Ph.D. Program

MGMTPHD 201A Probability, Statistics, and Computational Methods for Econometrics
Introduction to probabilistic, statistical, and computational tools needed for applied researchers in business fields. Probability theory, modes of convergence, hypothesis testing, Bayesian inference, R programming, linear algebra, numerical optimization, simulation methods, numerical integration

MGMTPHD 201B Theory and Application of Regression Analysis
Introduction to general regression analysis. Linear model, maximum likelihood and asymptotic tests, endogeneity, instrumental variables, differences-in-differences, regression-discontinuity design, propensity score matching, limited dependent variable models, introduction to panel data.

MGMTPHD 201C Time-Series Analysis
Introduction to time-series methods in analysis of business data. Basics of time series, optimal prediction, multiple equation time-series models, generalized method-of-moments, volatility modeling and nonnormalities, dynamic factor models.

Basics of single-person decision theory and introduction to non-cooperative game theory. Examination in some detail of von Neumann/Morgenstern expected utility theory. Other topics in decision theory include subjective expected utility theory and departures from expected utility behavior.

Survey course to (1) lay foundations for more advanced study of graphs, network flow models, and integer programming models and their applications, (2) establish connections between these technical foundations and real problems drawn from many areas of management, and (3) build professional skills needed to apply these tools

Foundations of operations planning, scheduling, and control, with emphasis on formal models and their applications. Aggregate planning, work force scheduling, inventory management, and detailed operations scheduling and control.

Scheduling models and results for single machine, flow shop, job shop, and resource-constrained project networks. Approaches include classical models, recent heuristic approaches, current research in coordinated interaction of computer models, and man/machine interaction.

The purpose of this course is to introduce students to dynamic programming (DP) as a general solution approach for problems that have an inter-temporal nature or lend themselves to being solved sequentially. The course will cover the DP recursion or Bellman equation mostly for discrete time problems. That includes finite and infinite horizon as well as deterministic and stochastic transitions. The continuous time case will only be covered for deterministic or Semi-Markovian settings.

Stochastic processes as applied to study of telecommunication systems, traffic engineering, business, and management. Discrete-time and continuous-time Markov chain processes. Renewal processes, regenerative processes, Markov-renewal, semi-Markov and semiregenerative stochastic processes. Decision and reward processes. Applications to traffic and queueing analysis of basic telecommunications and computer communication networks, Internet, and management systems.

Modeling, analysis, and design of queueing systems with applications to switching systems, communications networks, wireless systems and networks, and business and management systems. Modeling, analysis, and design of Markovian and non-Markovian queueing systems. Priority service systems. Queueing networks with applications to computer communications, Internet, and management networks.

Basic graduate course in linear optimization. Geometry of linear programming. Duality. Simplex method. Interior-point methods. Decomposition and large-scale linear programming. Quadratic programming and complementary pivot theory. Engineering applications. Introduction to integer linear programming and computational complexity theory.

Introduction to convex optimization and its applications. Convex sets, functions, and basics of convex analysis. Convex optimization problems (linear and quadratic programming, second-order cone and semidefinite programming, geometric programming). Lagrange duality and optimality conditions. Applications of convex optimization. Unconstrained minimization methods. Interior-point and cutting-plane algorithms. Introduction to nonlinear programming.

First-order algorithms for convex optimization: subgradient method, conjugate gradient method, proximal gradient and accelerated proximal gradient methods, block coordinate descent. Decomposition of large-scale optimization problems. Augmented Lagrangian method and alternating direction method of multipliers. Monotone operators and operator-splitting algorithms. Second-order algorithms: inexact Newton methods, interior-point algorithms for conic optimization.

Examination of mathematical methods used in graduate-level courses in microeconomics, macroeconomics, and quantitative methods. Topics include real analysis, linear algebra and matrices, calculus of many variables, static optimization, convex analysis, and dynamics and dynamic optimization.

Two input/two output model. Walrasian equilibrium and Pareto efficiency. Choice over time -- consumer savings and firm investment decisions. Choice under uncertainty -- state claims model, asset pricing.