MBA-ORBA Curriculum

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MS Curriculum

Required Courses
(18 credits)

Electives
(12 credits)

*Note: Students can take one course or the other, but not both.

**Note: Students can take one course or the other, but not both.

Based on student’s record, a required course may be waived; in that case an elective course can be substituted, so that the total number of credits earned equals 30. Other electives may be substituted for the program’s electives, upon approval of the program’s director.

Course Descriptions

16:711:517 - (3 cr)
Computational Methods of Operations Research

The course will be highly interactive with individual and group assignments and with intensive computer practice. The students will be offered various problems and projects to work on during the semester. Some of the projects will involve the use of certain software packages, while some others will require coding. In addition, each of the students will be required to solve homework assignments, mostly programming tasks. Grading will be based on homeworks and projects. The course concentrates on OR modeling and problem solving with AMPL, a mathematical modeling language. Additionally, elements of other programming environments will be described, and a few assignments will be given, in particular, in PERL to realize basic data structures and combinatorial algorithms; in C++ to develop basic routines, and interface with CPLEX and/or XPressMP; and on HTML, Javascript and CSS to develop home pages and interactive web-projects.

26:198:644 - (3 cr)
Data Mining

Introduction to data mining tasks (classification, clustering, association rules, sequential patterns, regression, deviation detection). Data and preprocessing: data cleaning, feature selection, dimensionality reduction. Classification: decision-tree based approach, rule-based approach, instance-based classifiers. Bayesian approach: naive and Bayesian networks, classification model evaluation. Clustering: partitional and hierarchical clustering methods, graph-based methods, density-based methods, cluster validation. Association analysis: a priori algorithm and its extensions, association pattern evaluation, sequential patterns and frequent subgraph mining. Anomaly detection: statistical-based and density-based methods.

16:711:557 - (3 cr)
Dynamic Programming

The shortest path problem. The principle of optimality. Label correcting algorithms. Controlled Markov chains. Finite horizon stochastic problems. Dynamic programming equations. Discounted infinite horizon problems. Value and policy iteration methods. Linear programming approach. Applications in inventory control, scheduling, logistics. The multiarmed bandit problem. Undiscounted infinite horizon problems. Stochastic shortest paths. Methods for solving undiscounted problems. Optimal stopping; asset pricing. Average cost problems. Methods for solving average cost problems. Controlled continuous time Markov chains. Introduction to approximate dynamic programming.

26:711:631 - (3 cr)
Financial Mathematics

Cash flow streams. Financial instruments (stocks, bonds, futures, options, cash flows). Utility functions. Arbitrage pricing theory. Application of martingales. Brownian motions. Ito's lemma. Black-Scholes theory. Parabolic PDEs and their numerical solutions. The Feynman-Kac solution. Exotic and path-dependent options (chooser, barrier, lookback, Asian, Bermudan, etc.). Interest rate models (Vasicek, Hull-White). Short introduction to stochastic programming models. Markowitz mean-variance models. Bond portfolio composition models. Term structures. The use of goal programming. Dynamic option selection models. Value at Risk models.

26:960:576 - (3 cr)
Financial Time Series

This course covers applied statistical methodologies pertaining to time series, with 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 throughout the course so prior knowledge of it is welcome, but not required.

16:711:613 - (3 cr)
Game Theory

Matrix games, max-min, min-max and saddle point. Pure and mixed strategies. Solvability in mixed strategies. Von Neumann's Theorem for matrix games. Bimatrix and n-matrix games. Nash equilibria and Nash solvability. Perfect equilibria and perfect solvability. Sophisticated equilibria and dominance solvability. Games in extensive, positional and normal form. Perfect information and solvability in pure strategies. Nash solvability of the cyclic games. Domination and dominance solvability. Backward induction. Dominance solvable extensive and secret veto voting schemes. Cooperative games. Coalitions. Transferable and non-transferable utilities, TU- and NTU-games. Cores and core-solvability. Bondareva-Shapley's Theorem and Scarf's Theorem. Effectivity functions and game forms, Moulin-Peleg's Theorem. Cooperative games in effectivity function form, Keiding's Theorem. Stable effectivity functions and stable families of coalitions. Intrduction to Social Choice Theory. Paradox Arrow. Social choice functions and correspondences. Boolean functions and graphs in game theory: Boolean duality and Nash solvability. Read-once Boolean functions, P4-free graphs and normal form of the positional games with perfect information. Stable effectivity functions and Berge's perfect graphs. Stable families of coalitions and normal hypergraphs. The Shapley value and the Banzhaf power index for cooperative games and approximation of pseudo-Boolean functions.

16:711:465 - (3 cr)
Integer Programming

Overview of discrete optimization models occurring in business, engineering, industry and the sciences Modelling with integer variables Specially structured problems:knapsack, covering and partitioning problems A quick introduction to complexity theory:problems, instances, worst-case complexity, polynomial algorithms, the classes P and NP Linear programming relaxations, integrality ofsolutions, unimodularity and applications for assignment problems, shortest path and network computations Enumerative methods:branch-and-bound, implicit enumeration, bounding techniques, Lagrangean and surrogate duality Cutting planes, Gomory's algorithm, lifting and projecting for binary optimization Heuristics: greedy algorithms, local search, truncated exponential schemes.

26:960:575 - (3 cr)
Introduction to Probability

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.

26:960:577 - (3 cr)
Introduction to Statistical Linear Models

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.

26:198:622 - (3 cr)
Machine Learning

Conditional probability and Bayes theorem.  Introduction to R. Introduction to Bayesian thinking. Single-parameter models. Multiparameter models. Introduction to Bayesian computation. Markov Chain Monte Carlo. Hierarchical modeling. Model comparison. Regression models. Gibbs sampling. Confidence and exchangeability. Conformal prediction.

16:711:550 - (3 cr)
Nonlinear Optimization

Convex sets. Separation. Cones. Convex functions. Elements of subdifferential calculus. Tangent cones. Metric regularity. Optimality conditions. Lagrangian duality. The method of steepest descent. Newton’s method. Conjugate gradient methods. Nongradient methods. Truncated Newton’s method. Feasible direction methods. Penalty methods. Dual and augmented Lagrangian methods. Sequential quadratic programming. Interior point methods. Introduction to Nondifferentiable Optimization.

26:960:580 - (3 cr)
Stochastic Processes

The course covers the theory and modeling of stochastic processes. Topics include: martingales, stopping theorems, elements of large deviations theory, Renewal Theory, Markov Chains, Semi-Markov Chains, Markovian Decision Processes. In addition, the class will cover some applications to finance theory, insurance, queueing and inventory models.

16:711:555 - (3 cr)
Stochastic Programming

Overview of statistical decision principles.Overview of stochastic programming model constructions: reliability type models, penalty type models, mixed models, static and dynamic type models. The simple recourse model and its numerical solution techniques. Convexity theory of probabilistic constrained models.Bounding and approximation of probabilities. Numerical solution of probabilistic constrained models. Two-stage programming under uncertainty and the solution of the relevant problem by Benders' decomposition. Multi-stage stochastic programming models. Scenario aggregation. Distribution theory of stochastic programming. Applications to production, inventory control, water resources, finance, power and communication systems.

26:799:661 - (3 cr)
Stochastic Models for Supply Chain Management

This course covers quantitative methods in supply chain management under uncertainty. The emphasis is on the foundations of dynamic optimization tools in stochastic inventory models.  We study key concepts such as Preservation and Attainment, Myopic Policies, optimality of (s,S) policies, capacitated inventory management, Bayesian Inventory Models, and Contracts in Supply Chains, Manufacturer’s Return Policies and Retail Competition. Other topics include: Supply Contracts with Quantity Commitment and Stochastic Demand. Option Contracts in Supply Chains. Competitive and Cooperative Inventory Policies.

16:711:614 - (3 cr)
Theory of Linear Optimization

Convex sets, polyhedra, Farkas lemma, canonical forms, simplex algorithm, duality theory, revised simplex method, primal-dual methods, complementary slackness theorem, maximal flows, transportation problems, 2-person game theory. Students will have the chance to apply the methods to real life problems. One of the aims of the course will be to teach the students the path: from real life problem to abstraction, to mathematical formulation, to solving the mathematical problem, to applying this solution in the real life framework.

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