Ph.D. in Operations Research

Ph.D. Program

This program is offered by the Department of Management Science and Information Systems (MSIS). It is the continuation of the previous concentration in Management Science and the program of Operations Research offered by the Rutgers Center for Operations Research (RUTCOR).

Primary areas of interest are applied statistics, optimization, business analytics, operations management, inventory theory, scheduling, manufacturing under uncertainty, queuing theory, and risk theory.

Faculty research interests range from methodology research to quantitative modeling to empirical studies. The MSIS department includes a number of world-renowned scholars. Many faculty members serve on editorial boards of major academic journals, have chaired at premier conferences in operations and management science and have been members of NSF panels and other advisory boards. Research by the MSIS faculty is widely published in books and leading journals.

The students should have solid college-level knowledge of linear algebra, analysis, and probability, and good programming skills. Students who aspire to doctoral study in Operations Research but need to strengthen their background may wish to consider our Master of Information Technology and Analytics program, which admits both part-time and full-time students. Students in this program take many of the same courses as our doctoral students in Operations Research and may use these courses towards their doctoral degree if they are later admitted to the doctoral program.

Requirements

Additional enrollments may be required:

  • Students are sometimes required to enroll in non-degree courses to improve their English or their writing. They may also need to enroll in the non-degree course Teacher Training Seminar as part of their preparation for teaching. These enrollments require payment of tuition, but they do not count towards the 72 credits required for the degree.
  • Students must enroll in 26:711:689 every semester until they have defended a dissertation proposal. This registration requires their attendance in MSIS weekly seminar. A grade is given, but the enrollment is for zero credits and no tuition is charged.

Students take three courses for degree credit each semester during the first two years. They take the qualifying examination at the end of the second year. During their third and fourth year, they write a dissertation. Within a year after passing the qualifying examination, the student should defend a dissertation proposal.

Course Information

Foundation/methodology requirement (4 courses)

  • 26:960:575 Introduction to Probability
  • 26:960:577 Introduction to Statistical Linear Models
  • 26:711:651 Linear Programming
  • 26:711:652 Nonlinear Optimization

Major (5 courses)

  • 26:711:525 Stochastic Models of Operations Research (pending approval)
  • 26:711:653 Discrete Optimization
  • 26:711:548 Topics in Applied Operations Research (pending approval)

And at least two courses out of the following list:

  • 26:198:644 Data Mining
  • 26:711:563 Stochastic Calculus for Finance
  • 26:960:576 Financial Time Series
  • 26:711:557 Dynamic Programming
  • 26:711:555 Stochastic Programming

Electives (3 courses, selected from the following)

  • 26:223:655 Econometrics - Time Series
  • 26:198:645 Privacy, Security, and Data Analysis
  • 26:630:675 Marketing Models
  • 26:711:685 Game Theory
  • 26:960:580 Stochastic Processes
  • 26:711:530 Semidefinite and Second Order Cone Programming
  • 26:799:660 Supply Chain Modeling and Algorithms
  • 26:799:661 Stochastic Models for Supply Chain Management
  • 26:799:685 Special Topics in Supply Chain Management
  • 26:711:685 Special Topics in Operations Research/Management Science
    • Theory of Boolean Functions
    • Convex Analysis and Optimization
  • or any other course approved by the doctoral coordinator

Teaching requirement: Each student must teach at least one course at RBS in the area in which he or she is earning a doctoral degree. Before doing so, the student is expected to enroll in 26:620:701 Teacher Training Seminar, which is taught in the spring semester each year.

First early research requirement (equivalent to one course): Students write a paper with a faculty member, to be presented to the department during the fall semester.

Second early research requirement (equivalent to one course): Write a paper (ideally a dissertation proposal) with a faculty member, to be presented to the department during the fall semester. Part-time students may postpone participation to the summer after the third year.

Other rules and requirements: For details of rules and requirements that apply to all doctoral students in RBS, see Policies and Procedures.

Course Descriptions

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.