Operations Research

(MSIS Department, Rutgers Business School)

 

26:711:530 Semidefinate and Second Order Cone Optimization
Not currently scheduled.
Theory, algorithms and applications of semidefinite and second order optimization problems, duality, complementarily, interior point algorithms, eigenvalue optimization, nonnegative polynomials, sum-of-square functional systems, applications in combinatorial optimization, control theory, statistics, and quantitative finance.

26:711:555 Stochastic Programming
The course focuses on modeling, analysis, an solution methods for optimization problems in the presence of uncertainty. It addresses expected value optimization, chance constraints, and risk-averse optimization. Two- and multi-stage problems will be discussed in depth, together with applications to data mining, finance, and supply chain management.

26:711:557 Dynamic Programming
Shortest path problems, label correcting algorithms. Controlled Markov chains. Finite horizon control problems, discounted and undiscounted infinite horizon problems, average cost problems. Dynamic programming equations. Value and policy iteration methods, linear programming approaches. Applications in scheduling, inventory control, logistics, finance, queueing, and other specific topics in Operations Research.

26:711:561 Mathematical Methods for Economics
Students may substitute 26:220:551. Either 26:711:561 or 26:220:551 is offered every spring.
We explore the quantitative tools and principles used to model operational procedures in economic and business systems—types of variables, mathematical sets, and functional forms in constrained and unconstrained optimization. Other topics include tractability, duality, Kuhn-Tucker theory, algorithms and computation. Prerequisite: Differential calculus.

26:711:562 Fundamentals of Optimization (pending approval)
Spring 2009 and every second spring thereafter.

26:711:563 Stochastic Calculus for Finance

Every Spring

 The objective of the course is to provide the students with knowledge and skill sufficient for correct formulation and analysis of continuous-time stochastic models involving stochastic integrals and stochastic differential equations. Particular attention will be devoted to application of stochastic calculus methods in finance, such as models of evolution of stock prices and interest rates, pricing of options, and pricing of other contingent claims. The course will also prepare the students for independent research on problems involving stochastic calculus techniques.

26:711:564 Optimization Models in Finance
Every fall.
The objective of this course is to introduce models and computational methods for static and dynamic optimization problems occurring in finance. Special attention will be devoted to portfolio optimization and to risk management problems. Prerequisites: Operations Management, Statistics.

26:711:651 Linear Programming
A survey of linear programming and its applications. Topics include linear programming models, basic simplex method, duality theory and complementary slackness, sensitivity analysis, degeneracy, matrix notation and revised simplex method, special linear programs such as transportation and network flow theory, applications in statistics, economics and finance models of linear programming, game theory, and introduction to interior point methods. Prerequisite: undergraduate linear algebra.

26:711:652 Nonlinear Optimization
Not currently scheduled.
Fundamentals of nonlinear optimization, with an emphasis on convex problems. Gradient, Newton, and other methods for unconstrained problems. Projection, linearization, penalty, barrier, and augmented Lagrangian methods for constrained problems. Lagrangian functions and duality theory. Assignments include computer programming and mathematical proofs. Prerequisite: 26:711:651.

26:711:653 Discrete Optimization
Not currently scheduled.
Combinatorial and discrete optimization problems on graphs and networks, knapsack, cutting stock, set covering and packing problems: theoretical properties, algorithms, complexity. Branch and bound methods, cuts, lifting. Applications.

26:960:575 Introduction to Probability
Every fall.
Foundations of probability. Discrete and continuous simple and multivariate probability distributions; random walks; generating functions; linear functions of random variable; approximate means and variances; exact methods of finding moments; limit theorems; stochastic processes including immigration-emigration, simple queuing, renewal theory, Markov chains. Prerequisite: Undergraduate or master’s-level course in statistics.

26:960:576 Financial Time Series
This course covers applied statistical methodologies pertaining to time series, with en emphasis on model building and accurate prediction. Completion of this course will provide students with enough insights and modeling tools to analyze time series data in the business world. Students are expected to have basic working knowledge of probability and statistics including linear regression, estimation and testing from the applied perspective. We will use R throughtout the course so prior knowledge of it is welcome, but not required.

26:960:577 Introduction to Statistical Linear Models
Every fall.
Linear models and their application to empirical data. The general linear model; ordinary-least-squares estimation; diagnostics, including departures from underlying assumptions, detection of outliners, effects of influential observations, and leverage; analysis of variance, including one-way and two-way layouts; analysis of covariance; polynomial and interaction models; weighted-least squares and robust estimation; model fitting and validation. Emphasizes matrix formulations, computational aspects and use of standard computer packages such as SPSS. Prerequisite: Undergraduate or master’s-level course in statistics.

26:960:580 Stochastic Processes
Review of probability theory with emphasis on conditional expectations; Markov chains; the Poisson process; continuous-time Markov chains; renewal theory; queuing theory; introduction to stochastic calculus, e.g., Ito’s Lemma. Prerequisite: 26:960:575.

26:960:670 Multivariate Analysis
Spring 2008 and every second spring thereafter.
Multivariate normal distributions, principal components, factor analysis, canonical correlation, discrimination and classification. Prerequisite: 26:960:577.

26:711:685 Special Topics in Management Science

Advanced Probability

Algorithmic Machine Learning

Computational Methods for Option Pricing

 Convex Analysis and Optimization

Data Intensive Analytics

Game Theory

Inventory Management

Procurement Auctions

Stochastic Programming

Stochastic Dynamics Models and their Applications in Supply Chains and Marketing

Fundamentals of Optimization

 

26:711:686 First Early Research Seminar in Management Science

26:711:687 Second Early Research Seminar in Management Science

26:711:688 Independent Study in Management Science

26:711:799 Dissertation Research in Management Science

 

Please note: Links to recent syllabi are provided where possible. In some cases, the link goes to the web site for the individual faculty member, where the syllabus is maintained. In other cases, the link allows you to download the syllabus. Other syllabi are available in the Program Office.

These syllabi are provided as information to potential applicants. They should also help current students make their individual study plans. But they are subject to change. Students should not buy books or make other plans related to a course until they have confirmed with the instructor that they have an up-to-date syllabus for the semester in which they are taking the course.