are discussed in comparison with other optimization algorithms.
551 Economic Analysis of Engineering Systems
Financial planning, including cash-flow analysis and inventory flow models. Engineering economic analysis, including discounted cash flows and taxation effects. Application of optimization techniques, as in equipment replacement of capacity expansion models. Issues in designing manufacturing systems. Student group project.
561 Queuing Systems: Theory and Application
Covers basic queuing models; delay and loss systems; finite source, finite capacity, balking, reneging; systems in series and in parallel; FCFS vs. LCFS; busy period problems; output; design; and control problems; priority systems; queuing networks; the product formula; time sharing; server vacations; and applications to equipment maintenance, computer operations and flexible manufacturing systems.
562 Inventory Management
The first portion of this course is devoted to the analysis of several deterministic and probabilistic models for the control of single and multiple items at one of many locations. The second portion is presented in an experiential learning format. The focus in on analyzing and designing an integrated production and distribution system for a global company. Applications are stressed throughout.
563 Applied Time-Series Analysis
The first part of this course treats regression methods to model seasonal and non-seasonal data. After that, Box-Jenkins models, which are versatile, widely used, and applicable to non-stationary and seasonal time series, are covered in detail. The various stages of model identification, estimation, diagnostic checking, and forecasting are treated. Analysis of real data is carried out. Assignments require computer work with a time-series package.
566 Extreme Value Analysis with Applications to Finance and Data Communications
The course will cover the basic models of extreme events used in hydrology, finance, insurance, environmental science (pollution controls), reliability, risk management. The basic models contain parameters that must be estimated and graphical and analytic estimation methods will be discussed. Extreme quantiles and very small excedence probabilities need to be estimated and usually the part of a distribution tail which is way beyond the range of the data needs to be considered. This leads to discussion of estimation needed for VAR (value-at-risk) calculations. The course material intersects the related field of heavy tailed modeling and the implications of heavy tails in insurance and
567 Credit Risk: Modeling, Valuation, and Management
Credit risk refers to losses due to changes in the credit quality of a counter party in a financial contract. The course is an introduction to the modeling and valuation of credit risks. Emphasis on how credit derivative instruments used for hedging credit risks, including credit swaps, spread options, and collateralized debt obligations.
568 Financial Engineering with Stochastic Calculus I
This course is an introduction to continuous-time models of financial engineering and the mathematical tools required to use them, starting with the Black-Scholes model. Driven by the problem of derivative security pricing and hedging in this model, the course develops a practical knowledge of stochastic calculus from an elementary standpoint, covering topics including Brownian motion, martingales, the Ito formula, the Feynman-Kac formula, and Girsanov transformations.
569 Financial Engineering with Stochastic Calculus II
Building on the foundation established in ORIE 468/568, this course presents no-arbitrage theories of complete markets, including models for equities, foreign exchange, and fixed income securities, in relation to the main problems of financial engineering: pricing and hedging of derivative securities, portfolio optimization, and risk management. Other topics include model calibration and incomplete markets.
574 Statistical Data Mining II
Continuation of OR&IE 474 covering more advanced techniques such as clustering with applications to market segmentation, discriminant analysis, artificial neural networks, support vector machines, additive models, radial basis function and spline models, principal components, model assessment and selection, bagging and boosting. Applications to business problems such as quantitative marketing and credit scoring are presented.
575 Experimental Design
Randomization, blocking, sample size determination, factorial designs, 2p full and fractional factorials, response surfaces, Latin squares, split plots, Taguchi designs. Engineering applications. Computing in MINITAB or SAS.
576 Regression
Covers nonlinear regression, advanced diagnostics for multiple linear regression, collinearity, ridge regression, logistic regression, nonparametric estimation including spline and kernel methods, and regressions with correlated errors. Computing in MINITAB or SAS.
577 Quality Control
Concepts and methods for process and acceptance control. Control charts for variables and attributes. Process capability analysis. Acceptance sampling. Continuous sampling plans. Life tests. Use of experimental design and Taguchi methods for off-line control.
580 Simulation Modeling and Analysis
Introduction to Monte Carlo and discrete-event simulation. Emphasis on tools and techniques needed in practice. Random variate generation, input and output analysis, modeling using a discrete-event simulation package.
625 Scheduling Theory
Scheduling and sequencing problems, including single-machine problems, parallel-machine scheduling, and shop scheduling. The emphasis is on the design and analysis of polynomial time optimization and approximation algorithms and on related complexity issues.
626 Advanced Production and Inventory Planning
Introduction to a variety of production and inventory control planning problems; the development of mathematical models corresponding to these problems; a study of approaches for finding solutions.
627 Computational Issues in Large Scale Data-Driven Models
Availability of massive datasets such as web logs and point-of-sale transactions raises new modeling and computational issues. This course provides and introduction to this emerging research area. Topics include data driven models in operation management, asymptotic statistics, uniform convergence of empirical process, and efficient computational methods. There is discussion of applications in engineering, economics, and marketing, along with current open research problems.
629 Foundation of Game Theory and Mechanism Design for Engineering Applications
Provides a vigorous foundation for the applications of mechanism design and game theory to problems in engineering such as data networks and computer science. The goal is to develop a deep understanding of the fundamental issues that are important in many applications while presenting many current open research problems.
630 Mathematical Programming I
Rigorous treatment of the theory and computational techniques of linear programming and its extensions, including formulation, duality theory, algorithms; sensitivity analysis; network flow problems and algorithms; theory of polyhedral convex sets, systems of linear equations and inequalities, Farka’s Lemma; and exploiting special structure in the simplex method and computational implementation.
631 Mathematical Programming II
A continuation of OR&IE 630. Introduction to nonlinear programming, interior-point methods for linear programming, complexity theory, and integer programming. Some discussion of dynamic programming, and elementary polyhedral theory.
632 Nonlinear Programming
Necessary and sufficient conditions for unconstrained and constrained optima. Duality theory. Computational methods for unconstrained (e.g., quasi-Newton) problems, linearly constrained (e.g., active set) problems, and nonlinearly constrained (e.g., successive quadratic programming) problems.
633 Graph Theory and Network Flows
Directed and undirected graphs. Bipartite graphs. Hamilton cycles and Euler tours. Connectedness, matching, and coloring. Flows in capacity-constrained networks. Maximum flow and minimum cost flow problems.
634 Combinatorial Optimization
Topics in combinatorics, graphs, and networks, including matching, matroids, polyhedral combinatorics, and optimization algorithms. Topics change each semester. This course may be taken more than once for credit.
635 Interior-Point Methods for Mathematical Programming
Interior-point methods for linear, quadratic, and semi-definite programming and, more generally, for convex programming. Discusses the basic ingredients- barrier functions, central paths, and potential functions- that go into the construction of polynomial-time algorithms and various ways of combining them. Emphasizes recent mathematical theory and the most modern viewpoints.
636 Integer Programming
Discrete optimization. Linear programming in which the values are restricted to integers. Theory, algorithms, and applications. Cutting-plane methods, enumerative methods, and group-theoretic methods; additional topics are drawn from recent research in this area.
637 Semidefinite Programming
Covers linear optimization over the cone of positive semidefinite symmetric matrices; applications to control theory, eigenvalue optimization, and strong relaxations of combinational methods, particularly interior-point algorithms.
639 Convex Analysis
Self contained development of convex analysis and optimization. Convex sets and functions, subgradients, continuity, Fenchel, conic, and Lagrangian duality. Nonsmooth analysis: Clarke and limiting subgradients. Self-concordance and smooth convex optimization. Bundle methods for nonsmooth convex optimization.
640 Stochastic Dynamic Programming
This course covers the theory of sequential decision making under uncertainty for expected discounted cost and average cost minimization over a finite and infinite horizon. Applications include inventory, manufacturing and telecommunications models.
650 Applied Stochastic Processes
An introduction to stochastic processes that presents the basic theory together with a variety of applications. Topics include Markov processes, renewal theory, random walks, branching processes, Brownian motion, stationary processes. Martingales, and point processes.
651 Probability
Sample spaces, events, sigma fields, probability, set induction, independence, random variables, expectation, review of important distributions and transformation techniques, convergence concepts, laws of large numbers and asymptotic normality, conditioning.
662 Advanced Stochastic Processes
Brownian motion, martingales, Markov processes, and topics selected from: diffusions, stationary processes, point processes, weak convergence for stochastic processes and applications to diffusion approximations, Levy processes, regenerative phenomena, random walks, and stochastic integrals.
663 Time-Series Analysis
Representations of stationary time series. The ARIMA models. Spectral analysis. Long-range dependence. Problems of estimation. Multivariate time series.
665 Storage and Data Communication Models
Covers a selection of topics including queues, storage, insurance risk, dams, and data communication. The basic assumptions of the underlying models are discussed with emphasis on their common features. The overall objective is the study of the stochastic processes that arise from these models. The approach is based on the fluctuation theory of random walks, Levy processes, and Markov-additive processes. Further topics for discussion include stochastic comparisons and statistical inference from the models with particular emphasis on data communication models. Current research on network models with discrete and fluid inputs is discussed.
670 Statistical Principles
Review of distribution theory of special interest in statistics: normal, chi-square, binomial, Poisson. t, and F; introduction to statistical decision theory; sufficient statistics; theory of minimum variance unbiased point estimation; maximum likelihood and Bayes estimation, basic principles of hypothesis testing, including Neyman-Pearson Lemma and likelihood ratio principle; confidence interval construction; introduction to linear models.
671 Intermediate Applied Statistics
Statistical inference based on the general linear model; least-squares estimators and their optimality properties; likelihood ratio tests and corresponding confidence regions; simultaneous inference. Applications in regression analysis and ANOVA models. Variance components and mixed models. Use of the computer as a tool for statistics is stressed.
672 Selected Topics in Environmental Statistics (also BTRY 672)
This course is a discussion group focusing on statistical problems arising in the environmental sciences. These issues are explored in a number of different ways, such as student presentations of research papers, directed readings, and outside speakers.
673 Empirical and Computational Issues in Finance
Designed to introduce students to existing empirical work in finance and to demonstrate the use of statistical, econometric, and numerical methods in the analysis of financial data. Topics include linear and nonlinear time series analysis, high-frequency data and market microstructure, continuous-time models, extreme values and quantile estimation, volatility models, and MCMC methods. Numerous methods using market data are presented.
674 Statistical Learning Theory for Data Mining
This course will provide a thorough grounding in probabilistic and computational methods for statistical data mining. We intend to cover a subset of the following topics from supervised and unsupervised data mining: The framework of learning. Performance measures and model selection. Methodology, theoretical properties and computing algorithms used in parametric and nonparametric methods for regression and classification. Frequentist and Bayesian methods.
676 Statistical Analysis of Life Data
Analysis of data from reliability, fatigue, and life-testing studies in engineering; biomedical applications. Survival distributions, hazard rate, censoring. Life tables. Estimation and hypothesis testing. Standards. Goodness of fit, hazard plotting. Covariance analysis, accelerated life testing. Multiple decrement models, competing risks. Sample-size determination. Adaptive sampling.
677 Sequential Methods in Statistics
The statistical theory of sequential design and analysis of experiments has many applications; including monitoring data from clinical trials in medical studies and quality control in manufacturing operations. This course covers classical sequential hypothesis test, Wald’s SPRT, stopping rules, Kiefer-Weiss test, optimality, group sequential methods, estimation, repeated confidence intervals, stochastic curtailment, adaptive design, ad Bayesian and decision theoretic approaches.
678 Bayesian Statistics and Data Analysis
Priors, posteriors, Bayes estimators, Bayes factors, credible regions, hierarchical models, computational methods (especially MCMC), empirical Bayes methods, Bayesian robustness. Includes data analysis and MCMC computation in WinBUGS and possibly other languages such as MATLAB.
680 Simulation
Introduction to Monte Carlo and discrete-event simulation. Emphasis on underlying theory. Random variate generation, input and output analysis, variance reduction, selection of current research topics.
728-729 Selected Topics In Applied Operations Research
Current research topics dealing with applications of operations research.
738-739 Selected Topics in Mathematical Programming
Current research topics in mathematical programming.
768-769 Selected Topics in Applied Probability
Topics chosen from current literature and research of the staff.
778-779 Selected Topics In Applied Statistics
Topics chosen from current literature and research of the staff.
790 Special Investigations
For individuals or small groups. Study of special topics or problems.
799 Thesis Research
For individuals doing thesis research for doctoral degrees.
891 Operations Research Graduate Colloquium
A weekly 1-1 /2-hour meeting devoted to presentations by distinguished visitors, by faculty members, and by advanced graduate students on topics of current research in the field of operations research.