291. PhD Sem-ODT
A special topics course.
291-OD1 Stochastic Models in Operations and Decisions (2 units)
This doctoral seminar covers some fundamental concepts in queueing systems and dynamic programming. We also apply these models to analyze the optimal decisions in a number of stochastic operations.
291-OD2 Research Seminars in Supply Chain Management (2 units)
This doctoral seminar provides some basic knowledge in several key research issues in supply chain management. We discuss a number of current research topics and challenges in supply chain management research.
291-OD3 Optimization Modeling and Methodology Part 1: Nonlinear Programming (2 units)
An overview of the different classes of nonlinear optimization problems with applications to management. Includes convexity and duality.
291-OD4 Optimization Modeling and Methodology Part 2: Integer and Network Programming (2 units)
Types of network optimization problems. Binary integer and mixed integer programs. Application to management.
291-OD5 Game Theory and Its Applications in Supply Chain Management (4 units)
This Ph.D. seminar course introduces some fundamental concepts and methodologies in cooperative and non-cooperative game theory and their applications in supply chain models. Each class is a combination of lectures and class discussions.
291-OD6 Large Scale Optimization (4 units)
This doctoral course explores various computational techniques that are useful for solving optimization problems with a large number of variables and/or constraints. We will study general techniques for computing optimal solutions to large problems using iterative methods, as well as ways to aggregate the solution space of some types of problems to yield near-optimal solutions. We will study Lagrangian relaxation, column generation, Dantzig-Wolfe decomposition, and Bender’s decomposition, from both a theoretical and practical perspective. Students will learn to formulate and solve large-scale problems using the modeling language AMPL, and learn how to exploit these techniques for their own research.
291-OD7 Network Models and Application (4 units, anticipated for 2014-2015, Gui)
The course introduces students to the optimization and game theoretic tools to study network systems. We also survey applications of network models in transportation, supply chain, Internet, e-commerce, and social networks. The course involves a mixture of lectures and discussion seminars.
291-OD8 Stochastic Programming (2 units, anticipated for 2014-2015 Lejeune)
This course will focus on Stochastic Modeling and Programming. Stochastic Programming is a discipline intersecting with probability theory and statistics on one hand and with mathematical programming on the other hand. It is a framework for modeling optimization problems that involve uncertainty. While deterministic optimization problems are formulated with known parameters, real world problems almost invariably include some unknown ones; their eventual outcome depends on the future realization of random events. Stochastic Programming relies upon the fact that probability distributions governing the data are known or can be estimated. The goal here is to find some policy that is feasible for (almost) all possible realizations and optimizes a function of the decision and the random variables. More generally, such models are formulated, analytically or numerically solved, and studied in order to provide useful information to the decision-maker.
291-OD9 Convex Math Programming: Optimization & Decomposition (4 units, Turner)
This doctoral course introduces students to the field of mathematical programming through the lens of convex optimization. We will study the theory of convex optimization, and learn how to identify, formulate, transform, and solve convex optimization problems.
Convex programs are an important class of mathematical programs because (1) many problems can be formulated as convex programs, and (2) we have efficient techniques to find globally optimal solutions to convex programs. However, translating and formulating a given problem as a convex program is not always easy; in fact, it can require a high level of expertise to verify that a math program is indeed convex. In this class, we will introduce a methodology called disciplined convex programming (DCP), which defines a set of rules derived from convex analysis If a math program is formulated following the DCP rules, it is guaranteed to be convex, eliminating the need to verify its convexity post-construction.
We will also study how classical decomposition techniques (e.g., column generation, Dantzig-Wolfe decomposition, Benders decomposition, and Lagrangian relaxation) can be helpful when solving large-scale convex optimization problems.
Students will choose a project which can be modeled as a convex optimization problem, and put to practice what they have learned using the modeling languages AMPL, MATLAB, CVX, and CVXPY. The techniques we will cover are applicable to a wide variety of business and engineering applications, and students are encouraged to choose a course project that is in line with their current research interests.
There are no formal prerequisites for this course beyond having a level of mathematical maturity which is expected of a PhD student at the Paul Merage School of Business. For example, it is expected that you know matrix algebra and multivariable calculus. Given that students may come from different backgrounds, I do not assume that students have a working knowledge of optimization theory. To get everyone up to speed, I will cover some background material in the first two lectures. But most importantly, if at some point during the course I start using terminology that you are unfamiliar with, please point this out so I can summarize any concepts which are unclear.
291-O10 Nonlinear Optimization (2 units, Scott)
Modelling nonlinear optimization problems, properties, geometric programming, convex programming, signomial programming, nonconvex programming, entropy optimization, applications to operations management, transportation planning, location, statistics and data mining.