Management Science Methods (MSM)

MSM 400. Mathematics Review. 0 credits

Review of mathematical concepts prerequisite to the MBA program. Topics include: sets, vectors and matrices, functions and relations, linear equations, laws of exponents limits and continuity, differentiation, maxima-minima, partial derivatives and simple integration.

MSM 491. Math for Management. 2 credits

This is a master's level math class that is more intensive than MSM 400. Analysis and concepts in modern business analysis rely heavily on quantitative methods. Necessary theories and intuition behind them will be covered. The focus of the course is primarily on applications in business, economics and related areas.

MSM 501. Quant Methods Colloquium. 0 credits

This is a forum for the presentation of on-going and recently completed work by students, faculty, and guest lecturers.

MSM 502. Linear Algebra. 3 credits

The goal of this course is to give an introduction to linear algebra. Topics include: Gaussian elimination, matrix operations, matrix inverses. Vector spaces and subspaces, linear independence, and the basis of a space. Row space and column space of a matrix, fundamental theorem of linear algebra, linear transformations. Orthogonal vectors and subspaces, orthogonal bases, and Gram-Schmidt method. Orthogonal projections, linear regression. Determinants: how to calculate them, properties, and applications. Calculating eigenvectors and eigenvalues, basic properties. Matrix diagonalization, application to difference equations and differential equations. Positive definite matrices, tests for positive definiteness, singular value decomposition. Classification of states, transience and recurrence, classes of states. Absorption, expected reward. Stationary and limiting distributions. Offered in the summer, primarily for entering doctoral students.

MSM 503. Optimization. 3 credits

This course covers Optimization in Rn, Weierstrass Theorem, Unconstrained optimization, Lagrange Theorem and equality constraints, Kuhn-Tucker Theorem and Inequality constraints, Convexity, Parametric Monotonicity and Supermodularity. Offered in the summer, primarily for entering doctoral students.

MSM 504. Theory Of Probability And Stochastic Processes I. 3 credits

The course provides an introduction to stochastic processes. Topics include the Poisson process, renewal theory, Markov chains, semi-Markov and Markov renewal processes, and regenerative processes.

MSM 505. Real Analysis. 3 credits

This course covers Optimization in Rn, Weierstrass Theorem, Unconstrained optimization, Lagrange Theorem and equality constraints, Kuhn-Tucker Theorem and Inequality constraints, Convexity, Parametric Monotonicity and Supermodularity. Offered in the summer, primarily for entering doctoral students.

MSM 506. Management Science Methods. 3 credits

The purpose of this course is to introduce PhD students to a variety of operations research and management science methods in an applied setting to develop their modeling abilities. The emphasis of the course is on defining problems, building models, and analyzing the models to gain some insight, in other words, critical research skills. This course will draw upon both deterministic optimization methods and stochastic models but not their theory. These will include linear programming including integer and network formulations, basic queueing models (M/M/1, M/M/n, M/G/1), and Monte Carlo simulation.

MSM 509. Informational Sciences and Large-Scale Algorithms. 3 credits

This course examines recent methodological and modeling advances for solving large business problems. It includes summaries of numerical analysis techniques, artificial intelligence and heuristic optimization techniques (neural networks, genetic algorithms, tabu search and simulated annealing), and modeling techniques (decomposition, aggregation, scaling and dimensional analysis). The advances in optimization techniques include primal and dual decomposition, distributed algorithms, various projection and relaxation approaches, inner and outer linearization, aggregation and bounds.

MSM 522. Optimization. 3 credits

This course introduces unconstrained and constrained optimization in finite dimensional spaces. Topics include convex sets and functions, Kuhn-Tucker theory, Lagrangian duality, parametric continuity, dynamic programming, and parametric monotonicity.

MSM 533. Dynamic Programming. 3 credits

Dynamic Programming (DP) is a recursive approach to obtaining optimal solutions to sequential decision problems. DP can be used for either finite-horizon or infinite-horizon problems, and is applicable to both deterministic and stochastic problems. This course will explore both theoretical and computational aspects of DP.

MSM 535. Network and Integer Programming. 3 credits

This course covers the solution of network problems and integer programs. Shortest path, minimum spanning tree, maximum flow, minimum-cost flow, and matching are some of the network problems covered. Algorithms for linear-integer and mixed-integer problems include branch and bound, implicit enumeration, primal and dual-cutting planes, group theoretic methods, Lagrangian relaxation and surrogate relaxation. These algorithms are illustrated on classical integer problems such as the knapsack, set covering/partitioning and traveling salesman.

MSM 542. Queueing Theory and Applications. 3 credits

The course offers in-depth study of queues and networks of queues, including single- and multiserver-queues; Markovian models of phase-type systems; open-and-closed networks of queues; product-form solutions and local balance; bottleneck-analysis approximations and computational aspects. It also covers applications to scheduling, resource allocation and capacity-expansion decisions in service systems, computer systems and job shops.

MSM 549. Markov Decision Processes. 3 credits

This course is as an introduction to sequential decision-making and it reviews the theoretical foundations of dynamic programming, stochastic control, and Markov decision processes. Much of the course is devoted to the theoretical, modeling, and computational aspects of Markov decision processes. Applications in the area of production and inventory, finance, and marketing are explored.